prop_compare {quest}

Proportion Comparisons for a Single Variable across 3+ Independent Groups (Chi-square Test of Independence)

Description

prop_compare tests for proportion differences across 3+ independent groups with a chi-square test of independence. The function also calculates the descriptive statistics for each group, Cramer's V and its confidence interval as a standardized effect size, and can provide the X by 2 contingency tables. prop_compare is simply a wrapper for prop.test plus some extra calculations.

Usage

prop_compare(
  x,
  nom,
  lvl = levels(as.factor(nom)),
  yates = TRUE,
  ci.level = 0.95,
  rtn.table = TRUE,
  check = TRUE
)

Arguments

x

numeric vector that only has values of 0 or 1 (or missing values), otherwise known as a dummy variable.

nom

atomic vector that takes on three or more unordered values (or missing values), otherwise known as a nominal variable.

lvl

character vector with length 2 specifying the unique values for the two groups. If nom is a factor, then lvl should be the factor levels rather than the underlying integer codes. This argument allows you to specify order of the proportions in the return object.

yates

logical vector of length 1 specifying whether the Yate's continuity correction should be applied for small samples. See chisq.test for details.

ci.level

numeric vector of length 1 specifying the confidence level. ci.level must range from 0 to 1.

rtn.table

logical vector of lengh 1 specifying whether the return object should include the X by 2 contingency table of counts with totals and the X by 2 overall percentages table. If TRUE, then the last two elements of the return object are "count" containing a matrix of counts and "percent" containing a matrix of overall percentages.

check

logical vector of length 1 specifying whether the input arguments should be checked for errors. For example, if nom has length different than the length of x. This is a tradeoff between computational efficiency (FALSE) and more useful error messages (TRUE).

Details

The confidence interval for Cramer's V is calculated with fisher's r to z transformation as Cramer's V is a kind of multiple correlation coefficient. Cramer's V is transformed to fisher's z units, a symmetric confidence interval for fisher's z is calculated, and then the lower and upper bounds are back-transformed to Cramer's V units.

Value

list of numeric vectors containing statistical information about the proportion comparisons: 1) nhst = chi-square test of independence stat info in a numeric vector, 2) desc = descriptive statistics stat info in a numeric vector, 3) std = standardized effect size and its confidence interval in a numeric vector, 4) count = numeric matrix with dim = [X+1, 3] of the X by 2 contingency table of counts with an additional row and column for totals (if rtn.table = TRUE), 5) percent = numeric matrix with dim = [X+1, 3] of the X by 2 contingency table of overall percentages with an additional row and column for totals (if rtn.table = TRUE).

1) nhst = chi-square test of independence stat info in a numeric vector

est

average proportion difference absolute value (i.e., |group j - group i|)

se

NA (to remind the user there is no standard error for the test)

X2

chi-square value

df

degrees of freedom (of the nominal variable)

p

two-sided p-value

2) desc = descriptive statistics stat info in a numeric vector (note there could be more than 3 groups - groups i, j, and k are just provided as an example):

prop_'lvl[k]'

proportion of group k

prop_'lvl[j]'

proportion of group j

prop_'lvl[i]'

proportion of group i

sd_'lvl[k]'

standard deviation of group k

sd_'lvl[j]'

standard deviation of group j

sd_'lvl[i]'

standard deviation of group i

n_'lvl[k]'

sample size of group k

n_'lvl[j]'

sample size of group j

n_'lvl[i]'

sample size of group i

3) std = standardized effect size and its confidence interval in a numeric vector

cramer

Cramer's V estimate

lwr

lower bound of Cramer's V confidence interval

upr

upper bound of Cramer's V confidence interval

4) count = numeric matrix with dim = [X+1, 3] of the X by 2 contingency table of counts with an additional row and column for totals (if rtn.table = TRUE).

The 3+ unique observed values of nom - plus the total - are the rows and the two unique observed values of x (i.e., 0 and 1) - plus the total - are the columns. The dimlabels are "nom" for the rows and "x" for the columns. The rownames are 1. 'lvl[i]', 2. 'lvl[j]', 3. 'lvl[k]', 4. "total". The colnames are 1. "0", 2. "1", 3. "total".

5) percent = numeric matrix with dim = [X+1, 3] of the X by 2 contingency table of overall percentages with an additional row and column for totals (if rtn.table = TRUE).

The 3+ unique observed values of nom - plus the total - are the rows and the two unique observed values of x (i.e., 0 and 1) - plus the total - are the columns. The dimlabels are "nom" for the rows and "x" for the columns. The rownames are 1. 'lvl[i]', 2. 'lvl[j]', 3. 'lvl[k]', 4. "total". The rownames are 1. "0", 2. "1", 3. "total".

See Also

prop.test the workhorse for prop_compare, props_compare for multiple dummy variables, prop_diff for only 2 independent groups (aka binary variable),

Examples

tmp <- replicate(n = 10, expr = mtcars, simplify = FALSE)
mtcars2 <- str2str::ld2d(tmp)
mtcars2$"cyl_fct" <- car::recode(mtcars2$"cyl",
   recodes = "4='four'; 6='six'; 8='eight'", as.factor = TRUE)
prop_compare(x = mtcars2$"am", nom = mtcars2$"cyl_fct")
prop_compare(x = mtcars2$"am", nom = mtcars2$"cyl_fct",
   lvl = c("four","six","eight")) # specify order of levels in return object

# more than 3 groups
prop_compare(x = ifelse(airquality$"Wind" >= 10, yes = 1, no = 0), nom = airquality$"Month")
prop_compare(x = ifelse(airquality$"Wind" >= 10, yes = 1, no = 0), nom = airquality$"Month",
   rtn.table = FALSE) # no contingency tables