Recently we had to write up a mock research proposal for uni. For my paper, I was trying to measure and compare prosocial behaviours between two groups of teenagers utilising an economic game. Essentially, in each game, the player had two choices, pro-social vs. selfish choice.

Under the ‘participant’ section I had suggest 95 participants based on this calculator:

https://select-statistics.co.uk/calculators/sample-size-calculator-two-proportions/

Here is the screenshot of the result:

Hence, I have written this:

However, the marker suggested this:

This all said I was wondering about the following questions (because my knowledge of statistics is superficial, I wasn’t confident to challenge the remark):

- Was the number of participants contingent on the effect size as the samples were two binomial distributions and the power could have been calculated by normalising the distributions?
- I would be deeply thankful if someone could show me the step-by-step power calculation by Brook (2019), as I would like to prove (if possible) how to calculate power with the proportion of prosocial behaviours and 95 participants.
- (https://select-statistics.co.uk/calculators/sample-size-calculator-two-proportions/).
- I came across another calculator that shows a formula to calculate power. The closest I got was looking at this: (http://powerandsamplesize.com/Calculators/Compare-2-Proportions/2-Sample-Equality). I know how to calculate the z, but how to I get the kappa and what z1-α/2 values?

Thank you immensely!