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Statistics LibreTexts

19.2: Power Curves

  • Page ID
    8815
  • We can also create plots that can show us how the power to find an effect varies as a function of effect size and sample size. We willl use the crossing() function from the tidyr package to help with this. This function takes in two vectors, and returns a tibble that contains all possible combinations of those values.

    effect_sizes <- c(0.2, 0.5, 0.8) 
    sample_sizes = seq(10, 500, 10)
    
    #
    input_df <- crossing(effect_sizes,sample_sizes)
    glimpse(input_df)
    ## Observations: 150
    ## Variables: 2
    ## $ effect_sizes <dbl> 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0…
    ## $ sample_sizes <dbl> 10, 20, 30, 40, 50, 60, 70, 80, 90, …

    Using this, we can then perform a power analysis for each combination of effect size and sample size to create our power curves. In this case, let’s say that we wish to perform a two-sample t-test.

    # create a function get the power value and
    # return as a tibble
    get_power <- function(df){
      power_result <- pwr.t.test(n=df$sample_sizes, 
                                 d=df$effect_sizes,
                                 type='two.sample')
      df$power=power_result$power
      return(df)
    }
    
    # run get_power for each combination of effect size 
    # and sample size
    
    power_curves <- input_df %>%
      do(get_power(.)) %>%
      mutate(effect_sizes = as.factor(effect_sizes)) 

    Now we can plot the power curves, using a separate line for each effect size.

    ggplot(power_curves, 
           aes(x=sample_sizes,
               y=power, 
               linetype=effect_sizes)) + 
      geom_line() + 
      geom_hline(yintercept = 0.8, 
                 linetype='dotdash')

    file90.png