pwrss (version 1.3.1)

power.chisq.gof: Power Analysis for Chi-square Goodness-of-Fit or Independence Tests

Description

Calculates power, sample size or effect size (only one can be NULL at a time) for Chi-square goodness-of-fit or independence tests.

Usage

power.chisq.gof(
  w = NULL,
  null.w = 0,
  df,
  n = NULL,
  power = NULL,
  alpha = 0.05,
  ceil.n = TRUE,
  verbose = 1,
  utf = FALSE
)

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 under alternative.

null.ncp

non-centrality parameter under null.

chisq.alpha

critical value.

w

Cohen's w effect size under alternative.

power

statistical power \((1-\beta)\).

n

total sample size.

Arguments

w

Cohen's w effect size under alternative. It can be any of Cohen's W, Phi coefficient, or Cramer's V but degrees of freedom should be specified accordingly. 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.

null.w

Cohen's w effect size under null.

df

integer; degrees of freedom. Defined as (n.cells - 1) if p1 is a vector, and as (n.rows - 1) * (n.cols - 1) if p1 is a matrix.

n

integer; total sample size.

power

statistical power, defined as the probability of correctly rejecting a false null hypothesis, denoted as \(1 - \beta\).

alpha

type 1 error rate, defined as the probability of incorrectly rejecting a true null hypothesis, denoted as \(\alpha\).

ceil.n

logical; whether sample size should be rounded up. TRUE by default.

verbose

1 by default (returns test, hypotheses, and results), if 2 a more detailed output is given (plus key parameters and definitions), if 0 no output is printed on the console.

utf

logical; whether the output should show Unicode characters (if encoding allows for it). FALSE by default.

Details

• NB: The pwrss.chisq.gofit() function is deprecated. However, it will remain available as a wrapper for the power.chisq.gof() function during a transition period.

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.vector <- c(0.28, 0.72)
null.prob.vector <- c(0.50, 0.50)
probs.to.w(prob.vector, null.prob.vector)

power.chisq.gof(w = 0.44, df = 1, power = 0.80, alpha = 0.05)


# ---------------------------------------------------------#
# 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?                      #
# ---------------------------------------------------------#

## from https://web.archive.org/web/20250601054306/https://time.com/growing-up-with-adhd/
## 5.6 percent of girls and 13.2 percent of boys are diagnosed with ADHD
prob.matrix <- rbind(c(0.056, 0.132),
                     c(0.944, 0.868))
colnames(prob.matrix) <- c("Girl", "Boy")
rownames(prob.matrix) <- c("ADHD", "No ADHD")
prob.matrix

probs.to.w(prob.matrix)

power.chisq.gof(w = 0.1302134, df = 1, power = 0.80, alpha = 0.05)


# --------------------------------------------------------#
# 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?                 #
# --------------------------------------------------------#

## from https://doi.org/10.1016/j.jad.2019.11.121
prob.matrix <- 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.matrix) <- c("Normal", "Mild", "Moderate",
                           "Severe", "Extremely Severe")
colnames(prob.matrix) <- c("Female", "Male")
prob.matrix

probs.to.w(prob.matrix)

power.chisq.gof(w = 0.03022008, df = 4, power = 0.80, alpha = 0.05)