Package 'UBStats'

Confidence intervals for the difference between means

Description

CI.diffmean() builds confidence intervals for the difference between the means of two independent or paired populations.

Usage

CI.diffmean(
  x,
  y,
  type = "independent",
  sigma.x = NULL,
  sigma.y = NULL,
  conf.level = 0.95,
  by,
  sigma.by = NULL,
  sigma.d = NULL,
  var.test = FALSE,
  digits = 2,
  force.digits = FALSE,
  use.scientific = FALSE,
  data,
  ...
)

Arguments

x, y	Unquoted strings identifying two numeric variables with the same length whose means have to be compared. x and y can be the names of vectors in the workspace or the names of columns in the data frame specified in the data argument. It is possible to use a mixed specification (e.g, one vector and one column in data).
type	A length-one character vector specifying the type of samples. Allowed values are "independent" or "paired".
sigma.x, sigma.y	Optional numeric values specifying the possibly known populations' standard deviations (when x and y are specified). If NULL (default) standard deviations are estimated using the data.
conf.level	Numeric value specifying the required confidence level; default to 0.95.
by	Optional unquoted string, available only when type = "independent", identifying a variable (of any type), defined same way as x, taking only two values used to split x into two independent samples. Given the two ordered values taken by by (alphabetical or numerical order, or order of the levels for factors), say by1 and by2, the confidence interval is built for the difference between the populations means in the by1- and in the by2-group. Note that only one between y and by can be specified.
sigma.by	Optional numeric value specifying the possibly known standard deviations for the two independent samples identified via by (when x and by are specified). sigma.by can be a single value indicating the same standard deviation in the two by-groups, or a vector with two values, specifying the standard deviations in the two by-groups. To avoid errors, in the latter case the vector should be named, with names coinciding with the two levels of by.
sigma.d	Optional numeric value specifying the possibly known standard deviation of the difference when samples are paired.
var.test	Logical value indicating whether to run a test on the equality of variance for two (independent) samples or not (default).
digits	Integer value specifying the number of decimals used to round statistics; default to 2. If the chosen rounding formats some non-zero values as zero, the number of decimals is increased so that all values have at least one significant digit, unless the argument force.digits is set to TRUE.
force.digits	Logical value indicating whether reported values should be forcedly rounded to the number of decimals specified in digits even if non-zero values are rounded to zero (default to FALSE).
use.scientific	Logical value indicating whether numbers in tables should be displayed using scientific notation (TRUE); default to FALSE.
data	An optional data frame containing x and/or y. If not found in data, the variables are taken from the environment from which CI.diffmean() is called.
...	Additional arguments to be passed to low level functions.

Value

A table reporting the confidence intervals for the difference between the populations' means. For independent samples in the case of unknown variances, the intervals are built both under the assumption that the variances are equal and under the assumption that they differ, using percentiles from both the normal and the Student's t distribution. If

Author(s)

Raffaella Piccarreta [email protected]

See Also

TEST.diffmean() to test hypotheses on the difference between two populations' means.

Examples

data(MktDATA, package = "UBStats")

# Independent samples (default type), UNKNOWN variances
#  CI for the difference between means of males and females
#  - Using x,y: build vectors with data on the two groups
AOV_M <- MktDATA$AOV[MktDATA$Gender == "M"]
AOV_F <- MktDATA$AOV[MktDATA$Gender == "F"]
CI.diffmean(x = AOV_M, y = AOV_F)
#  - Change confidence level
CI.diffmean(x = AOV_M, y = AOV_F, conf.level = 0.99)
#  - Using x,by: groups identified by ordered levels of by
CI.diffmean(x = AOV, by = Gender, conf.level = 0.99, data = MktDATA)
#    Since order is F, M, CI is for mean(F) - mean(M)
#    To get the interval for mean(M) - mean(F)
Gender.R <- factor(MktDATA$Gender, levels = c("M", "F"))
CI.diffmean(x = AOV, by = Gender.R, conf.level = 0.99,  
            data = MktDATA)
#  - Testing hypotheses on equality of unknown variances
CI.diffmean(x = AOV_M, y = AOV_F, conf.level = 0.99, 
            var.test = TRUE)

#  - Output results: only information on the CI
out.ci_diffM<-CI.diffmean(x = AOV_M, y = AOV_F)
#  - Output results: list with information on CI and test on var
out.ci_diffM.V<-CI.diffmean(x = AOV_M, y = AOV_F, var.test = TRUE)

# Independent samples (default type), KNOWN variances
#  CI for the difference between means of males and females
#  - Using x,y: build vectors with data on the two groups
AOV_M <- MktDATA$AOV[MktDATA$Gender == "M"]
AOV_F <- MktDATA$AOV[MktDATA$Gender == "F"]
CI.diffmean(x = AOV_M, y = AOV_F, 
            sigma.x = 10, sigma.y = 20)
#  - Using x,by: groups identified by ordered levels of by
CI.diffmean(x = AOV, by = Gender, 
            sigma.by = c("M" = 10, "F"=20), data = MktDATA)
#    To change the sign, order levels as desired
Gender.R <- factor(MktDATA$Gender, levels = c("M", "F"))
CI.diffmean(x = AOV, by = Gender.R, 
            sigma.by = c("M" = 10, "F"=20), data = MktDATA)
#  - Output results 
out.ci_diffM<-CI.diffmean(x = AOV_M, y = AOV_F, 
                          sigma.x = 10, sigma.y = 20)

# Paired samples: UNKNOWN variances
# - Default settings
CI.diffmean(x = NStore_Purch, y = NWeb_Purch,
            type = "paired", data=MktDATA)
# - Change confidence level
CI.diffmean(x = NStore_Purch, y = NWeb_Purch,
            type = "paired", conf.level = 0.9, data = MktDATA)
# Paired: KNOWN variances
CI.diffmean(x = NStore_Purch, y = NWeb_Purch,
            type = "paired", conf.level = 0.9, 
            sigma.d = 2, data = MktDATA)
#  - Output results 
out.ci_diffM<-CI.diffmean(x = NStore_Purch, y = NWeb_Purch,
                          type = "paired", conf.level = 0.9, 
                          sigma.d = 2, data = MktDATA)

# Arguments force.digits and use.scientific
#  An input variable taking very low values
SmallX<-MktDATA$AOV/5000
SmallX_M <- SmallX[MktDATA$Gender == "M"]
SmallX_F <- SmallX[MktDATA$Gender == "F"]
# - Default: manages possible excess of rounding
CI.diffmean(x = SmallX_M, y = SmallX_F)
# - Force to the requested nr of digits (default, 2)
CI.diffmean(x = SmallX_M, y = SmallX_F,
            force.digits = TRUE)
# - Allow scientific notation
CI.diffmean(x = SmallX_M, y = SmallX_F, 
            use.scientific = TRUE)

---

Confidence intervals for the difference between proportions

Description

CI.diffprop() builds confidence intervals for the difference between the proportion of successes in two independent populations.

Usage

CI.diffprop(
  x,
  y,
  success.x = NULL,
  success.y = NULL,
  conf.level = 0.95,
  by,
  digits = 2,
  force.digits = FALSE,
  use.scientific = FALSE,
  data,
  ...
)

Arguments

x, y	Unquoted strings identifying the variables of interest. x and y can be the names of vectors or factors in the workspace or the names of columns in the data frame specified in the data argument. It is possible to use a mixed specification (e.g, one vector and one column in data).
success.x, success.y	If x,y are factors, character vectors, or numeric non-binary vectors, success must be used to indicate the category/value corresponding to success in the populations. These arguments can be omitted (NULL, default) if x,y are binary numeric vectors (taking values 0 or 1 only; in this case success is assumed to correspond to 1) or a logical vector (in these cases success is assumed to correspond to TRUE).
conf.level	Numeric value specifying the required confidence level; default to 0.95.
by	Optional unquoted string identifying a variable (of any type), defined same way as x, taking only two values used to split x into two independent samples. Given the two ordered values taken by by (alphabetical or numerical order, or order of the levels for factors), say by1 and by2, the confidence interval is built for the difference between the populations proportions in the by1- and in the by2-group. Note that only one between y and by can be specified.
digits	Integer value specifying the number of decimals used to round statistics; default to 2. If the chosen rounding formats some non-zero values as zero, the number of decimals is increased so that all values have at least one significant digit, unless the argument force.digits is set to TRUE.
force.digits	Logical value indicating whether reported values should be forcedly rounded to the number of decimals specified in digits even if non-zero values are rounded to zero (default to FALSE).
use.scientific	Logical value indicating whether numbers in tables should be displayed using scientific notation (TRUE); default to FALSE.
data	An optional data frame containing x and/or y. If not found in data, the variables are taken from the environment from which CI.diffprop() is called.
...	Additional arguments to be passed to low level functions.

Value

A table reporting the confidence intervals for the difference between the proportions of successes in two independent populations.

Author(s)

Raffaella Piccarreta [email protected]

See Also

TEST.diffprop() to test hypotheses on the difference between the proportions of successes in two populations.

Examples

data(MktDATA, package = "UBStats")

# Proportions of success defined on non-binary and 
#  non-logical vectors; 'success' coded same way
#  for both vectors
#  - Using x,y: build vectors with data on the two groups
WouldSuggest_F <- MktDATA$WouldSuggest[MktDATA$Gender == "F"]
WouldSuggest_M <- MktDATA$WouldSuggest[MktDATA$Gender == "M"]
CI.diffprop(x = WouldSuggest_M, y = WouldSuggest_F, 
            success.x = "Yes")

PastCampaigns_F<-MktDATA$PastCampaigns[MktDATA$Gender=="F"]
PastCampaigns_M<-MktDATA$PastCampaigns[MktDATA$Gender=="M"]
CI.diffprop(x = PastCampaigns_M, y = PastCampaigns_F,
            success.x = 0, conf.level = 0.99)
            
#  - Using x,by: groups identified by ordered levels of by
CI.diffprop(x = PastCampaigns, by = Gender,
            success.x=0, conf.level = 0.99, 
            data = MktDATA)
#    Since order is F, M, CI is for prop(F) - prop(M)
#    To get the interval for prop(M) - prop(F)
Gender.R <- factor(MktDATA$Gender, levels = c("M", "F"))
CI.diffprop(x = PastCampaigns, by = Gender.R,
            success.x=0, conf.level = 0.99, data = MktDATA)
 
# Proportions of success defined based on 
#  binary or logical vectors; 'success'
#  coded same way for both vectors
#  - Binary variable (success=1): based on x,y
LastCampaign_F<-MktDATA$LastCampaign[MktDATA$Gender=="F"]
LastCampaign_M<-MktDATA$LastCampaign[MktDATA$Gender=="M"]
CI.diffprop(x = LastCampaign_M, y = LastCampaign_F)
#  - Binary variable (success=1): based on x,y
#    see above for recoding of levels of Gender
Gender.R <- factor(MktDATA$Gender, levels = c("M", "F"))
CI.diffprop(x = LastCampaign, by = Gender.R, data = MktDATA)
#  - Logical variable (success=TRUE): based on x,y
Deals_w_child <- MktDATA$Deals.ge50[MktDATA$Children>0]
Deals_no_child <- MktDATA$Deals.ge50[MktDATA$Children==0]
CI.diffprop(x = Deals_w_child, y = Deals_no_child, conf.level = 0.9)

