Question

At a western hospital, there were a total of 932 births in 20 consecutive weeks. Of these births, 216 occurred on weekends. Based on these data, are births rates different on weekends compared to weekdays? Use a chi-square test.

I have already done the chi-square test with 1 proportion. The question I need help with is listing 2 other statistical tests that can be used to test the hypothesis and what the advantages/disadvantages are.

Answer 1

Solution:

2 other statistical tests that can be used to test the hypothesis are:

1) An alternative to chi-square is Fisher's exact test.

Advantages of using Fisher's exact test instead of Chi square test.

• Unlike chi-square--an approximate statistic, Fisher's is exact, and it allows for directional (confirmatory) as well as non-directional (exploratory) hypothesis-testing.
• All value in 2 x 2 table greater then or equal to 5, then you can use the chi-square test. Any one having in 2 x 2 table less than 5 then you will go to Fisher exact test.

Advantages of using Chi square test instead of Fisher's exact test.

The test is exact in guaranteeing that the type I error is less than or equal to what you specify. It can however be much less, i.e., P-values are too large and power is lost. In this sense ordinary chi-square tests are generally "more accurate" than "exact" tests.

2) One proportion z test

Advantages of using Chi square test instead of one proportion z-test.

A chi-square goodness-of-fit test can be conducted when there is one categorical variable with more than two levels. If there are exactly two categories, then a one proportion z test may be conducted. The levels of that categorical variable must be mutually exclusive.