Power Analysis for Fisher's Exact Test (Independent Proportions)

Calculates power or sample size for Fisher's exact test on independent binary outcomes. Approximate and exact methods are available.

Validated via PASS and G*Power.

Usage

power.exact.fisher(prob1, prob2, n2 = NULL, n.ratio = 1,
                   alpha = 0.05, power = NULL,
                   alternative = c("two.sided", "one.sided"),
                   method = c("exact", "approximate"),
                   ceiling = TRUE, verbose = TRUE, pretty = FALSE)

Arguments

prob1: probability of success in the first group.
prob2: probability of success in the second group.
n2: integer; sample size for the second group.
n.ratio: n1 / n2 ratio.
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 \(\alpha\).
alternative: character; direction or type of the hypothesis test: "two.sided" or "one.sided".
method: character; method used for power calculation. "exact" specifies Fisher's exact test, while "approximate" refers to the Z-Test based on the normal approximation.
ceiling: logical; if TRUE rounds up sample size in each group.
verbose: logical; if FALSE no output is printed on the console.
pretty: logical; whether the output should show Unicode characters (if encoding allows for it). FALSE by default.

Value

parms: list of parameters used in calculation.
test: type of the test, which is "exact" or "z".
odds.ratio: odds ratio.
mean: mean of the alternative distribution.
sd: standard deviation of the alternative distribution.
null.mean: mean of the null distribution.
null.sd: standard deviation of the null distribution.
z.alpha: critical value(s).
power: statistical power \((1-\beta)\).
n: sample sizes for the first and second groups, specified as c(n1, n2).
n.total: total sample size, which is sum of cell frequencies in 2 x 2 table (f11 + f10 + f01 + f00), or number of rows in a data frame with group variable stacked.

References

Bennett, B. M., & Hsu, P. (1960). On the power function of the exact test for the 2 x 2 contingency table. Biometrika, 47(3/4), 393-398. doi:10.2307/2333309

Fisher, R. A. (1935). The logic of inductive inference. Journal of the Royal Statistical Society, 98(1), 39-82. doi:10.2307/2342435

Examples

# example data for a randomized controlled trial
# subject  group    success
# <int>    <dbl>      <dbl>
#   1        1          1
#   2        0          1
#   3        1          0
#   4        0          1
#   5        1          1
#   ...     ...        ...
#   100      0          0

# prob1 = mean(success | group = 1)
# prob2 = mean(success | group = 0)

# post-hoc exact power
power.exact.fisher(prob1 = 0.60, prob2 = 0.40, n2 = 50)
#> +--------------------------------------------------+
#> |                POWER CALCULATION                 |
#> +--------------------------------------------------+
#> 
#> Independent Proportions
#> 
#>   Method          : Fisher's Exact
#> 
#> ---------------------------------------------------
#> Hypotheses
#> ---------------------------------------------------
#>   H0 (Null Claim) : prob1 - prob2 = 0 
#>   H1 (Alt. Claim) : prob1 - prob2 != 0 
#> 
#> ---------------------------------------------------
#> Results
#> ---------------------------------------------------
#>   Sample Size          = 50 and 50
#>   Type 1 Error (alpha) = 0.050
#>   Type 2 Error (beta)  = 0.538
#>   Statistical Power    = 0.462  <<
#> 

# we may have 2 x 2 joint probs such as
# -------------------------------------
#             | group (1) | group (0) |
# -------------------------------------
# success (1) |  0.24    |   0.36     |
# -------------------------------------
# success (0) |  0.16    |   0.24     |
# -------------------------------------

# convert joint probs to marginal probs
marginal.probs.2x2(prob11 = 0.24, prob10 = 0.36,
                   prob01 = 0.16, prob00 = 0.24)
#> prob1 prob2   rho 
#>   0.6   0.4   0.0