Difference in Proportions Hypothesis Test

From GM-RKB
Jump to navigation Jump to search

A Difference in Proportions Hypothesis Test is a statistical hypothesis test based on comparing whether population proportions have an equal statistic.



References

2014

  • https://onlinecourses.science.psu.edu/stat414/node/268
    • QUOTE: So far, all of our examples involved testing whether a single population proportion p equals some value p0. Now, let's turn our attention for a bit to testing whether one population proportion p1 equals a second population proportion p2. Additionally, most of our examples thus far have involved left tailed tests in which the alternative hypothesis involved [math]\displaystyle{ H_A: p \lt p_0 }[/math] or right tailed tests in which the alternative hypothesis involved [math]\displaystyle{ H_A: p \gt p_0 }[/math]. Here, let's consider an example that tests the equality of two proportions against the alternative that they are not equal. Using statistical notation, we'll test [math]\displaystyle{ H_0: p_1 = p_2 }[/math] versus [math]\displaystyle{ HA: p_1 ≠ p_2 }[/math]

      The test statistic for testing the difference in two population proportions, that is, for testing the null hypothesis [math]\displaystyle{ H_0: p_1−p_2=0 }[/math] is: [math]\displaystyle{ Z=\frac{(\hat{p}_1−\hat{p}_2)−0}{\sqrt{\hat{p}(1−\hat{p})(\frac{1}{n_1}+\frac{1}{n_2})}} }[/math] where: [math]\displaystyle{ \hat{p}=\frac{Y1+Y2}{n1+n2} }[/math] the proportion of "successes" in the two samples combined.

2012

  • http://stattrek.com/hypothesis-test/difference-in-proportions.aspx
    • QUOTE: Every hypothesis test requires the analyst to state a null hypothesis and an alternative hypothesis. The table below shows three sets of hypotheses. Each makes a statement about the difference d between two population proportions, P1 and P2. (In the table, the symbol ≠ means " not equal to ".)

      The first set of hypotheses (Set 1) is an example of a two-tailed test, since an extreme value on either side of the sampling distribution would cause a researcher to reject the null hypothesis. The other two sets of hypotheses (Sets 2 and 3) are one-tailed tests, since an extreme value on only one side of the sampling distribution would cause a researcher to reject the null hypothesis.

Set 	Null hypothesis 	Alternative hypothesis 	Number of tails
1 	P1 - P2 = 0 	P1 - P2 ≠ 0 	2
2 	P1 - P2 > 0 	P1 - P2 < 0 	1
3 	P1 - P2 < 0 	P1 - P2 > 0 	1