v_chi_sq: V for Chi-Square

In MOTE: Effect Size and Confidence Interval Calculator

V for Chi-Square

Description

This function displays V and its non-central confidence interval for the specified \chi^2 statistic.

Usage

v_chi_sq(x2, n, r, c, a = 0.05)

v.chi.sq(x2, n, r, c, a = 0.05)

Arguments

x2	chi-square statistic
n	sample size
r	number of rows in the contingency table
c	number of columns in the contingency table
a	significance level

Details

V is calculated by finding the square root of \chi^2 divided by the product of the sample size and the smaller of the two degrees of freedom.

V = \sqrt{\frac{\chi^2}{n \times df_{\mathrm{small}}}}

Learn more on our example page.

**Note on function and output names:** This effect size is now implemented with the snake_case function name 'v_chi_sq()' to follow modern R style guidelines. The original dotted version 'v.chi.sq()' is still available as a wrapper for backward compatibility, and both functions return the same list. The returned object includes both the original element names (e.g., 'v', 'vlow', 'vhigh', 'n', 'df', 'x2', 'p', 'estimate', 'statistic') and newer snake_case aliases (e.g., 'v_value', 'v_lower_limit', 'v_upper_limit', 'sample_size', 'df_total', 'chi_square', 'p_value'). New code should prefer 'v_chi_sq()' and the snake_case output names, but existing code using the older names will continue to work.

Value

v

V statistic

vlow

lower level confidence interval of V

vhigh

upper level confidence interval of V

n

sample size

df

degrees of freedom

x2

\chi^2 statistic

p

p-value

estimate

the V statistic and confidence interval in APA style for markdown printing

statistic

the \chi^2 statistic in APA style for markdown printing

Examples

# The following example is derived from the "chisq_data"
# dataset, included in the MOTE library.

# Individuals were polled about their number of friends (low, medium, high)
# and their number of kids (1, 2, 3+) to determine if there was a
# relationship between friend groups and number of children, as we
# might expect that those with more children may have less time for
# friendship maintaining activities.

chisq.test(chisq_data$kids, chisq_data$friends)

v_chi_sq(x2 = 2.0496, n = 60, r = 3, c = 3, a = .05)

# Backwards-compatible dotted name (deprecated)
v.chi.sq(x2 = 2.0496, n = 60, r = 3, c = 3, a = .05)

MOTE documentation built on Dec. 15, 2025, 9:06 a.m.