pwrss.chisq.gofit {pwrss}

Goodness-of-Fit or Independence (Chi-square Test)

Description

Calculates statistical power or minimum required sample size (only one can be NULL at a time) for Chi-square goodness-of-fit or independence test.

Usage

pwrss.chisq.gofit(p1 = c(0.50, 0.50),
                  p0 = .chisq.fun(p1)$p0,
                  w = .chisq.fun(p1)$w,
                  df = .chisq.fun(p1)$df,
                  n = NULL, power = NULL,
                  alpha = 0.05, verbose = TRUE)

Arguments

p1

a vector or matrix of cell probabilities under alternative hypothesis

p0

a vector or matrix of cell probabilities under null hypothesis. Calculated automatically when p1 is specified. The default can be overwritten by the user via providing a vector of the same size or matrix of the same dimensions as p1

w

effect size. Computed from p1 and p0 automatically; however, it can be any of Cohen's W, Phi coefficient, Cramer's V, etc. when specified by the user. Phi coefficient is defined as sqrt(X2/n) and Cramer's V is defined as sqrt(X2/(n*v)) where v is min(nrow - 1, ncol - 1) and X2 is the chi-square statistic

df

degrees of freedom. Defined as (ncells - 1) if p1 is a vector, and as (nrows - 1) * (ncols - 1) if p1 is a matrix

n

total sample size

power

statistical power (1-\beta)

alpha

probability of type I error

verbose

if FALSE no output is printed on the console

Value

parms

list of parameters used in calculation

test

type of the statistical test (Chi-square test)

df

degrees of freedom

ncp

non-centrality parameter

power

statistical power (1-\beta)

n

total sample size

References

Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum Associates.

Examples

# ---------------------------------------------------------#
# Example 1: Cohen's W                                     #
# goodness-of-fit test for 1 x k or k x 1 table            #
# How many subjects are needed to claim that               #
# girls choose STEM related majors less than males?       #
# ---------------------------------------------------------#

## Option 1: Use cell probabilities
## from https://www.aauw.org/resources/research/the-stem-gap/
## 28 percent of the  workforce in STEM field is women
prob.mat <- c(0.28, 0.72) # null hypothesis states that c(0.50, 0.50)
pwrss.chisq.gofit(p1 = c(0.28, 0.72),
                  alpha = 0.05, power = 0.80)

## Option 2: Use Cohe's W = 0.44
## df is k - 1 for Cohen's W
pwrss.chisq.gofit(w = 0.44, df = 1,
                  alpha = 0.05, power = 0.80)


# ---------------------------------------------------------#
# Example 2: Phi Coefficient (or Cramer's V or Cohen's W)  #
# test of independence for 2 x 2 contingency tables        #
# How many subjects are needed to claim that               #
# girls are underdiagnosed with ADHD?                      #
# ---------------------------------------------------------#

## Option 1: Use cell probabilities
## from https://time.com/growing-up-with-adhd/
## 5.6 percent of girls and 13.2 percent of boys are diagnosed with ADHD
prob.mat <- rbind(c(0.056, 0.132),
                  c(0.944, 0.868))
colnames(prob.mat) <- c("Girl", "Boy")
rownames(prob.mat) <- c("ADHD", "No ADHD")
prob.mat
pwrss.chisq.gofit(p1 = prob.mat,
                  alpha = 0.05, power = 0.80)

## Option 2: Use Phi coefficient = 0.1302134
## df is 1 for Phi coefficient
pwrss.chisq.gofit(w = 0.1302134, df = 1,
                  alpha = 0.05, power = 0.80)


# --------------------------------------------------------#
# Example 3: Cramer's V (or Cohen's W)                    #
# test of independence for j x k contingency tables       #
# How many subjects are needed to detect the relationship #
# between depression severity and gender?                 #
# --------------------------------------------------------#

## Option 1: Use cell probabilities
## from https://doi.org/10.1016/j.jad.2019.11.121
prob.mat <- cbind(c(0.6759, 0.1559, 0.1281, 0.0323, 0.0078),
                  c(0.6771, 0.1519, 0.1368, 0.0241, 0.0101))
rownames(prob.mat) <- c("Normal", "Mild", "Moderate", "Severe", "Extremely Severe")
colnames(prob.mat) <- c("Female", "Male")
prob.mat
pwrss.chisq.gofit(p1 = prob.mat,
                  alpha = 0.05, power = 0.80)

# Option 2: Use Cramer's V = 0.03022008 based on 5 x 2 contingency table
# df is (nrow - 1) * (ncol - 1) for Cramer's V
pwrss.chisq.gofit(w = 0.03022008, df = 4,
                  alpha = 0.05, power = 0.80)