# Tests on the difference between proportions `TEST.diffprop()` tests hypotheses on the difference between the proportion of successes in two independent populations. ```r 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. ## Returns A table reporting the results of the test on the difference between the proportions of successes in two independent populations. ## Examples ```r 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) ``` ## See Also `CI.diffprop()` to build confidence intervals for the difference between two populations' proportions of successes. ## Author(s) Raffaella Piccarreta raffaella.piccarreta@unibocconi.it

TEST.diffprop function