# Proportions defined on 
#  non-binary and non-logical vectors, with 'success'
#  coded differently (only specification x,y is reasonable here)
WouldSuggest_Other<-c(rep("OK",310),rep("KO",650-310))
CI.diffprop(x = WouldSuggest, y = WouldSuggest_Other, 
            success.x = "Yes", success.y = "OK",
            data = MktDATA)

# Proportions based on combined conditions
# - Build logical vector/s indicating whether a condition 
#   is satisfied
IsTop<-MktDATA$AOV>80
IsTop_OK<-IsTop[MktDATA$WouldSuggest == "Yes"]
IsTop_KO<-IsTop[MktDATA$WouldSuggest == "No"]
CI.diffprop(x = IsTop_OK, y = IsTop_KO, conf.level = 0.9)

Deals<-MktDATA$NDeals>=5
Deals_Married <- Deals[MktDATA$Marital_Status=="Married" & 
                         MktDATA$Children==0] 
Deals_Single <- Deals[MktDATA$Marital_Status=="Single"] 
CI.diffprop(x = Deals_Married, y = Deals_Single, conf.level = 0.9)

# Output results           
Gender.R <- factor(MktDATA$Gender, levels = c("M", "F"))
out.ci_diffP<-CI.diffprop(x = PastCampaigns, by = Gender.R,
                          success.x=0, conf.level = 0.99, 
                          data = MktDATA)

# Arguments force.digits and use.scientific
#  An input variable taking very low values
HighAOV <- MktDATA$AOV>150
# - Default: manages possible excess of rounding
CI.diffprop(x = HighAOV[MktDATA$Gender=="M"], 
            y = HighAOV[MktDATA$Gender=="F"])
#  - Force to the exact number of digits (default, 2)
CI.diffprop(x = HighAOV[MktDATA$Gender=="M"], 
            y = HighAOV[MktDATA$Gender=="F"],
            force.digits = TRUE)
#  - Allow scientific notation
CI.diffprop(x = HighAOV[MktDATA$Gender=="M"], 
            y = HighAOV[MktDATA$Gender=="F"],
            use.scientific = TRUE)

---

Confidence intervals for the mean

Description

CI.mean() builds confidence intervals for the mean of a population.

Usage

CI.mean(
  x,
  sigma = NULL,
  conf.level = 0.95,
  digits = 2,
  force.digits = FALSE,
  use.scientific = FALSE,
  data,
  ...
)

Arguments

x	An unquoted string identifying the numeric variable whose mean is of interest. x can be the name of a vector in the workspace or the name of one of the columns in the data frame specified in the data argument.
sigma	An optional numeric value specifying the population standard deviation. If NULL (default) the population standard deviation is estimated using the data.
conf.level	Numeric value specifying the required confidence level; default to 0.95.
digits	Integer value specifying the number of decimals used to round statistics; default to 2. If the chosen rounding formats some non-zero values as zero, the number of decimals is increased so that all values have at least one significant digit, unless the argument force.digits is set to TRUE.
force.digits	Logical value indicating whether reported values should be forcedly rounded to the number of decimals specified in digits even if non-zero values are rounded to zero (default to FALSE).
use.scientific	Logical value indicating whether numbers in tables should be displayed using scientific notation (TRUE); default to FALSE.
data	An optional data frame containing x. If not found in data, x is taken from the environment from which CI.mean() is called.
...	Additional arguments to be passed to low level functions.

Value

A table reporting the confidence interval for the population mean. If the variance is unknown, the interval is built using percentiles from both the normal and the Student's t distribution.

Author(s)

Raffaella Piccarreta [email protected]

See Also

TEST.mean() to test hypotheses on a population mean.

Examples

data(MktDATA, package = "UBStats")

# CI for the mean with KNOWN variance; default options
CI.mean(AOV, sigma = 30, data = MktDATA)

# CI for the mean with UNKNOWN variance;  
# - change digits and confidence level 0.99
CI.mean(AOV, conf.level = 0.99, digits = 3, data = MktDATA)

# Arguments force.digits and use.scientific
#  A variable taking very small values
SmallX<-MktDATA$AOV/5000 
#  - Default: manages possible excess of rounding
CI.mean(SmallX)
#  - Forcing digits to the default values (2)
CI.mean(SmallX, force.digits = TRUE)
#  - Allow scientific notation
CI.mean(SmallX, use.scientific = TRUE)

# Output the table with the requested interval
out.ci_mean<-CI.mean(AOV, data = MktDATA)

---

Confidence intervals for the proportion

Description

CI.prop() builds confidence intervals for the proportion of successes in a population.

Usage

CI.prop(
  x,
  success = NULL,
  conf.level = 0.95,
  digits = 2,
  force.digits = FALSE,
  use.scientific = FALSE,
  data,
  ...
)

Arguments

x	An unquoted string identifying the variable of interest. x can be the name of a vector or a factor in the workspace or the name of one of the columns in the data frame specified in the data argument.
success	If x is a factor, a character vector, or a numeric non-binary vector, success must be used to indicate the category/value corresponding to success. The argument can be omitted (NULL, default) if x is a binary numeric vector (takes values 0 or 1 only; in this case success is assumed to be 1) or a logical vector (in these cases success is assumed to be TRUE).
conf.level	Numeric value specifying the required confidence level; default to 0.95.
digits	Integer value specifying the number of decimals used to round statistics; default to 2. If the chosen rounding formats some non-zero values as zero, the number of decimals is increased so that all values have at least one significant digit, unless the argument force.digits is set to TRUE.
force.digits	Logical value indicating whether reported values should be forcedly rounded to the number of decimals specified in digits even if non-zero values are rounded to zero (default to FALSE).
use.scientific	Logical value indicating whether numbers in tables should be displayed using scientific notation (TRUE); default to FALSE.
data	An optional data frame containing x. If not found in data, x is taken from the environment from which CI.prop() is called.
...	Additional arguments to be passed to low level functions.

Value

A table reporting the confidence intervals for the population proportion of successes.

Author(s)

Raffaella Piccarreta [email protected]

See Also

TEST.prop() to test hypotheses on the proportion of successes in a population.

Examples

data(MktDATA, package = "UBStats")

# Success = one value of a character vector or factor
CI.prop(WouldSuggest, success = "Yes", data = MktDATA)

# - change confidence level and rounding
CI.prop(Education, success = "Post-Grad", 
        conf.level = 0.9, digits = 4, 
        data = MktDATA)

# Success = numeric value
CI.prop(Children, success = 2, data = MktDATA)

# Binary variable ('success' is 1 by default)
CI.prop(LastCampaign, digits = 3, data = MktDATA)

# Logical variable ('success' is TRUE by default)
CI.prop(RespCampaign, conf.level = 0.9, digits = 3, data = MktDATA)

# Success based on combined conditions
# - Build a (logical) vector indicating whether a condition is satisfied
IsTop <- MktDATA$CustClass == "Gold" | MktDATA$CustClass == "Platinum"
CI.prop(IsTop, conf.level = 0.9)
# - A very rare event
HighAOV <- MktDATA$AOV>150
CI.prop(HighAOV, conf.level = 0.9)

# Arguments force.digits, use.scientific
# - Default: manages possible excess of rounding
CI.prop(HighAOV)
# - Forcing digits to the default values (2)
CI.prop(HighAOV, force.digits = TRUE)
# - Allow scientific notation
CI.prop(HighAOV, use.scientific = TRUE)

# Output results
out_ci_prop<-CI.prop(HighAOV)

---

Analysis of a univariate distribution using plots

Description

distr.plot.x() generates plots of a univariate distribution.

Usage

distr.plot.x(
  x,
  freq = "counts",
  plot.type,
  ord.freq = "none",
  breaks,
  adj.breaks = TRUE,
  interval = FALSE,
  bw = FALSE,
  color = NULL,
  use.scientific = FALSE,
  data,
  ...
)

Arguments

x	An unquoted string identifying the variable whose distribution has to be analysed. x can be the name of a vector or a factor in the workspace or the name of one of the columns in the data frame specified in the data argument.
freq	A single character specifying the frequencies to be displayed. Allowed options (possibly abbreviated) are "counts", "percentages", "proportions", "densities" (for histograms and density plots).
plot.type	A single character specifying the type of plot to build. Allowed options are "pie", "bars", "spike", "histogram", "density", "boxplot", and "cumulative".
ord.freq	A single character vector that can be specified when plot.type = "pie" or plot.type = "bars". It indicates whether the levels of x should be displayed in a standard order (ord.freq = "none", the default) or in an increasing or decreasing order (ord.freq = "increasing" or ord.freq = "decreasing").
breaks	Allows to classify a numerical variable x into intervals. It can be an integer indicating the number of intervals of equal width used to classify x, or a vector of increasing numeric values defining the endpoints of intervals (closed on the left and open on the right; the last interval is closed on the right too). To cover the entire range of values the maximum and the minimum values should be included between the first and the last break. It is possible to specify a set of breaks covering only a portion of the x range.
adj.breaks	Logical value indicating whether the endpoints of intervals of a numerical variable x when classified into intervals should be displayed avoiding scientific notation; default to TRUE.
interval	Logical value indicating whether x is a variable measured in intervals (TRUE). If the detected intervals are not consistent (e.g. overlapping intervals, or intervals with upper endpoint higher than the lower one), the variable is analyzed as it is, even if results are not necessarily consistent; default to FALSE.
bw	Logical value indicating whether plots should be colored in scale of greys (TRUE) rather than using a standard palette (FALSE, default).
color	Optional string vector allowing to specify colors to use in the plot rather than a standard palette (NULL, default).
use.scientific	Logical value indicating whether numbers on axes should be displayed using scientific notation (TRUE); default to FALSE.
data	An optional data frame containing x. If not found in data, x is taken from the environment from which distr.plot.x() is called.
...	Additional arguments to be passed to low level functions.

Value

No return value, called for side effects.

Author(s)

Raffaella Piccarreta [email protected]

See Also

distr.table.x() for tabulating a univariate distribution.

distr.table.xy() for tabulating a bivariate distribution.

distr.plot.xy() for plotting a bivariate distribution.

