anopaN2Power {ANOPA}

Computing power within the ANOPA.

Description

The function 'anopaN2Power()' performs an analysis of statistical power according to the 'ANOPA' framework. See Laurencelle and Cousineau (2023) for more. 'anopaPower2N()' computes the sample size to reach a given power. Finally, 'anopaProp2fsq()' computes the f^2 effect size from a set of proportions.

Usage

anopaPower2N(power, P, f2, alpha)

anopaN2Power(N, P, f2, alpha)

anopaProp2fsq(props, ns, unitaryAlpha, method="approximation")

Arguments

N

sample size;

P

number of groups;

f2

effect size Cohen's $f^2$;

alpha

(default if omitted .05) the decision threshold.

power

target power to attain;

ns

sample size per group;

props

a set of expected proportions (if all between 0 and 1) or number of success per group.

method

for computing effect size $f^2$ is 'approximation' or 'exact' only.

unitaryAlpha

for within-subject design, the measure of correlation across measurements.

Details

Note that for anopaProp2fsq(), the expected effect size $f^2$ depends weakly on the sample sizes. Indeed, the Anscombe transform can reach more extreme scores when the sample sizes are larger, influencing the expected effect size.

Value

anopaPower2N() returns a sample size to reach a given power level. anopaN2Power() returns statistical power from a given sample size. anopaProp2fsq() returns $f^2$ the effect size from a set of proportions and sample sizes.

References

Laurencelle L, Cousineau D (2023). “Analysis of frequency tables: The ANOFA framework.” The Quantitative Methods for Psychology, 19, 173–193. doi:10.20982/tqmp.19.2.p173.

Examples

# 1- Example of the article:
# with expected frequences .34 to .16, assuming as a first guess groups of 25 observations:
f2 <- anopaProp2fsq( c( 0.32, 0.64, 0.40, 0.16), c(25,25,25,25) );
f2
# f-square is 0.128.

# f-square can be converted to eta-square with
eta2 <- f2 / (1 + f2)


# With a total sample of 97 observations over four groups,
# statistical power is quite satisfactory (85%).
anopaN2Power(97, 4, f2)

# 2- Power planning.
# Suppose we plan a four-classification design with expected proportions of:
pred <- c(.35, .25, .25, .15)
# P is the number of classes (here 4)
P <- length(pred)
# We compute the predicted f2 as per Eq. 5
f2 <- 2 * sum(pred * log(P * pred) )
# the result, 0.0822, is a moderate effect size.

# Finally, aiming for a power of 80%, we run
anopaPower2N(0.80, P, f2)
# to find that a little more than 132 participants are enough.