binary is Binomial
Hence you use the Binomial distribution if the sample size is small
And you can use the normal approximation (Central Limit Theorem) if n is large.
The t distribution is incorrect.
I have before and after responses (0 or 1) for each participant and would like to know how to analyze it.
Is it performed exactly like a normal paired sample t-test or do I need to do something different because the responses are binary?
Around 700, it will vary.
I know binary is binomial but how do I actually test it?
Example data:
H0: The treatment has no effect.Code:|Participant | Before | After | | 1 | 0 | 1 | | 2 | 1 | 1 | | 3 | 0 | 0 | | 4 | 0 | 1 | | 5 | 0 | 0 | | 6 | 1 | 1 | | 7 | 1 | 1 | | . | . | . | | . | . | . | | . | . | . |
H1: The treatment has an effect.
USE the normal approximation to the binomial
It can be found in every undergrad stat book and I'm sure it's online too.
Gauss proved it 200 years ago.
It's the most basic CLT.
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But this seems to be a paired difference test (same person)?
You have two populations
Hence you should subtract one set from the other
and perform a one sample test.
Are you trying to prove that there is an improvement?
Let
Then use
Under the null, S has mean 0.
Use the CLT, the rejection region is via the normal.
calculate the variance of S and obtain a test stat.
My apologies: I understand that I'm probably quite frustrating but...
The binomial relies upon me knowing the probability of getting a 0 or 1.
Put it this way, if the data was numerical (not binary) I would point the enquirer in this direction: Paired Sample T-Test
This explains how to test the hypothesis and which test statistic to use.
All you've said so far is "use the normal approximation to the binomial".