Examples

data(MktDATA, package = "UBStats")

# Pie charts 
# - A character variable: grey scale
distr.plot.x(x = LikeMost, plot.type = "pie", bw = TRUE, data = MktDATA)
# - A discrete numeric variable: user-defined palette
distr.plot.x(x = Children, plot.type = "pie", 
             color=c("red","gold","green","forestgreen"),
             data = MktDATA)

# Bar charts 
# - A factor: standard order of levels 
distr.plot.x(x = Education, plot.type = "bars", 
             freq = "percentage", data = MktDATA)
# - A factor: levels arranged by decreasing percentage 
distr.plot.x(x = Education, plot.type = "bars", 
             freq = "perc", ord.freq = "dec", data = MktDATA)
# - A discrete variable (note: distance between values
#   not taken into account)
distr.plot.x(x = NPickUp_Purch, plot.type = "bars",
             freq = "percentage", data = MktDATA)

# Spike plots 
# - A discrete variable
distr.plot.x(x = NPickUp_Purch, plot.type = "spike", 
             freq = "percent", data = MktDATA)
# - A factor (levels placed at the same distance)
distr.plot.x(x = Education, plot.type = "spike", 
             freq = "prop",data = MktDATA)
# - A variable measured in classes (levels placed at the 
#   same distance)
distr.plot.x(x = Income.S, interval = TRUE,
             plot.type = "spike", 
             freq = "prop",data = MktDATA)
# - A numeric variable classified into intervals
#   (levels placed at the same distance)
distr.plot.x(x = AOV, breaks = 5, plot.type = "spike", 
             data = MktDATA)

# Cumulative distribution plots
# - A discrete variable
distr.plot.x(x = Children, plot.type = "cum", data = MktDATA)
# - A continuous numerical variable 
distr.plot.x(x = AOV, plot.type = "cum", 
             freq = "perc", data = MktDATA)
# - A numeric variable classified into intervals
distr.plot.x(AOV, plot.type = "cum", 
             breaks = c(0,20,40,60,80,100,180), data = MktDATA)
# - A variable measured in classes
distr.plot.x(Income, plot.type = "cum", interval = TRUE, 
             freq = "percent", data = MktDATA)
# - A factor
distr.plot.x(x = Education, plot.type = "cum", 
             freq = "prop",data = MktDATA)

# Histograms 
# - A continuous numerical variable: no breaks provided
#    default classes built by R
distr.plot.x(x = AOV, plot.type = "histogram", data = MktDATA)
# - A continuous numerical variable: equal width intervals
distr.plot.x(x = AOV, plot.type = "histogram", 
             breaks = 10, data = MktDATA)
# - A continuous numerical variable: specified breaks
distr.plot.x(AOV, plot.type = "histogram", 
             breaks = c(0,20,40,60,80,100,180), 
             data = MktDATA)
# - A variable measured in classes
distr.plot.x(Income, plot.type = "histogram", 
             interval = TRUE, data = MktDATA)

# Density plots 
# - A  numerical variable
distr.plot.x(x = AOV, plot.type = "density", data = MktDATA)
# - A  numerical variable: breaks are ignored
distr.plot.x(AOV, plot.type = "density", 
             breaks = c(0,20,40,60,80,100,180), 
             data = MktDATA)
# - A variable measured in classes
distr.plot.x(Income, plot.type = "density", 
             interval = TRUE, data = MktDATA)

# Boxplots (only for numerical unclassified variables)
# - A  numerical variable
distr.plot.x(x = TotVal, plot.type = "boxplot", data = MktDATA)
# - A  numerical variable: with specified breaks
#   the plot is not built
# distr.plot.x(AOV, plot.type = "boxplot", 
#              breaks = c(0,20,40,60,80,100,180), 
#              data = MktDATA)

# Arguments adj.breaks, use.scientific
#  A variable with a very wide range (very small densities)
LargeX<-MktDATA$AOV*5000000 
#  - Default formatting for intervals' endpoints
distr.plot.x(LargeX, breaks = 5, plot.type = "spike")
#  - Scientific notation for intervals' endpoints
distr.plot.x(LargeX, breaks = 5,plot.type = "spike",
             adj.breaks = FALSE)
#  - Default formatting for axes
distr.plot.x(LargeX, breaks = 5,plot.type = "histogram",
             freq = "densities")
#  - Scientific notation for axes
distr.plot.x(LargeX, breaks = 5,plot.type = "histogram",
             freq = "densities",use.scientific = TRUE)

---

Analysis of a bivariate distribution using plots

Description

distr.plot.xy() generates plots of a bivariate distribution.

Usage

distr.plot.xy(
  x,
  y,
  plot.type,
  bar.type = "stacked",
  freq = "counts",
  freq.type = "joint",
  breaks.x,
  breaks.y,
  interval.x = FALSE,
  interval.y = FALSE,
  bw = FALSE,
  color = NULL,
  var.c,
  breaks.c,
  interval.c = FALSE,
  adj.breaks = TRUE,
  fitline = FALSE,
  legend = TRUE,
  use.scientific = FALSE,
  data,
  ...
)

Arguments

x, y	Unquoted strings identifying the variables whose distribution has to be graphically displayed. x and y can be the name of a vector or a factor in the workspace or the name of one of the columns in the data frame specified in the data argument. Note that in the plot x is reported on the horizontal axis while y is reported on the vertical axis.
plot.type	A single character specifying the type of plot to build. Allowed options are "bars", "scatter", and "boxplot". If both x and y are character vectors or factors and bar.type = "scatter" a bubble plot is built, with dots having a size proportional to the joint frequency of each pair of observed values. If bar.type = "boxplot", at least one input variable must be numeric; when both the variables are numeric the conditional distributions of y|x are displayed, unless otherwise specified using freq.type="x|y".
bar.type	A single character indicating whether in a bar plot stacked (bar.type = "stacked", default) or side-by-side (bar.type = "beside") bars should be displayed.
freq	A single character specifying the frequencies to be displayed when a bar plot is requested (plot.type="bars"). Allowed options (possibly abbreviated) are "counts", "percentages" and "proportions".
freq.type	A single character specifying the type of frequencies to be displayed when a bar plot is requested (plot.type="bars"). Allowed options are joint (default) for joint frequencies, x|y for the distributions of x conditioned to y, and y|x for the distributions of y conditioned to x. The option x|y can also be used when plot.type="boxplot".
breaks.x, breaks.y	Allow to classify the variables x and/or y, if numerical, into intervals. They can be integers indicating the number of intervals of equal width used to classify x and/or y, or vectors of increasing numeric values defining the endpoints of the intervals (closed on the left and open on the right; the last interval is closed on the right too). To cover the entire range of values taken by one variable, the maximum and the minimum values should be included between the first and the last break. It is possible to specify a set of breaks covering only a portion of the variable's range.
interval.x, interval.y	Logical values indicating whether x and/or y are variables measured in classes (TRUE). If the detected intervals are not consistent (e.g. overlapping intervals, or intervals with upper endpoint higher than the lower one), the variable is analyzed as it is, even if results are not necessarily consistent; default to FALSE.
bw	Logical value indicating whether plots should be colored in scale of greys (TRUE) rather than using a standard palette (FALSE, default).
color	Optional string vector allowing to specify colors to use in the plot rather than a standard palette (NULL, default).
var.c	An optional unquoted string identifying one variable used to color points in a scatter plot (plot.type="scatter"), that can be defined same way as x. This is allowed only when at least one of the input variables x and y is numeric.
breaks.c	Allows to classify the variable var.c, if numerical, into intervals. It can be defined as breaks.x.
interval.c	Logical value indicating whether var.c is a variable measured in intervals (TRUE) or not, as described for interval.x; default to FALSE.
adj.breaks	Logical value indicating whether the endpoints of intervals of a numerical variable (x, or y, or var.c) when classified into intervals should be displayed avoiding scientific notation; default to TRUE.
fitline	Logical value indicating whether the line of best fit (also called trend line or regression line) should be added to a scatter plot (fitline = TRUE) or not (fitline = FALSE; default).
legend	Logical value indicating whether a legend should be displayed in the plot (legend = TRUE; default) or not (legend = FALSE).
use.scientific	Logical value indicating whether numbers on axes should be displayed using scientific notation (TRUE); default to FALSE.
data	An optional data frame containing x and/or y and/or var.c (the variable used to color points in scatter plots). If not found in data, the variables are taken from the environment from which distr.plot.xy() is called.
...	Additional arguments to be passed to low level functions.

Value

No return value, called for side effects.

Author(s)

Raffaella Piccarreta [email protected]

See Also

distr.table.xy() for tabulating a bivariate distribution.

distr.table.x() for tabulating a univariate distribution.

distr.plot.x() for plotting a univariate distribution.

Examples

data(MktDATA, package = "UBStats")

# Bivariate bar plots
# - Two discrete variables (factor or vector with few levels)
#   Joint counts
distr.plot.xy(CustClass, Children,plot.type = "bars", 
              freq = "Counts", freq.type = "joint",
              data = MktDATA)
# - Two discrete variables (factor or vector with few levels)
#   Joint percentages, side-by-side bars
#   User-defined colors
distr.plot.xy(Children,CustClass, plot.type = "bars", 
              bar.type = "beside",
              freq = "percent", freq.type = "joint",
              color = c("red","gold","green","forestgreen"),
              data = MktDATA)
# - One numeric variable classified into intervals
#   and one variable measured in classes
#   Conditional percentages of x|y 
distr.plot.xy(TotPurch, Income, plot.type = "bars", 
              freq = "percent",freq.type = "x|y",
              breaks.x = c(0,5,10,15,20,35),
              interval.y = TRUE, data = MktDATA)
#   Conditional percentages of y|x 
distr.plot.xy(TotPurch, Income, plot.type = "bars", 
              freq = "percent",freq.type = "y|x",
              breaks.x = c(0,5,10,15,20,35),
              interval.y = TRUE, data = MktDATA)

# Side-by-side boxplots
# - A continuous variable conditioned to a factor, 
#   a character, or a classified variable
#   The distributions of the numeric variable conditioned
#   to the factor (or character) are displayed
distr.plot.xy(x = AOV, y = Education, plot.type = "boxplot",
              data = MktDATA)
distr.plot.xy(x = Income.S, y = AOV, plot.type = "boxplot",
              interval.x = TRUE, data = MktDATA)
distr.plot.xy(x = Baseline, y = TotPurch, plot.type = "boxplot",
              breaks.y = c(0,5,10,15,20,35),
              data = MktDATA)
# - Two numerical variables. By default distributions 
#   of y|x are displayed unless differently 
#   specified in freq.type
distr.plot.xy(x = NPickUp_Purch, y = NWeb_Purch,
              plot.type = "boxplot", data = MktDATA)
distr.plot.xy(x = NPickUp_Purch, y = NWeb_Purch,
              plot.type = "boxplot",freq.type = "x|y",
              data = MktDATA)

# Scatter plots
# - Two numerical variables: default options
distr.plot.xy(Baseline, TotVal, plot.type = "scatter", 
              fitline = TRUE, data = MktDATA)
# - Two numerical variables: colors based on discrete var 
distr.plot.xy(Baseline, TotVal, plot.type = "scatter", 
              var.c = Marital_Status,  
              fitline = TRUE, data = MktDATA)
distr.plot.xy(Baseline, TotVal, plot.type = "scatter", 
              var.c = Income, interval.c = TRUE, 
              fitline = TRUE, data = MktDATA)
distr.plot.xy(Baseline, TotVal, plot.type = "scatter", 
              var.c = TotPurch, breaks.c = 10, 
              fitline = TRUE, data = MktDATA)
# - Two numerical variables: colors based 
#   on a continuous numerical variable
distr.plot.xy(Baseline, TotVal, plot.type = "scatter", 
              var.c = AOV, fitline = TRUE, data = MktDATA)

