What is a situation where you would test for homogeneity?

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seskew192atp · Accepted Answer

Chi-square test of homogeneity:
Independent simple random samples are taken from two or more populations, where every individual is being classified based on one categorical variable. Here, the hypothesis testing is done to check whether any homogeneity exists. In other words, the homogeneity tests claims that different populations are from the same proportions of specified characteristics. This test is called as the chi-square test of homogeneity.
The test hypotheses are given below:

H_{0}

: The proportion of each population sharing specified characteristics is same for all populations.

H_{1}

: The proportion of each population sharing specified characteristics is not same for all populations.
Test statistic for the chi-square test of independence:

χ^{2} = \sum (\frac{{(O - E)}^{2}}{E})

with degrees of freedom d.f.=(R-1)(C-1)
Where, the sum is over all cells in the contingency table.
R= number of rows in contingency table.
C=number of columns in contingency table.
E= Expected frequency.
For each cell, the value of expected frequency is obtained as given below:

E = \frac{(Row total) \times (Column total)}{Sample size}

The basic assumptions underlie in the application of the chi-square is given below:
In order to apply chi-square distribution, the sample size should be large so that, for each cell,

E \geq 5

.

What is a situation where you would test for homogeneity?

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