CODEWITHSUNDEEP
rpower-analysis
brushyourteeth
brushyourteeth

Reputation: 11

Compute minimal sample size in ANCOVA power analysis?

I'm trying to find out what the minimal sample size is for an ANCOVA I need to run for my experiment, the experiment includes 5 different abiotic measurements from 6 different fields (as in, an actual field outside, not a 'scientific field'). In order to assess the minimum amount of observations I would need per field I want to perform a power calculation, for this purpose I'm currently thinking of using Shieh et al., (2020)'s method using the package 'Superpower' and the function 'power_oneway_ancova'. It looks like this:

power_oneway_ancova(
  mu = c(400,450,500),
  n_cov = 3,
  sd = 100,
  r2 = .25,
  alpha_level = .05,
  #n = c(17,17,17),
  beta_level = .2,
  round_up = TRUE,
  type = "exact")

Because I want to include scientifically relevant/ realistic means and standard deviations, I would have to manually input different sample sizes for every different measurement type in order to find what sample size results in a minimum power of 0.8, which seems really inefficient and time consuming. Does anyone know of a package that allows me to input a preferred power and infer minimum sample size from that? Or maybe does someone with better programming skills than I know of a way to somehow automate this process and have R run until it finds a sample size that results in a minimum power of 0.8?

Upvotes: 1

Views: 62

Answers (2)

qdread
qdread

Reputation: 3973

As Ben's answer shows, your code as written already calculates the minimum sample size n per group required to get >80% power, because beta_level is 1 - power.

You can also show this graphically by computing the power for any desired range of sample sizes:

sample_sizes <- 10:20

powers <- sapply(sample_sizes, function(n) power_oneway_ancova(
  mu = c(400,450,500),
  n_cov = 3,
  sd = 100,
  r2 = .25,
  alpha_level = .05,
  n = rep(n, 3),
  round_up = TRUE,
  type = "exact")$power
)

plot(sample_sizes, powers, xlab = 'Sample size per group', ylab = 'Power (1 - beta)')
abline(h = 80, col = 'blue', lwd = 2)

The output shows that n = 17 per group is the smallest value above the "magic number" of 80%.

Power curve for ANCOVA

Upvotes: 2

Ben Bolker
Ben Bolker

Reputation: 226742

I think the function can already give you the answer you want. The beta_level = 0.2 argument specifies that for given alpha_level, r2, and specified means and SDs, you want a false-negative rate of at most 0.2 == a power of at least 0.8.

pp <- power_oneway_ancova(
  mu = c(400,450,500),
  n_cov = 3,
  sd = 100,
  r2 = .25,
  alpha_level = .05,
  beta_level = .2,
  round_up = TRUE,
  type = "exact")
print(pp)

In this output, the boldfaced values tell you the total sample size and sample sizes per condition required to get a power of at least 0.8 (= 1-beta_level).

     Power Calculation for 1-way ANCOVA 

            dfs = 2, 45
              N = 51
              n = 17, 17, 17
          n_cov = 3
             mu = 400, 450, 500
             sd = 100
             r2 = 0.25
    alpha_level = 0.05
     beta_level = 0.1878274
          power = 81.21726
           type = exact

Upvotes: 3

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