# - One numerical variable and one factor or character 
distr.plot.xy(Baseline, Marital_Status, plot.type = "scatter", 
              fitline = TRUE, data = MktDATA)
distr.plot.xy(Income.S, Baseline, plot.type = "scatter", 
              interval.x = TRUE,
              fitline = TRUE, data = MktDATA)
#   color based on a third variable
distr.plot.xy(TotPurch, TotVal, plot.type = "scatter", 
              breaks.x = c(0,5,10,15,20,35),
              var.c = AOV,
              fitline = TRUE, data = MktDATA)

# - Two factors or character vectors: bubble plots
distr.plot.xy(Education, LikeMost, plot.type = "scatter", 
              data = MktDATA)
# - Two classified variables (i.e. not properly numerical): 
#   bubble plots, changed color
distr.plot.xy(Income.S, TotPurch, plot.type = "scatter",
              interval.x = TRUE,
              breaks.y = c(0,5,10,15,20,35),
              color = "orchid", data = MktDATA)

# Arguments adj.breaks and use.scientific 
#  Variable with very wide ranges
LargeC<-MktDATA$AOV*5000000 
LargeX<-MktDATA$Baseline*1000000 
LargeY<-MktDATA$TotVal*1000000
#  - Default: no scientific notation
distr.plot.xy(LargeX, LargeY, plot.type = "scatter", 
              var.c = LargeC, data = MktDATA)
distr.plot.xy(LargeX, LargeY, plot.type = "scatter", 
              breaks.x = 10, var.c = LargeC, 
              data = MktDATA)
#  - Scientific notation for axes 
distr.plot.xy(LargeX, LargeY, plot.type = "scatter", 
              breaks.x = 10, var.c = LargeC, 
              use.scientific = TRUE,
              data = MktDATA)
#  - Scientific notation for intervals' endpoints
distr.plot.xy(LargeX, LargeY, plot.type = "scatter", 
              breaks.x = 10, var.c = LargeC, 
              adj.breaks = FALSE,
              data = MktDATA)
#  - Scientific notation for intervals endpoints and axes
distr.plot.xy(LargeX, LargeY, plot.type = "scatter", 
              var.c = LargeC, fitline = TRUE, 
              adj.breaks = FALSE, use.scientific = TRUE,
              data = MktDATA)
distr.plot.xy(LargeX, LargeY, plot.type = "scatter", 
              breaks.x = 10, var.c = LargeC, 
              adj.breaks = FALSE, use.scientific = TRUE,
              data = MktDATA)

---

Summary statistics for a single variable

Description

distr.summary.x() computes summary statistics of a vector or a factor.

Usage

distr.summary.x(
  x,
  stats = c("summary"),
  by1,
  by2,
  breaks.by1,
  interval.by1 = FALSE,
  breaks.by2,
  interval.by2 = FALSE,
  adj.breaks = TRUE,
  digits = 2,
  f.digits = 4,
  force.digits = FALSE,
  use.scientific = FALSE,
  data,
  ...
)

Arguments

x	An unquoted string identifying the variable whose distribution has to be summarized. x can be the name of a vector or a factor in the workspace or the name of one of the columns in the data frame specified in the data argument.
stats	A character vector specifying the summary statistics to compute (more summaries can be specified). Specific types of summaries can be requested with the following options: "summary": min, q1, median, mean, q3, max, sd, var; "central": central tendency measures; "dispersion": measures of dispersion; "fivenumbers": five-number summary; "quartiles", "quintiles", "deciles", "percentiles": set of quantiles. It is also possible to request the following statistics: "q1", "q2", "q3", "mean", "median", "mode" (which returns the mode, the number of modes and the proportion of cases with modal value respectively), "min", "max", "sd", "var", "cv" (coefficient of variation), "range", "IQrange" (interquartile range), and "p1", "p2",..., "p100" (i.e. specific percentiles).
by1, by2	Unquoted strings identifying optional variables (typically taking few values/levels) used to build conditional summaries, that can be defined same way as x.
breaks.by1, breaks.by2	Allow classifying the variables by1 and/or by2, if numerical, into intervals. They can be integers indicating the number of intervals of equal width used to classify by1 and/or by2, or vectors of increasing numeric values defining the endpoints of intervals (closed on the left and open on the right; the last interval is closed on the right too). To cover the entire range of values the maximum and the minimum values should be included between the first and the last break. It is possible to specify a set of breaks covering only a portion of the range of by1 and/or by2.
interval.by1, interval.by2	Logical values indicating whether by1 and/or by2 are variables measured in classes (TRUE). If the intervals for one variable are not consistent (e.g. overlapping intervals, or intervals with upper endpoint higher than the lower one), the variable is analysed as it is, even if results are not necessarily consistent; default to FALSE.
adj.breaks	Logical value indicating whether the endpoints of intervals of the numerical variables by1 or by2, when classified into intervals, should be displayed avoiding scientific notation; default to TRUE.
digits, f.digits	Integer values specifying the number of decimals used to round respectively summary statistics (default: digits=4) and proportions percentages (default: f.digits=2). If the chosen rounding formats some non-zero values as zero, the number of decimals is increased so that all values have at least one significant digit, unless the argument force.digits is set to TRUE.
force.digits	Logical value indicating whether the requested summaries should be forcedly rounded to the number of decimals specified in digits and f.digits even if non-zero values are rounded to zero (default to FALSE).
use.scientific	Logical value indicating whether numbers in tables should be displayed using scientific notation (TRUE); default to FALSE.
data	An optional data frame containing x and/or the variables specifying the layers, by1 and by2. If not found in data, the variables are taken from the environment from which distr.summary.x() is called.
...	Additional arguments to be passed to low level functions.

Value

A list whose elements are tables (converted to dataframes) with the requested summaries, possibly conditioned to by1 and/or by2. The values taken by the conditioning variables are arranged in standard order (logical, alphabetical or numerical order for vectors, order of levels for factors, ordered intervals for classified variables or for variables measured in classes).

Author(s)

Raffaella Piccarreta [email protected]

See Also

summaries.plot.x() to graphically display conditioned tendency summaries of a univariate distribution.

distr.table.x() for tabulating a univariate distribution.

distr.plot.x() for plotting a univariate distribution.

Examples

data(MktDATA, package = "UBStats")

# Marginal summaries
# - Numerical variable: Default summaries
distr.summary.x(x = AOV, data = MktDATA)
# - Numerical variable: More summaries
distr.summary.x(x = AOV, 
                stats = c("central","dispersion","fivenum"),
                data = MktDATA)
distr.summary.x(x = AOV, stats = c("mode","mean","sd","cv","fivenum"),
                data = MktDATA)
# - Character or factor (only proper statistics calculated)
distr.summary.x(x = LikeMost, stats = c("mode","mean","sd","cv","fivenum"),
                data = MktDATA)
distr.summary.x(x = Education, stats = c("mode","mean","sd","cv","fivenum"),
                data = MktDATA)

# Measures conditioned to a single variable
# - Numerical variable by a character vector
distr.summary.x(x = TotVal, 
                stats = c("p5","p10","p25","p50","p75","p90","p95"),
                by1 = Gender, digits = 1, data = MktDATA)
# - Numerical variable by a numerical variable
#   classified into intervals
distr.summary.x(x = TotVal, 
                stats = c("central","dispersion"),
                by1 = AOV, breaks.by1 = 5,
                digits = 1, data = MktDATA)
# - Numerical variable by a variable measured in classes
distr.summary.x(x = TotVal, 
                stats = c("central","dispersion"),
                by1 = Income.S, 
                interval.by1 = TRUE,
                digits = 1, data = MktDATA)

# Measures conditioned to two variables
distr.summary.x(x = TotVal, stats = "fivenumbers", 
                by1 = Gender, by2 = Kids, data = MktDATA)
distr.summary.x(x = TotVal, stats = "fivenumbers", 
                by1 = Income.S, by2 = Gender,
                interval.by1 = TRUE, data = MktDATA)
distr.summary.x(x = TotVal, stats = "fivenumbers",
                by1 = Gender, by2 = AOV,
                breaks.by2 = 5, data = MktDATA)

# Arguments adj.breaks and use.scientific
#  Variables with a very wide range
LargeX<-MktDATA$TotVal*1000000
LargeBY<-MktDATA$AOV*5000000 
#  - Default: no scientific notation
distr.summary.x(LargeX, by1=LargeBY, breaks.by1 = 5, 
                data = MktDATA)
#  - Scientific notation for summaries 
distr.summary.x(LargeX, by1=LargeBY, breaks.by1 = 5, 
                use.scientific = TRUE, data = MktDATA)
#  - Scientific notation for intervals endpoints
distr.summary.x(LargeX, by1=LargeBY, breaks.by1 = 5, 
                adj.breaks = FALSE, data = MktDATA)
#  - Scientific notation for intervals endpoints and summaries
distr.summary.x(LargeX, by1=LargeBY, breaks.by1 = 5, 
                adj.breaks = FALSE, use.scientific = TRUE,
                data = MktDATA)

# Output the list with the requested summaries
Out_TotVal<-distr.summary.x(x = TotVal, 
                            by1 = Income.S, by2 = Gender,
                            interval.by1 = TRUE,
                            stats = c("central","fivenum","dispersion"),
                            data = MktDATA)

---

Analysis of a univariate distribution using frequency tables

Description

distr.table.x() computes the frequency table of a vector or a factor.

Usage

distr.table.x(
  x,
  freq = c("counts", "proportions"),
  total = TRUE,
  breaks,
  adj.breaks = TRUE,
  interval = FALSE,
  f.digits = 2,
  p.digits = 0,
  d.digits = 5,
  force.digits = FALSE,
  use.scientific = FALSE,
  data,
  ...
)

Arguments

x	An unquoted string identifying the variable whose distribution has to be analysed. x can be the name of a vector or a factor in the workspace or the name of one of the columns in the data frame specified in the data argument.
freq	A character vector specifying the set of frequencies to be displayed (more options are allowed). Allowed options (possibly abbreviated) are "counts", "percentages", "proportions", "densities" (only for variables classified into intervals or measured in classes), and "cumulative". If no frequency is specified, "counts" and "proportions" are displayed by default. If only "cumulative" is specified, counts and proportions are displayed too, with their respective cumulative frequencies.
total	Logical value indicating whether the sum of the requested frequencies should be added to the table; default to TRUE.
breaks	Allows to classify a numerical variable x into intervals. It can be an integer indicating the number of intervals of equal width used to classify x, or a vector of increasing numeric values defining the endpoints of intervals (closed on the left and open on the right; the last interval is closed on the right too). To cover the entire range of values the maximum and the minimum values should be included between the first and the last break. It is possible to specify a set of breaks covering only a portion of the x range.
adj.breaks	Logical value indicating whether the endpoints of intervals of a numerical variable x when classified into intervals should be displayed avoiding scientific notation; default to TRUE.
interval	Logical value indicating whether x is a variable measured in intervals (TRUE). If the detected intervals are not consistent (e.g. overlapping intervals, or intervals with upper endpoint higher than the lower one), the variable is tabulated as it is, even if results are not necessarily consistent; default to FALSE.
f.digits, p.digits, d.digits	Integer values specifying the number of decimals used to round respectively proportions (default: f.digits=2), percentages (default: p.digits=0), and densities (default: d.digits=5). If the chosen rounding formats some non-zero values as zero, the number of decimals is increased so that all values have at least one significant digit, unless the argument force.digits is set to TRUE.
force.digits	Logical value indicating whether frequencies and densities should be forcedly rounded to the number of decimals specified in f.digits, p.digits, and d.digits even if non-zero values are rounded to zero (default to FALSE).
use.scientific	Logical value indicating whether numbers in tables (typically densities) should be displayed using scientific notation (TRUE); default to FALSE.
data	An optional data frame containing x. If not found in data, x is taken from the environment from which distr.table.x() is called.
...	Additional arguments to be passed to low level functions.

