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I want to know whether the proportions for two samples are the same.

0-hypothesis: The proportions are the same for both samples Alternative hypothesis: The proportions are different.

I know the sample sizes (200 and 1800) and the proportions (45 % and 40 %).

The problem is that I arrive at different conclusions when I do different kinds of tests.

When calculating confidence intervals (95 %), I arrive at the conclusion that the CI's are overlapping, meaning that I can't reject the 0 hypothesis.

SampleSize1 = 200 SampleSize2 = 1800 SampleOccurrences1 = 90 SampleOccurrences2 = 680 SampleProportion1 = 45 % SampleProportion2 = 38 %

I calculate the confidence interval for each of the samples using Excel:

z = 1.96 StdError = SQRT(SampleProportionX*(1-SampleProportionX)/SampleSizeX) MarginOfError = z * StdError Confidence interval = SampleProportionX +/- MarginOfError

As the confidence intervals are overlapping, I can't reject the 0-hypothesis.

When calculating the Z-value, I arrive at the conclusion that the 0-hypothesis should be rejected.

I calculate the Z-value as follows:

p1 = SampleProportion1 p2 = SampleProportion2 p = (SampleOccurrences1 + SampleOccurrences2) / (SampleSize1 + SampleSize2)

Z = (SampleProportion1 - SampleProportion2) / SQRT(p*(1-p)*(1 / SampleSize1 + 1 / SampleSize2))

As Z > 1.96, I reject the 0-hypothesis.

Why do I get different results, and which test is the correct to use?

Chris
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  • Welcome to Cross Validated! You'll need to explain in a little more detail how you're performing the tests & calculating the confidence intervals. – Scortchi - Reinstate Monica Jul 08 '20 at 07:43
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    Testing for overlapping confidence intervals can be done but does not yield the level of confidence you might think. See https://stats.stackexchange.com/a/18259/919. – whuber Jul 08 '20 at 14:22

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