# Hypothesis testing

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• #37584

Chelle
Participant

When do we use F-test and when should we use T-test?

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#110915

Bob J
Participant

Chelle,
You should use the F test when you have variable data and want to compare the variance (or associated standard deviation) between sample sets….
You should use the t test when you have variable data and want to compare the means of two sample sets…
Practically, the F test is applicable when you are trying to reduce variation and the t test is applicable when you are working to shift (or stabilize) the mean.
Hope this helps…
Best Regards,
Bob J

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#110955

Chelle
Participant

But isn’t it right that we do f-test first before we do t-test?

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#110962

Ron Manubay
Member

Since you have different t-test formula for equal and unequal variance, I would say that YES, it would be good to do f-test first.

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#110982

Bob J
Participant

Chelle,
That is correct if you are working with means (t test) and you want to determine whether or not you want to assume equal variances when running the test.
Otherwise, you can use the F test as a stand alone to assess two populations to see if there is a significant difference in the respective variances.
Hope this helps….
Best Regards,
Bob J

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#110984

Mike Carnell
Participant

Chelle,
You need to start with a normality test. If you have non normal data you need to test medians not means (you can also transform the data).
Good luck.

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#111083

Chelle
Participant

Hello Mike,How do you test medians?Thanks.

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#111086

Darth
Participant

This should keep you busy for a while.
Mood’s median test can be used to test the equality of medians from two or more populations and, like the Kruskal-Wallis Test, provides a nonparametric alternative to the one-way analysis of variance. Mood’s median test is sometimes called a median test or sign scores test. Mood’s median test tests:
Ho: the population medians are all equal  versus  Ha: the medians are not all equal
An assumption of Mood’s median test is that the data from each population are independent random samples and the population distributions have the same shape. Mood’s median test is robust against outliers and errors in data and is particularly appropriate in the preliminary stages of analysis. Mood’s median test is more robust than is the Kruskal-Wallis test against outliers, but is less powerful for data from many distributions, including the normal.
You can perform a Kruskal-Wallis test of the equality of medians for two or more populations.This test is a generalization of the procedure used by the Mann-Whitney test and, like Mood’s Median test, offers a nonparametric alternative to the one-way analysis of variance. The Kruskal-Wallis hypotheses are:
Ho: the population medians are all equal  versus  Ha: the medians are not all equal
An assumption for this test is that the samples from the different populations are independent random samples from continuous distributions, with the distributions having the same shape. The Kruskal-Wallis test is more powerful than Mood’s median test for data from many distributions, including data from the normal distribution, but is less robust against outliers.
You can perform a two-sample rank test (also called the Mann-Whitney test, or the two-sample Wilcoxon rank sum test) of the equality of two population medians, and calculate the corresponding point estimate and confidence interval. The hypotheses are
Ho: h1 = h2   versus  Ha: h1 ¹ h2 ,   where h is the population median.
An assumption for the Mann-Whitney test is that the data are independent random samples from two populations that have the same shape (hence the same variance) and a scale that is continuous or ordinal (possesses natural ordering) if discrete. The two-sample rank test is slightly less powerful (the confidence interval is wider on the average) than the two-sample test with pooled sample variance when the populations are normal, and considerably more powerful (confidence interval is narrower, on the average) for many other populations. If the populations have different shapes or different standard deviations, a 2-Sample t without pooling variances may be more appropriate.

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