Value

A table (converted to dataframe) listing the values taken by the variable, arranged in standard order (logical, alphabetical or numerical order for vectors, order of levels for factors, ordered intervals for classified variables or for variables measured in classes), and the requested set of frequencies.

Author(s)

Raffaella Piccarreta [email protected]

See Also

distr.plot.x() for plotting a univariate distribution.

distr.table.xy() for tabulating a bivariate distribution.

distr.plot.xy() for plotting a bivariate distribution.

Examples

data(MktDATA, package = "UBStats")

# Character vectors, factors, and discrete numeric vectors
distr.table.x(Education, data = MktDATA)

distr.table.x(Children, freq = c("count","prop","cum"),
              data = MktDATA)

# Numerical variable classified into intervals
# - Classes of equal width
distr.table.x(AOV, breaks = 6, freq = c("Count","Prop","Perc","Cum"),
              p.digits = 2, data = MktDATA)
# - Classes with specified endpoints
distr.table.x(AOV, breaks = c(0,20,30,50,100,180),
              freq = c("Count","Perc","Cum","Densities"), 
              p.digits = 2, data = MktDATA)
# Numerical variable measured in classes
# - Variable measured in classes
distr.table.x(Income, freq = c("count","prop","cum","dens"),
              interval = TRUE, data = MktDATA)
# - An example of non-consistent intervals. 
#   Densities are not calculated
x.inconsistent <- c(rep("0;10",30),rep("10;20",25),rep("25;8",25),
                    rep("15;31",15),rep("20;45",16),rep("30;40",18))
distr.table.x(x.inconsistent, freq = c("count","prop","cum","dens"),
              interval = TRUE)

# Arguments adj.breaks, use.scientific, and force.digits
#  A variable with a very wide range (very small densities)
LargeX <- MktDATA$AOV*5000000 
# - Default: manages possible excess of rounding
distr.table.x(LargeX, breaks = 5, 
              freq = c("count","percent","densities"))
# - Forcing digits to the default values 
distr.table.x(LargeX, breaks = 5,
              freq=c("count","percent","dens"),
              force.digits = TRUE)
#  - Scientific notation for frequencies/densities 
distr.table.x(LargeX, breaks = 5,
              freq = c("count","percent","dens"),
              use.scientific = TRUE)
#  - Scientific notation both for intervals’ endpoints 
#    and for frequencies/densities
distr.table.x(LargeX, breaks = 5, adj.breaks = FALSE,
              freq = c("count","percent","dens"),
              use.scientific = TRUE)

# Output a dataframe with the table
table.AOV<-distr.table.x(AOV, breaks = c(0,20,30,50,100,180),
                         freq = c("Count","Perc","Cum","Dens"), 
                         data = MktDATA)

---

Analysis of a bivariate distribution using cross-tables

Description

distr.table.xy() displays tables of joint or conditional distributions.

Usage

distr.table.xy(
  x,
  y,
  freq = "counts",
  freq.type = "joint",
  total = TRUE,
  breaks.x,
  breaks.y,
  adj.breaks = TRUE,
  interval.x = FALSE,
  interval.y = FALSE,
  f.digits = 2,
  p.digits = 0,
  force.digits = FALSE,
  data,
  ...
)

Arguments

x, y	Unquoted strings identifying the variables whose joint distribution has to be analysed. x and y can be the name of a vector or a factor in the workspace or the name of one of the columns in the data frame specified in the data argument. Note that in the table x is displayed on the rows and y on the columns.
freq	A character vector specifying the set of frequencies to be displayed (more options are allowed). Allowed options (possibly abbreviated) are "counts", "percentages" and "proportions".
freq.type	A character vector specifying the types of frequencies to be displayed (more types are allowed). Allowed options are joint (default) for joint frequencies, x|y (or column) for the distributions of x conditioned to y, and y|x (or row) for the distributions of y conditioned to x.
total	Logical value indicating whether the sum of the requested frequencies should be added to the table; default to TRUE.
breaks.x, breaks.y	Allow to classify the variables x and/or y, if numerical, into intervals. They can be integers indicating the number of intervals of equal width used to classify x and/or y, or vectors of increasing numeric values defining the endpoints of the intervals (closed on the left and open on the right; the last interval is closed on the right too). To cover the entire range of values taken by one variable, the maximum and the minimum values should be included between the first and the last break. It is possible to specify a set of breaks covering only a portion of the variable's range.
adj.breaks	Logical value indicating whether the endpoints of intervals of a numerical variable (x or y) when classified into intervals should be displayed avoiding scientific notation; default to TRUE.
interval.x, interval.y	Logical values indicating whether x and/or y are variables measured in classes (TRUE). If the detected intervals are not consistent (e.g. overlapping intervals, or intervals with upper endpoint higher than the lower one), the variable is tabulated as it is, even if results are not necessarily consistent; default to FALSE.
f.digits, p.digits	Integer values specifying the number of decimals used to round respectively proportions (default: f.digits=2) and percentages (default: p.digits=0). If the chosen rounding formats some non-zero values as zero, the number of decimals is increased so that all values have at least one significant digit, unless the argument force.digits is set to TRUE.
force.digits	Logical value indicating whether proportions and percentages should be forcedly rounded to the number of decimals specified in f.digits and p.digits even if non-zero values are rounded to zero (default to FALSE).
data	An optional data frame containing x and/or y. If not found in data, the variables are taken from the environment from which distr.table.xy() is called.
...	Additional arguments to be passed to low level functions.

Value

A list whose elements are the requested tables (converted to dataframes) listing the values taken by the two variables arranged in standard order (logical, alphabetical or numerical order for vectors, order of levels for factors, ordered intervals for classified variables or for variables measured in classes) and the specified joint or conditional types of frequencies.

Author(s)

Raffaella Piccarreta [email protected]

See Also

distr.plot.xy() for plotting a bivariate distribution.

distr.table.x() for tabulating a univariate distribution.

distr.plot.x() for plotting a univariate distribution.

Examples

data(MktDATA, package = "UBStats")

# Character vectors, factors, and discrete numeric vectors
# - Default: joint counts
distr.table.xy(LikeMost, Children, data = MktDATA) 

# - Joint and conditional distribution of x|y
#   counts and proportions, no totals
distr.table.xy(LikeMost, Education, freq = c("counts","Prop"), 
               freq.type = c("joint","x|y"), total = FALSE,
               data = MktDATA)
# - Joint and conditional row and column distributions (%) 
distr.table.xy(CustClass, Children, freq = "Percentages", 
               freq.type = c("joint","row","column"),
               data = MktDATA)

# Numerical variables classified or measured in classes
# - A numerical variable classified into intervals 
#   and a factor
distr.table.xy(CustClass, TotPurch, 
               breaks.y = c(0,5,10,15,20,35),
               freq = c("Counts","Prop"), freq.type = "y|x", 
               data = MktDATA)

# - Two numerical variables, one measured in classes
#   and the other classified into intervals 
distr.table.xy(Income.S, TotPurch, interval.x = TRUE,
               breaks.y = c(0,5,10,15,20,35),
               freq = c("Counts","Prop"), 
               freq.type = c("row","col"), data = MktDATA)

# Argument force.digits
# - Default: manages possible excess of rounding
distr.table.xy(CustClass, Children, freq = "Percentages", 
               freq.type = c("x|y"),data = MktDATA)
# - Force to the required rounding
distr.table.xy(CustClass, Children, freq = "Percentages", 
               freq.type = c("x|y"), 
               force.digits = TRUE, data = MktDATA)

# Output the list with the requested tables
tables.xy<-distr.table.xy(Income.S, TotPurch, 
                          interval.x = TRUE,
                          breaks.y = c(0,5,10,15,20,35),
                          freq = c("Counts","Prop"), 
                          freq.type = c("joint","row","col"), 
                          data = MktDATA)

---

Extract Model Residuals and other Regression Diagnostics

Description

LM.output() Provides fitted values, residuals and other basic quantities used to check the quality of regression fits.

Usage

LM.output(object, data)

Arguments

object	An object returned by function lm.
data	An optional data frame containing the data frame possibly specified in the call of function lm.

Value

A dataframe containing the variables in the model and the model's fitted values, residuals and influence statistics, merged with the dataframe specified in the call of function lm, or with the dataframe possibly specified in data (if it is consistent with the model's output)

Author(s)

Raffaella Piccarreta [email protected]

Examples

data(MktDATA, package = "UBStats")

# Model and output based on a given dataframe
mod1 <- lm(TotVal ~ Baseline + Kids + Age, data = MktDATA)
# Equivalent calls (since data is specified in lm() 
mod1_out <- LM.output(mod1, data = MktDATA)
dim(mod1_out)
mod1_out <- LM.output(mod1)
dim(mod1_out) # same as above

# Model based on a dataframe's columns
mod2 <- lm(MktDATA$TotVal ~ MktDATA$Baseline + 
           MktDATA$Kids + MktDATA$Age)
mod2_out <- LM.output(mod2)
# note: colnames in mod2_out
colnames(mod2_out)
# note that the dataframe in 'data' is not considered
# as compatible, because the names of columns differ
mod2_out <- LM.output(mod2, data = MktDATA)

---

Data: MktDATA

Description

This dataset is a modification of the original MktDATA.Orig dataset and it is provided for user convenience.

Usage

data(MktDATA)

Format

A data frame with 2224 observations and 26 variables.

---

Data: MktDATA.Orig

Description

This dataset contains the variables from a survey on a set of customers of a company operating in the retail food sector. The company sells products from 3 major categories (referred to as A, B, C) The customers can order and acquire products in the company physical stores, or through the company's website (in this case, they can order on the website and pick up the order in one store). Information is collected on customers' activity in the last two years (observation period), as well as some information retrieved through questionnaires or fidelity cards. During such period different marketing strategies were adopted to improve customers' fidelization, and 5 marketing campaigns were launched; a last campaign was launched at the end of the observation period.

