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

Source: R/proportions.fisher.R
power.exact.fisher.Rd

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

Validated using the PASS documentation and G*Power.

Usage

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

Arguments

prob1

probability of success in the first group.

prob2

probability of success in the second group.

n.ratio

n1 / n2 ratio.

n2

integer; sample size for the second group.

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; the 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

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.

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 the 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. https://doi.org/10.2307/2333309

Fisher, R. A. (1935). The logic of inductive inference. Journal of the Royal Statistical Society, 98(1), 39-82. https://doi.org/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)        : prob1 - prob2  = 0
#>   H1 (Alternative) : 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