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PSY 2007 W6 Assignment 2 T-test

PSY 2007 W6 Assignment 2 T-test


A t-test is a statistical test that is used to compare the means of two groups. It is often used in hypothesis testing to determine whether a process or treatment actually has an effect on the population of interest, or whether two groups are different from one another.

You want to know whether the mean petal length of iris flowers differs according to their species. You find two different species of irises growing in a garden and measure 25 petals of each species. You can test the difference between these two groups using a t-test.

  • The null hypothesis (H0) is that the true difference between these group means is zero.
  • The alternate hypothesis (Ha) is that the true difference is different from zero.

A t-test can only be used when comparing the means of two groups (a.k.a. pairwise comparison). If you want to compare more than two groups, or if you want to do multiple pairwise comparisons, use an ANOVA test or a post-hoc test.

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The t-test is a parametric test of difference, meaning that it makes the same assumptions about your data as other parametric tests. The t-test assumes your data:

  1. are independent
  2. are (approximately) normally distributed.
  3. have a similar amount of variance within each group being compared (a.k.a. homogeneity of variance)

If your data do not fit these assumptions, you can try a nonparametric alternative to the t-test, such as the Wilcoxon Signed-Rank test for data with unequal variances.

What type of t-test should I use?

When choosing a t-test, you will need to consider two things: whether the groups being compared come from a single population or two different populations, and whether you want to test the difference in a specific direction.

One-sample, two-sample, or paired t-test?

  • If the groups come from a single population (e.g. measuring before and after an experimental treatment), perform a paired t-test.
  • If the groups come from two different populations (e.g. two different species, or people from two separate cities), perform a two-sample t-test (a.k.a. independent t-test).
  • If there is one group being compared against a standard value (e.g. comparing the acidity of a liquid to a neutral pH of 7), perform a one-sample t-test.

One-tailed or two-tailed t-test?

  • If you only care whether the two populations are different from one another, perform a two-tailed t-test.
  • If you want to know whether one population mean is greater than or less than the other, perform a one-tailed t-test.

In your test of whether petal length differs by species:

  • Your observations come from two separate populations (separate species), so you perform a two-sample t-test.
  • You don’t care about the direction of the difference, only whether there is a difference, so you choose to use a two-tailed t-test.

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