Usage

data(MktDATA.Orig)

Format

A data frame with 2224 observations and the following 19 variables (levels of the variables listed in alphabetical order):

• CustId (num): customer's identification label

• Gender (chr): customer's gender (F, M)

• Age (num): customer's age (in years)

• Education (chr): customer's level of education(College, Graduate, HighSchool, Post-Grad)

• Marital_Status (chr): customer's marital status (Divorced, Married, Single, Together, Widow)

• Children (num): number of children in the household

• Kids (num): number of kids aged less than 12 in the household

• Income (chr): customer's income (measured in classes)

• Baseline (num): index (from 0 to 1) assigned by the marketing dept indicating how promising the customer was judged at the beginning of the observation period

• LikeMost (chr): Most frequently bought category in the last two years (P.A, P.B, P.C)

• TotVal (num): amount spent in the last 2 years

• NPickUp_Purch (num): number of purchases made through company's website and picked up in physical store

• NWeb_Purch (num): number of purchases made through company's website and delivered at home

• NStore_Purch (num): number of purchases made in a physical store

• NDeals (num): number of products purchases with discount

• CustClass (chr): customer's classification (assigned by the marketing dept) based on past profitability (Bronze, Gold, Platinum, Silver)

• PastCampaigns (num): number of offers accepted by the customer in the last 2 years' marketing campaigns

• LastCampaign (num): binary variable (0/1) indicating whether (1) or not (0) the customer accepted the offer in the campaign launched at the end of the observation period

• WouldSuggest (chr): variable signalling whether (Yes) or not (No) the customer declared they would suggest the company's products to friends and family

Source

The data set has been adapted from https://www.kaggle.com/code/dmitryuarov/customers-clustering-eda.

---

Plot of central and non-central conditional tendency measures for a single numeric variable

Description

summaries.plot.x() plots location statistics for a numeric vector conditioned to the levels of one or more variables.

Usage

summaries.plot.x(
  x,
  stats = "mean",
  plot.type = "bars",
  conf.level = 0.95,
  by1,
  by2,
  breaks.by1,
  interval.by1 = FALSE,
  breaks.by2,
  interval.by2 = FALSE,
  adj.breaks = TRUE,
  bw = FALSE,
  color = NULL,
  legend = TRUE,
  use.scientific = FALSE,
  data,
  ...
)

Arguments

x	An unquoted string identifying a numerical variable whose tendency measures have to be graphically displayed. x can be the name of a vector in the workspace or the name of one of the columns in the data frame specified in the data argument.
stats	A single character specifying the conditioned tendency measure/s to display in the plot. The available options are "mean", "median", "ci.mean" (to plot the means and the confidence intervals for the means), and specific sets of quantiles, namely "quartiles", "quintiles", "deciles", and "percentiles" (note that for quantiles only one single layer can be specified).
plot.type	A single character specifying the type of plot used to compare the requested measures conditioned to the levels of one variable, by1, possibly broken down by the levels of a second variable, by2, if specified. The available options are: "bars": Available only when stats is "mean", "median", or "ci.mean" and one single layer (by1) is specified. For each level of by1 a bar is built whose height coincides with the conditional mean or median. Confidence intervals for the means are reported when stats = "ci.mean". "points": Available only when stats is "mean", "median", and "ci.mean". Confidence intervals for the means are reported when stats = "ci.mean" and one single layer is specified. "lines": Points joined by lines; this is the unique option available for quantiles.
conf.level	A number between 0 and 1 indicating the confidence level of the intervals for the conditional means when stats = "ci.mean" is specified (default to 0.95).
by1, by2	Unquoted strings identifying variables (typically taking few values/levels) used to build conditional summaries, that can be defined same way as x. At least one layer has to be specified. The conditional measures are plotted against the values of by1, broken down by the levels of by2, if specified.
breaks.by1, breaks.by2	Allow classifying the variables by1 and/or by2, if numerical, into intervals. They can be integers indicating the number of intervals of equal width used to classify by1 and/or by2, or vectors of increasing numeric values defining the endpoints of intervals (closed on the left and open on the right; the last interval is closed on the right too). To cover the entire range of values the maximum and the minimum values should be included between the first and the last break. It is possible to specify a set of breaks covering only a portion of the range of by1 and/or by2.
interval.by1, interval.by2	Logical values indicating whether by1 and/or by2 are variables measured in classes (TRUE). If the intervals for one variable are not consistent (e.g. overlapping intervals, or intervals with upper endpoint higher than the lower one), the variable is analysed as it is, even if results are not necessarily consistent; default to FALSE.
adj.breaks	Logical value indicating whether the endpoints of intervals of the numerical variables by1 or by2, when classified into intervals, should be displayed avoiding scientific notation; default to TRUE.
bw	Logical value indicating whether plots should be colored in scale of greys (TRUE) rather than using a standard palette (FALSE, default).
color	Optional string vector to specify colors to use in the plot rather than a standard palette (NULL, default).
legend	Logical value indicating whether a legend should be displayed in the plot (legend = TRUE; default) or not (legend = FALSE).
use.scientific	Logical value indicating whether numbers on axes should be displayed using scientific notation (TRUE); default to FALSE.
data	An optional data frame containing x and/or the variables specifying the layers, by1 and by2. If not found in data, the variables are taken from the environment from which distr.summary.x() is called.
...	Additional arguments to be passed to low level functions.

Value

A table (converted to dataframe) reporting the requested statistics conditioned to the levels of the specified layers.

Author(s)

Raffaella Piccarreta [email protected]

See Also

distr.summary.x() for tabulating summary measures of a univariate distribution.

distr.plot.x() for plotting a univariate distribution.

distr.table.x() for tabulating a univariate distribution.

Examples

data(MktDATA, package = "UBStats")

# Means (and their CI) or medians by a single variable
# - Barplot of means (default) by a character 
summaries.plot.x(x = TotVal, stats = "mean",  
               by1 = Gender, data = MktDATA)
# - Barplot of medians by a numerical variable
#   classified into intervals: user-defined color
summaries.plot.x(x = TotVal, stats = "median", 
                 by1 = AOV, breaks.by1 = 5, 
                 color = "purple", data = MktDATA)
# - Lineplot of means and their CI by a variable 
#   measured in classes
summaries.plot.x(x = TotVal, 
                 stats = "ci.mean", plot.type = "lines",
                 by1 = Income.S, interval.by1 = TRUE,
                 data = MktDATA)
# - Barplot of means and their CI by a 
#   numerical variable; change the confidence level
summaries.plot.x(x = TotVal, 
                 stats = "ci.mean", conf.level = 0.90,
                 plot.type = "bars", 
                 by1 = NWeb_Purch, data = MktDATA)
# - Note: no plot built for a variable with 
#   too many levels (>20)
# summaries.plot.x(x = TotVal, 
#                  stats = "ci.mean", plot.type = "lines",
#                  by1 = AOV, data = MktDATA)

# Quantiles by a single variable
# - Only lines plots allowed for quantiles
summaries.plot.x(x = Baseline, 
                 stats = "deciles", plot.type = "lines",
                 by1 = NDeals, data = MktDATA)
summaries.plot.x(x = Baseline, 
                 stats = "quartiles", plot.type = "lines",
                 by1 = Marital_Status, data = MktDATA)

# Means and medians by two variables
# - Default: only lines allowed
summaries.plot.x(x = TotVal, stats = "mean", 
                 by1 = Education, by2 = Kids, 
                 data = MktDATA)
summaries.plot.x(x = TotVal, stats = "median", 
                 by1 = Income.S, by2 = Gender,
                 interval.by1 = TRUE,
                 data = MktDATA)
summaries.plot.x(x = Baseline, stats = "mean", 
                 by1 = CustClass, by2 = AOV,
                 breaks.by2 = 5, data = MktDATA)
# - "ci.mean" not allowed with two layers
CustClass_Kids<-paste0(MktDATA$CustClass,"-",MktDATA$Kids)
summaries.plot.x(x = Baseline, stats = "ci.mean", 
                 conf.level = 0.99, by1 = CustClass_Kids,
                 color = "gold", data = MktDATA)

# Arguments adj.breaks and use.scientific
#  Variables with a very wide range
LargeX<-MktDATA$TotVal*1000000
LargeBY<-MktDATA$AOV*5000000 
#  - Default: no scientific notation
summaries.plot.x(LargeX, plot.type = "bars",
                 by1=LargeBY, breaks.by1 = 5, data = MktDATA)
#  - Scientific notation for summaries (axes) 
summaries.plot.x(LargeX, plot.type = "lines",
                 by1=LargeBY, breaks.by1 = 5, 
                 use.scientific = TRUE, data = MktDATA)
#  - Scientific notation for intervals endpoints
summaries.plot.x(LargeX, stats = "ci.mean",
                 plot.type = "lines",
                 by1=LargeBY, breaks.by1 = 5,
                 adj.breaks = FALSE, data = MktDATA)
#  - Scientific notation for intervals endpoints and summaries
summaries.plot.x(LargeX, stats = "quartiles",
                 plot.type = "lines", 
                 by1=LargeBY, breaks.by1 = 5, 
                 adj.breaks = FALSE, use.scientific = TRUE,
                 data = MktDATA)

# Output the table with the requested summaries 
Out_TotVal<-summaries.plot.x(x = TotVal, stats = "ci.mean", 
                             by1 = Education, data = MktDATA)

---

Tests on the difference between means

Description

TEST.diffmean() tests hypotheses on the difference between the means of two independent or paired populations.

Usage

TEST.diffmean(
  x,
  y,
  type = "independent",
  mdiff0 = 0,
  alternative = "two.sided",
  sigma.x = NULL,
  sigma.y = NULL,
  by,
  sigma.by = NULL,
  sigma.d = NULL,
  var.test = FALSE,
  digits = 2,
  force.digits = FALSE,
  use.scientific = FALSE,
  data,
  ...
)

Arguments

x, y	Unquoted strings identifying the numeric variables with the same length whose means have to be compared. x and y can be the names of vectors in the workspace or the names of columns in the data frame specified in the data argument. It is possible to use a mixed specification (e.g, one vector and one column in data).
type	A length-one character vector specifying the type of samples. Allowed values are "independent" or "paired".
mdiff0	Numeric value that specifies the null hypothesis to test for (default is 0).
alternative	A length-one character vector specifying the direction of the alternative hypothesis. Allowed values are "two.sided" (difference between populations' means differs from mdiff0; default), or "less" (difference between populations' means is lower than mdiff0), or "greater" (difference between populations' means is higher than mdiff0).
sigma.x, sigma.y	Optional numeric values specifying the possibly known populations' standard deviations (when x and y are specified). If NULL (default) standard deviations are estimated using the data.
by	Optional unquoted string, available only when type = "independent", identifying a variable (of any type), defined same way as x, taking only two values used to split x into two independent samples. Given the two ordered values taken by by (alphabetical or numerical order, or order of the levels for factors), say by1 and by2, hypotheses are tested on the difference between the populations means in the by1- and in the by2-group. Note that only one between y and by can be specified.
sigma.by	Optional numeric value specifying the possibly known standard deviations for the two independent samples identified via by (when x and by are specified). sigma.by can be a single value indicating the same standard deviation in the two by-groups, or a vector with two values, specifying the standard deviations in the two by-groups. To avoid errors, in the latter case the vector should be named, with names coinciding with the two levels of by.
sigma.d	Optional numeric value specifying the possibly known standard deviation of the difference when samples are paired.
var.test	Logical value indicating whether to run a test on the equality of variance for two (independent) samples or not (default).
digits	Integer value specifying the number of decimals used to round statistics; default to 2. If the chosen rounding formats some non-zero values as zero, the number of decimals is increased so that all values have at least one significant digit, unless the argument force.digits is set to TRUE.
force.digits	Logical value indicating whether reported values should be forcedly rounded to the number of decimals specified in digits even if non-zero values are rounded to zero (default to FALSE).
use.scientific	Logical value indicating whether numbers in tables should be displayed using scientific notation (TRUE); default to FALSE.
data	An optional data frame containing x and/or y or by. If not found in data, the variables are taken from the environment from which TEST.diffmean() is called.
...	Additional arguments to be passed to low level functions.

