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    Is 3% difference significant in an experiment?




    I am trying to see if certain change in a survey will impact the response rate.

    I sent the survey to 3277 people in the experimental group (with the change implemented) and to 3253 in the control group (without the change implemented).
    In the first group 22% of people filled the survey out, in the second group it was 25%.

    How significant is the difference? What method would you recommend for checking it?

    A little note: I have not much idea about statistics, had classes 15 years ago so if you can explain it in a super simple way, it would be great :-)
    Thank you!

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    Re: Is 3% difference significant in an experiment?

    In this problem you can use the Z-test for comparing two proportions. The Z-statistic equals

    Z-stat = (p2 - p1) / Standard Error = (p2 - p1) / sqrt(p * (1 - p) * (1 / N1 + 1 / N2)),

    where

    N1 = 3277,
    p1 = 0.22,
    N2 = 3253,
    p2 = 0.25,
    p = (p1 * N1 + p2 * N2) / (N1 + N2) = 0.2349449.

    So we have

    Z-stat = 2.859009,

    which corresponds to the p-value = 0.004249667 << 0.05 = significance level. So the difference is sample response rates is statistically significant and we accept the hypothesis stating that the true response rates are different.

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    Re: Is 3% difference significant in an experiment?


    A somewhat more important problem is that about 75% have not responded. Can you infer anything from such an investigation?

    There was a control and a treatment group. Did you randomize the participants to either treatment or control? If randomization, can you assume that the non-response event is independent of the measured variable?

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