I have survey data for N=200. One of the questions is a multiple choice question:
"Which Proposal will you vote for – A, B, Do not know"
Following % of respondents selected :
A = 35%
B = 45%
Do not know = 20%
How can I determine whether the difference between the response rate for choice A (35%) and response rate for choice B (45%) is statistically significant? Should I use a One Sample t-test?
I think I know how to determine the statistical significance of the response rate for one choice (E.g. A=35%. Probability that one of three options will be selected randomly = 33%. Compute Standard Error SE = SQRT (33x(1-33)/N). Compute z = (35%-33%)/SE. Find p-value that corresponds to this z value. Compute two tail-tailed p-value. Compare if two tailed p-value < alpha (e.g. 5%))
However, I am struggling to understand how to determine the statistical significance of the difference between the response rates for 2 choices of the same question
Thanks
Best Answer
I think that to use a t-test, the data would need to come from a normal distribution.
But you can use a $\chi^2$-test to determine if the proportions are sufficiently uniform (which is to say, sufficiently similar to $40\%-40\%$).
Your null hypothesis would be that $P(A) = P(B)$ and your alternative hypothesis $P(A)\neq P(B)$.
Hopefully that helped a little. (I'm keeping it short because of the self-study tag.)