Value

A table reporting the results of the test on the difference between the populations' means. For independent samples in the case of unknown variances the test is run both under the assumption that the variances are equal and under the assumption that they differ, using percentiles from both the normal and the Student's t distribution.

Author(s)

Raffaella Piccarreta [email protected]

See Also

CI.diffmean() to build confidence intervals for the difference between two populations' means.

Examples

data(MktDATA, package = "UBStats")

# Independent samples (default type), UNKNOWN variances
#  Bilateral test on difference between means of males and females
#  - Using x,y: build vectors with data on the two groups
AOV_M <- MktDATA$AOV[MktDATA$Gender == "M"]
AOV_F <- MktDATA$AOV[MktDATA$Gender == "F"]
TEST.diffmean(x = AOV_M, y = AOV_F, mdiff0 = 0)
#  - Using x,by: groups identified by ordered levels of by
TEST.diffmean(x = AOV, by = Gender, mdiff0 = 0, data = MktDATA)
#    Since order is F, M, hypothesis are on mean(F) - mean(M)
#    To test hypotheses on mean(M) - mean(F)
Gender.R <- factor(MktDATA$Gender, levels = c("M", "F"))
TEST.diffmean(x = AOV, by = Gender.R , mdiff0 = 0, 
              data = MktDATA)
#  - Testing also hypotheses on equality of unknown variances
TEST.diffmean(x = AOV_M, y = AOV_F, mdiff0 = 0, 
              var.test = TRUE)

#  - Output results: test on differences
out.test_diffM<-TEST.diffmean(x = AOV_M, y = AOV_F)
#  - Output results: list with both test on means and variances
out.test_diffM.V<-TEST.diffmean(x = AOV_M, y = AOV_F, var.test = TRUE)

# Independent samples (default type), KNOWN variances
#  Test hypotheses on the difference between means of males and females
#  - Using x,y: build vectors with data on the two groups
AOV_M <- MktDATA$AOV[MktDATA$Gender == "M"]
AOV_F <- MktDATA$AOV[MktDATA$Gender == "F"]
TEST.diffmean(x = AOV_M, y = AOV_F, mdiff0 = 10, 
              alternative = "greater", sigma.x = 10, sigma.y = 20)
#  - Using x,by: groups identified by ordered levels of by
#    Adjust considering the ordering of levels
TEST.diffmean(x = AOV, by = Gender, mdiff0 = -10,
              alternative = "less",
              sigma.by = c("M" = 10, "F"=20), data = MktDATA)
#    To change the sign, order levels as desired
Gender.R <- factor(MktDATA$Gender, levels = c("M", "F"))
TEST.diffmean(x = AOV, by = Gender.R, mdiff0 = 10,
              alternative = "greater",
              sigma.by = c("M" = 10, "F"=20), data = MktDATA)
#  - Output results 
out.test_diffM<-TEST.diffmean(x = AOV_M, y = AOV_F, mdiff0 = 10, 
                              alternative = "greater", 
                              sigma.x = 10, sigma.y = 20)

# Paired samples: UNKNOWN variances
# - Default settings
TEST.diffmean(x = NStore_Purch, y = NWeb_Purch, 
              type = "paired", 
              mdiff0 = 1.5, alternative = "greater", data=MktDATA)
# Paired: KNOWN variances
TEST.diffmean(x = NStore_Purch, y = NWeb_Purch,
              type = "paired", mdiff0 = 1.5, alternative = "greater",
              sigma.d = 2, data = MktDATA)
#  - Output results 
out.test_diffM<-TEST.diffmean(x = NStore_Purch, 
                              y = NWeb_Purch,
                              type = "paired", mdiff0 = 1.5, alternative = "greater",
                              sigma.d = 2, data = MktDATA)

# Arguments force.digits and use.scientific
#  An input variable taking very low values
SmallX<-MktDATA$AOV/50000
SmallX_M <- SmallX[MktDATA$Gender == "M"]
SmallX_F <- SmallX[MktDATA$Gender == "F"]
#  - Default output
TEST.diffmean(x = SmallX_M, y = SmallX_F)
#  - Request to use the exact number of digits (default, 2)
TEST.diffmean(x = SmallX_M, y = SmallX_F,
              force.digits = TRUE)
#  - Request to allow scientific notation
TEST.diffmean(x = SmallX_M, y = SmallX_F, 
              use.scientific = TRUE)

---

Tests on the difference between proportions

Description

TEST.diffprop() tests hypotheses on the difference between the proportion of successes in two independent populations.

Usage

TEST.diffprop(
  x,
  y,
  success.x = NULL,
  success.y = NULL,
  pdiff0 = 0,
  alternative = "two.sided",
  by,
  digits = 2,
  force.digits = FALSE,
  use.scientific = FALSE,
  data,
  ...
)

Arguments

x, y	Unquoted strings identifying the variables of interest. x and y can be the names of vectors or factors in the workspace or the names of columns in the data frame specified in the data argument. It is possible to use a mixed specification (e.g, one vector and one column in data).
success.x, success.y	If x,y are factors, character vectors, or numeric non-binary vectors, success must be used to indicate the category/value corresponding to success in the populations. These arguments can be omitted (NULL, default) if x,y are binary numeric vectors (taking values 0 or 1 only; in this case success is assumed to correspond to 1) or a logical vector (in these cases success is assumed to correspond to TRUE).
pdiff0	Numeric value that specifies the null hypothesis to test for (default is 0).
alternative	A length-one character vector specifying the direction of the alternative hypothesis. Allowed values are "two.sided" (difference between populations' proportions differs from pdiff0; default), or "less" (difference between populations' proportions is lower than pdiff0), or "greater" (difference between populations' proportions is higher than pdiff0).
by	Optional unquoted string identifying a variable (of any type), defined same way as x, taking only two values used to split x into two independent samples. Given the two ordered values taken by by (alphabetical or numerical order, or order of the levels for factors), say by1 and by2, hypotheses are tested on the difference between the populations proportions in the by1- and in the by2-group. Note that only one between y and by can be specified.
digits	Integer value specifying the number of decimals used to round statistics; default to 2. If the chosen rounding formats some non-zero values as zero, the number of decimals is increased so that all values have at least one significant digit, unless the argument force.digits is set to TRUE.
force.digits	Logical value indicating whether reported values should be forcedly rounded to the number of decimals specified in digits even if non-zero values are rounded to zero (default to FALSE).
use.scientific	Logical value indicating whether numbers in tables should be displayed using scientific notation (TRUE); default to FALSE.
data	An optional data frame containing x and/or y or by. If not found in data, the variables are taken from the environment from which TEST.diffprop() is called.
...	Additional arguments to be passed to low level functions.

Value

A table reporting the results of the test on the difference between the proportions of successes in two independent populations.

Author(s)

Raffaella Piccarreta [email protected]

See Also

CI.diffprop() to build confidence intervals for the difference between two populations' proportions of successes.

Examples

data(MktDATA, package = "UBStats")

# Proportions of success defined on non-binary and 
#  non-logical vectors; 'success' coded same way
#  for both vectors
#  - Using x,y: build vectors with data on the two groups
WouldSuggest_F <- MktDATA$WouldSuggest[MktDATA$Gender == "F"]
WouldSuggest_M <- MktDATA$WouldSuggest[MktDATA$Gender == "M"]
TEST.diffprop(x = WouldSuggest_M, y = WouldSuggest_F, 
              success.x = "Yes", pdiff0 = 0.1, alternative = "less")

PastCampaigns_F<-MktDATA$PastCampaigns[MktDATA$Gender=="F"]
PastCampaigns_M<-MktDATA$PastCampaigns[MktDATA$Gender=="M"]
TEST.diffprop(x = PastCampaigns_M, y = PastCampaigns_F,
              success.x = 0, pdiff0 = 0.2)

#  - Using x,by: groups identified by ordered levels of by
TEST.diffprop(x = PastCampaigns, by = Gender,
              success.x=0, pdiff0 = 0.2, data = MktDATA)
#    Since order is F, M, test is on prop(F) - prop(M)
#    To get the interval for prop(M) - prop(F)
Gender.R <- factor(MktDATA$Gender, levels = c("M", "F"))
TEST.diffprop(x = PastCampaigns, by = Gender.R,
              success.x=0, pdiff0 = 0.2, data = MktDATA)

# Proportions of success defined based on 
#  binary or logical vectors; 'success'
#  coded same way for both vectors
#  - Binary variable (success=1): based on x,y
LastCampaign_F<-MktDATA$LastCampaign[MktDATA$Gender=="F"]
LastCampaign_M<-MktDATA$LastCampaign[MktDATA$Gender=="M"]
TEST.diffprop(x = LastCampaign_M, y = LastCampaign_F)
#  - Binary variable (success=1): based on x,y
#    see above for recoding of levels of Gender
TEST.diffprop(x = LastCampaign, by = Gender, data = MktDATA)
Gender.R <- factor(MktDATA$Gender, levels = c("M", "F"))
TEST.diffprop(x = LastCampaign, by = Gender.R, data = MktDATA)
#  - Logical variable (success=TRUE): based on x,y
Deals_w_child <- MktDATA$Deals.ge50[MktDATA$Children>0]
Deals_no_child <- MktDATA$Deals.ge50[MktDATA$Children==0]
TEST.diffprop(x = Deals_w_child, y = Deals_no_child, 
              pdiff0 = 0.2, alternative = "less",)
# Proportions defined on 
#  non-binary and non-logical vectors, with 'success'
#  coded differently (only specification x,y is reasonable here)
WouldSuggest_Other<-c(rep("OK",310),rep("KO",650-310))
TEST.diffprop(x = WouldSuggest, y = WouldSuggest_Other, 
              success.x = "Yes", success.y = "OK",
              pdiff0 = 0.1, alternative = "greater",
              data = MktDATA)

