UBStats: a package for teaching and learning introductory statistics

Description

The UBStats package has been developed to support instructors and students involved in basic statistics courses at Bocconi University (Milan, Italy). It contains a limited number of functions, with very similar and coherent syntax, to easily perform descriptive and inferential statistical analyses.

The main functions included in the package are:

• distr.table.x() and distr.plot.x() to tabulate and plot the distribution of a single variable of any type

• distr.table.xy() and distr.plot.xy() to tabulate and plot the joint and conditional distributions for two variables and to build scatterplots

• distr.summary.x() and summaries.plot.x() to calculate summaries of univariate distributions and/or conditional summaries and to plot conditional location measures (means, medians or quantiles)

• CI.mean() and TEST.mean() to build confidence intervals and to test hypotheses on the mean

• CI.prop() and TEST.prop() to build confidence intervals and to test hypotheses on the proportion

• CI.diffmean() and TEST.diffmean() to build confidence intervals and to test hypotheses on the difference between means

• CI.diffprop() and TEST.diffprop() to build confidence intervals and to test hypotheses on the difference between proportions

• TEST.diffvar() to test hypotheses on the equality of two variances

Details

The package has some distinctive features making it a convenient support to students, attending courses on statistics using RStudio, approaching the software for the first time.

Descriptive statistical analyses can be performed for any type of variables, with easy and intuitive procedures to tabulate also numerical variables classified into intervals and/or variables measured in intervals. Collections of univariate summary statistics can be easily obtained, also for factors. Univariate and bivariate distributions can be graphically displayed using two functions only, with a quite rich set of (basic) options.

Inferential statistical analyses can be easily performed based on a reduced set of functions with very similar syntax.

A peculiar characteristic of the package is that in the case of errors the procedure is not immediately interrupted. The functions collect all the possible warnings and error and print a list of all the encountered problems before the possible interruption due to unmanageable errors. This makes the package very convenient for students who approach the study of statistics using RStudio for the first time.

To make suggestions about further developments please feel free to write to raffaella.piccarreta@unibocconi.it.

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

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 raffaella.piccarreta@unibocconi.it

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

Value

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

Author(s)

Raffaella Piccarreta raffaella.piccarreta@unibocconi.it

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

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 raffaella.piccarreta@unibocconi.it

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

Value

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

Author(s)

Raffaella Piccarreta raffaella.piccarreta@unibocconi.it

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)

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

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 raffaella.piccarreta@unibocconi.it

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.

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

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 raffaella.piccarreta@unibocconi.it

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

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 raffaella.piccarreta@unibocconi.it

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

Value

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

Author(s)

Raffaella Piccarreta raffaella.piccarreta@unibocconi.it

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

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 raffaella.piccarreta@unibocconi.it

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

Value

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

Author(s)

Raffaella Piccarreta raffaella.piccarreta@unibocconi.it

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)

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

Value

No return value, called for side effects.

Author(s)

Raffaella Piccarreta raffaella.piccarreta@unibocconi.it

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

Value

No return value, called for side effects.

Author(s)

Raffaella Piccarreta raffaella.piccarreta@unibocconi.it

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

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 raffaella.piccarreta@unibocconi.it

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

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 raffaella.piccarreta@unibocconi.it

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

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 raffaella.piccarreta@unibocconi.it

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)

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

Value

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

Author(s)

Raffaella Piccarreta raffaella.piccarreta@unibocconi.it

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)