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Comparing two proportions in the same survey
When can we be confident in a difference of two proportions?
Statistics courses often deal with the problem of two independent proportions. Researchers conduct two surveys or experiments, which are independent of one another. The calculation is for proportions in the two independent samples. The question is: are the two proportions different?
This article returns to the problem of comparing two proportions in the same survey.
The key differences
A YouGov survey question asks who “would make the best Prime Minister”. There are four options:
- Boris Johnson;
- Keir Starmer;
- Not sure;
- Refused.
Could Starmer’s lead be due to the random error that surveys have?
The traditional problem relates to proportions in independent samples. Researchers might wish to know what proportion of people select an option. Those two surveys could be at different times, or for different populations.
Our problem is distinct: in the same survey question, do proportions in options differ?
