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I've used a prop.test to compare proportions. I understand the results but I don't know how to reports the statistical results in my thesis:

The results show a significant difference, the proportion in group 2 is greater than in group 1 (χ2 (1)= 38.764, p < 0.001).

(I've turned off the Yates' continuity correction, since the numbers are above 10. I hope this was correct)

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I'm a big fan of reporting

a) The estimate of the difference, and b) A confidence interval for that difference.

So you could say something to the effect of

I used a two sample test of proportions to estimate the difference between groups. I estimate that the difference in betweeen and name is 0.082 (95% confidence interval: 0.056 - 0.100).

I'm not a big fan of reporting p values anymore, though some journals may require them. Whatever you do, just make sure you use appropriate significant figures (I am, and always have been, bad at that).

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  • $\begingroup$ They should also list the distribution and degrees of freedom / test used to find the confidence interval. $\endgroup$ – M Waz Jul 18 at 16:04
  • $\begingroup$ Oh my bad, yea TIL prop.test uses a chi-squared test. Yea, those things should be listed then. $\endgroup$ – Demetri Pananos Jul 18 at 16:19
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You can simply say:

The estimated difference in proportions between group 2 and group 1 is 0.082 (95% confidence interval of 0.056 and 0.100, $\chi^2$ = 38.784 with one degree of freedom from Pearson's Chi-Squared test).

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