# Proportions based on combined conditions
# - Build logical vector/s indicating whether a condition 
#   is satisfied
IsTop<-MktDATA$AOV>80
IsTop_OK<-IsTop[MktDATA$WouldSuggest == "Yes"]
IsTop_KO<-IsTop[MktDATA$WouldSuggest == "No"]
TEST.diffprop(x = IsTop_OK, y = IsTop_KO, pdiff0 = 0.05,
              alternative = "greater")

Deals<-MktDATA$NDeals>=5
Deals_Married <- Deals[MktDATA$Marital_Status=="Married" & 
                         MktDATA$Children==0] 
Deals_Single <- Deals[MktDATA$Marital_Status=="Single"] 
TEST.diffprop(x = Deals_Married, y = Deals_Single,
              alternative = "less")

# Output results           
out.test_diffP<-TEST.diffprop(x = Deals_Married, y = Deals_Single,
                              alternative = "less")

# Arguments force.digits and use.scientific
#  An input variable taking very low values
HighAOV <- MktDATA$AOV>150
# - Default: manages possible excess of rounding
TEST.diffprop(x = HighAOV[MktDATA$Gender=="M"], 
              y = HighAOV[MktDATA$Gender=="F"])
#  - Force to the exact number of digits (default, 2)
TEST.diffprop(x = HighAOV[MktDATA$Gender=="M"], 
              y = HighAOV[MktDATA$Gender=="F"],
              force.digits = TRUE)
#  - Allow scientific notation
TEST.diffprop(x = HighAOV[MktDATA$Gender=="M"], 
              y = HighAOV[MktDATA$Gender=="F"],
              use.scientific = TRUE)

---

Tests on variances

Description

TEST.diffvar() tests the hypothesis of equality between the variances of two independent populations.

Usage

TEST.diffvar(
  x,
  y,
  by,
  digits = 2,
  force.digits = FALSE,
  use.scientific = FALSE,
  data,
  ...
)

Arguments

x, y	Unquoted strings identifying the numeric variables with the same length whose variances have to be compared. x and y can be the names of vectors in the workspace or the names of columns in the data frame specified in the data argument. It is possible to use a mixed specification (e.g, one vector and one column in data).
by	Optional unquoted string identifying a variable (of any type), defined same way as x, taking only two values used to split x into two independent samples. Since the null hypothesis of equal variances is tested against the bilateral alternative only, the order of the levels of by is irrelevant (differently from what holds for functions building confidence intervals or testing hypotheses on the differences between means or proportions). Note that only one between y and by can be specified.
digits	Integer value specifying the number of decimals used to round statistics; default to 2. If the chosen rounding formats some non-zero values as zero, the number of decimals is increased so that all values have at least one significant digit, unless the argument force.digits is set to TRUE.
force.digits	Logical value indicating whether reported values should be forcedly rounded to the number of decimals specified in digits even if non-zero values are rounded to zero (default to FALSE).
use.scientific	Logical value indicating whether numbers in tables should be displayed using scientific notation (TRUE); default to FALSE.
data	An optional data frame containing x and/or y. If not found in data, the variables are taken from the environment from which TEST.diffvar() is called.
...	Additional arguments to be passed to low level functions.

Value

A table reporting the results of the test on the difference between the variances of two independent populations.

Author(s)

Raffaella Piccarreta [email protected]

See Also

CI.diffmean() to build confidence intervals for the difference between two populations' means.

TEST.diffmean() to test hypotheses on the difference between two populations' means.

Examples

data(MktDATA, package = "UBStats")

# Using x,y: build vectors with data on the two groups
AOV_M <- MktDATA$AOV[MktDATA$Gender == "M"]
AOV_F <- MktDATA$AOV[MktDATA$Gender == "F"]
TEST.diffvar(x = AOV_M, y = AOV_F)
TEST.diffvar(x = AOV_F, y = AOV_M) # same

# Using x,by: groups identified by ordered levels of by
TEST.diffvar(x = AOV, by = Gender, data=MktDATA)

# Output results
out_test.diffV<-TEST.diffvar(x = AOV_M, y = AOV_F)

# Arguments force.digits and use.scientific
#  An input variable taking very low values
SmallX<-MktDATA$AOV/50000
SmallX_M <- SmallX[MktDATA$Gender == "M"]
SmallX_F <- SmallX[MktDATA$Gender == "F"]
#  - Default output
TEST.diffvar(x = SmallX_M, y = SmallX_F)
#  - Request to use the exact number of digits (default, 2)
TEST.diffvar(x = SmallX_M, y = SmallX_F,
             force.digits = TRUE)
#  - Request to allow scientific notation
TEST.diffvar(x = SmallX_M, y = SmallX_F, 
             use.scientific = TRUE)

---

Test on the mean

Description

TEST.mean() tests hypotheses on the mean of a population.

Usage

TEST.mean(
  x,
  sigma = NULL,
  mu0 = 0,
  alternative = "two.sided",
  digits = 2,
  force.digits = FALSE,
  use.scientific = FALSE,
  data,
  ...
)

Arguments

x	An unquoted string identifying the numeric variable whose mean is of interest. x can be the name of a vector in the workspace or the name of one of the columns in the data frame specified in the data argument.
sigma	An optional numeric value specifying the population standard deviation. If NULL (default) the population standard deviation is estimated using the data.
mu0	Numeric value that specifies the null hypothesis to test for (default is 0).
alternative	A length-one character vector specifying the direction of the alternative hypothesis. Allowed values are "two.sided" (population mean differs from mu0; default), or "less" (population mean is lower than mu0), or "greater" (population mean is higher than mu0).
digits	Integer value specifying the number of decimals used to round statistics; default to 2. If the chosen rounding formats some non-zero values as zero, the number of decimals is increased so that all values have at least one significant digit, unless the argument force.digits is set to TRUE.
force.digits	Logical value indicating whether reported values should be forcedly rounded to the number of decimals specified in digits even if non-zero values are rounded to zero (default to FALSE).
use.scientific	Logical value indicating whether numbers in tables should be displayed using scientific notation (TRUE); default to FALSE.
data	An optional data frame containing x. If not found in data, x is taken from the environment from which TEST.mean() is called.
...	Additional arguments to be passed to low level functions.

Value

A table reporting the results of the test on the population mean. If the variance is unknown, the test is run using percentiles from both the normal and the Student's t distribution.

Author(s)

Raffaella Piccarreta [email protected]

See Also

CI.mean() to build confidence intervals for the population mean.

Examples

data(MktDATA, package = "UBStats")

# Test on the mean; KNOWN variance
# - Bilateral test
TEST.mean(NStore_Purch, sigma = 9, mu0 = 5, 
          alternative = "two.sided", data = MktDATA)
# - Unilateral test
TEST.mean(NStore_Purch, sigma = 9,mu0 = 5,
          alternative = "greater", data = MktDATA)

# Test on the mean; UNKNOWN variance;
# - Unilateral test
TEST.mean(TotVal, mu0 = 600, alternative = "less",
          data = MktDATA)

# Arguments force.digits and use.scientific
# An input variable taking very low values
SmallX<-MktDATA$AOV/500
# Default output
TEST.mean(SmallX, mu0 = 0.1)
# Request to use the exact number of digits (default, 2)
TEST.mean(SmallX, mu0 = 0.1,force.digits=TRUE)
# Request to allow scientific notation
TEST.mean(SmallX, mu0 = 0.1,use.scientific=TRUE)

# Output results
out.test_mean<-TEST.mean(TotVal, mu0 = 600, alternative = "less",
                         data = MktDATA)

---

Test on the proportion

Description

TEST.prop() tests hypotheses on the proportion of successes in a population.

Usage

TEST.prop(
  x,
  success = NULL,
  p0 = 0.5,
  alternative = "two.sided",
  digits = 2,
  force.digits = FALSE,
  use.scientific = FALSE,
  data,
  ...
)

Arguments

x	An unquoted string identifying the variable of interest. x can be the name of a vector or a factor in the workspace or the name of one of the columns in the data frame specified in the data argument.
success	If x is a factor, a character vector, or a numeric non-binary vector, success must be used to indicate the category/value corresponding to success. The argument can be omitted (NULL, default) if x is a binary numeric vector (takes values 0 or 1 only; in this case success is assumed to be 1) or a logical vector (in these cases success is assumed to be TRUE).
p0	Numeric value that specifies the null hypothesis to test for (default is 0).
alternative	A length-one character vector specifying the direction of the alternative hypothesis. Allowed values are "two.sided" (population proportion differs from p0; default), or "less" (population proportion is lower than p0), or "greater" (population proportion is higher than p0).
digits	Integer value specifying the number of decimals used to round statistics; default to 2. If the chosen rounding formats some non-zero values as zero, the number of decimals is increased so that all values have at least one significant digit, unless the argument force.digits is set to TRUE.
force.digits	Logical value indicating whether reported values should be forcedly rounded to the number of decimals specified in digits even if non-zero values are rounded to zero (default to FALSE).
use.scientific	Logical value indicating whether numbers in tables should be displayed using scientific notation (TRUE); default to FALSE.
data	An optional data frame containing x. If not found in data, x is taken from the environment from which TEST.prop() is called.
...	Additional arguments to be passed to low level functions.

Value

A table reporting the results of the test on the population proportion of successes.

Author(s)

Raffaella Piccarreta [email protected]

See Also

CI.prop() to build confidence intervals for the population proportion of successes.

Examples

data(MktDATA, package = "UBStats")

# Success = one value of a character vector or factor
# - Bilateral test
TEST.prop(WouldSuggest, success = "Yes", p0 = 0.7, 
         data = MktDATA)
# - Unilateral test, change digits
TEST.prop(Education, success = "Post-Grad", p0 = 0.3, 
          alternative = "less", digits = 4,data = MktDATA)

# Success = numeric value; bilateral test
TEST.prop(Children, success = 2, p0 = 0.3, data = MktDATA)

# Binary variable (success = 1 by default); unilateral
TEST.prop(LastCampaign, p0 = 0.1, alternative = "greater", 
          digits = 3, data = MktDATA)

# Logical variable (success = TRUE by default); unilateral test
TEST.prop(Deals.ge50, p0 = 0.13, alternative = "greater", 
          digits = 3, data = MktDATA)

# Success based on combined conditions
# - Build a (logical) vector 
IsTop <- MktDATA$CustClass == "Gold" |
  MktDATA$CustClass == "Platinum"
TEST.prop(IsTop, p0 = 0.2, data = MktDATA)

HighAOV <- MktDATA$AOV>150
TEST.prop(HighAOV, p0 = 0.1)
TEST.prop(HighAOV, p0 = 0.1, force.digits = TRUE)
TEST.prop(HighAOV, p0 = 0.1, use.scientific = TRUE)

# Output results
out_test_prop<-TEST.prop(IsTop, p0 = 0.2, data = MktDATA)

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