# Binomial distribution and power in a research proposal

#### Pinkbat

##### New Member
Hello!

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):

Thank you immensely!

#### katxt

##### Well-Known Member
What you are effectively saying is (I think) "A difference of 20% is important to me and if the difference is in fact that big, I want to be reasonably sure of catching it. How many do I need in each group to be 80% sure of getting a significant result if in fact the true values are in fact 40% and 60%?"
If that is what you meant, then the effect size is 20%. There may be cunning ways of manipulating this to get a Cohen type effect size, but in my view your common sense interpretation (if indeed that is what you meant) is fine. kat

#### Pinkbat

##### New Member
What you are effectively saying is (I think) "A difference of 20% is important to me and if the difference is in fact that big, I want to be reasonably sure of catching it. How many do I need in each group to be 80% sure of getting a significant result if in fact the true values are in fact 40% and 60%?"
If that is what you meant, then the effect size is 20%. There may be cunning ways of manipulating this to get a Cohen type effect size, but in my view your common sense interpretation (if indeed that is what you meant) is fine. kat
Thank you Kat !!