Can You Always Use a t-Test? The t-test described here is actually Students's t-test, to give it its full name. This test is a parametric test, which means that it makes some assumptions about the data. If these assumptions are not true, the test can give misleading results. We will look at those assumptions here. These assumptions concern the shape of the distribution of the data, which can be seen from a frequency histogram:
The samples being compared should have a reasonably symmetrical distribution;
The samples being compared should have a mean which is close to the centre of the distribution;
The distribution should have only one mode (highest point in the frequency histogram).
You will probably notice that these conditions are very similar to those of a normal distribution. There are pages on normal distributions and frequency histograms if you want to recap those topics.A t-test works best on normally distributed data. If the distribution is not normal, but still satisfies the conditions above, (it is flat, for example), then a t-test will still work as long as you have enough values in your sample (25 to 30 is usually okay). If your data is heavily skewed, then you may need a very large sample before a t-test will work. In such cases, an alternate non-parametric test should be used.
Exploration
Below are pictures of 6 different frequency histograms taken from samples that are small enough to require normal distribution-like properties. Decide whether or not you could perform a t-test on the data that produced each one.
Flat (or Even)
Nearly Flat
Normal
Bimodal
Skewed Left
Skewed Right
Application
Now we will look at your data here and satisfy ourselves that it is suitable for a t-test.
Here is the histogram for items correctly recalled when recall interval is 100 msecs. This plot has 1 highest bar, which is for the range 14 to < 15. There are 8 bars in your histogram and the highest is at position 5, so there are 3 bars to the right and 4 bars to the left. There is strong symmetry in the distribution of the data.
Look at the shape of your histogram and answer the questions below to decide whether or not the distribution of your data is normal.
Is the histogram symmetrical?
Is the mode (the highest bar) at the centre of the histogram?
Samples and Populations
