I am trying to determine whether the observed differences in the proportions for two samples are significantly different.
- 0-hypothesis: The proportions are the same for both samples
- Alternative hypothesis: The proportions are different.
These are the known factors:
- SampleSize1 = 200
- SampleSize2 = 1800
- SampleOccurrences1 = 90
- SampleOccurrences2 = 680
- SampleProportion1 = 45 %
- SampleProportion2 = 38 %
I conducted two different tests, but arrive at different conclusions.
Calculating confidence intervals (95 %)
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.
Calculating the Z-value
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?