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1. There are 3 chi-square tests - The goodness of fit test, the test of independence, and the test for homogeneity. What's the difference among the three? Why would you use one over another?
2. There are one-sampled and two-sampled t-tests and BOTH can be either one-tailed or two-tailed. When is a t-test one-tailed? When is it two-tailed? Can you give me examples for both?
Explanation & Answer
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1
QUESTION 1:
There are 3 chi-square tests - The goodness of fit test, the test of independence, and the test for
homogeneity. What's the difference among the three? Why would you use one over another?
Answer
Difference of goodness of fit test, the test of independence, and the test for homogeneity
In goodness of fit test, we compare observed value of one variable with assumed
distribution while in the independence test, we test whether two variables are independent or not.
The independence tests and the homogeneity tests were obtained the same for categorical
variables and the test procedures, but they differ in finding expected frequencies. Among these
three chi-square tests, I would use the homogeneity test. This is because, as we use this test, we
can evaluate if the variances are equal. Also, we know assumptions for independent samples ttest which states that population variances should be approximately equal and if this assumption
of homogeneity of variance is violated, then finding the pooled variance for this test cannot be
meaningful because of comparative difference between the population variances increases.
2
QUESTION 2:
There are one-sampled and two-sampled t-tests and BOTH can be either one-tailed or twotailed. When is a t-test one-tailed? When is it two-tailed? Can you give me examples for both?
Answer
When it comes to one-tailed test, the statistical hypothesis test in which alternative hypothesis
has only one end. Determines if there is a relationship between variables in single direction
For example:
A carpenter wishes to claim that his power of fan last longer than 12 hours. A random sample of
power of fan is 8 and has mean power of 9 hours and a standard deviation of 2 hours. Set up fan
finding hypothesis tests at 5% level...
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