ARE THERE ASSUMPTIONS THAT MUST BE OBSERVED WHEN USING THE t-TEST?
While the t-test has been described as a a robust statistical tool, it is based on a model that makes several assumptions about the data that must be met prior to analysis. Unfortunately, students conducting research tend not to report whether their data meet the assumptions of the t-test. These assumptions need ro be evaluated, because the accuracy of your interpretation of the data depends on wether assumptions are violated. The following are three main assumptions that are generic to all t-tests.
1. Instrumentation (Scale of Measurement)
The data that you collect for the dependent variable should be based on an instrument or scale that is continuous or ordinal. For example, scores that you obtain from a 5-point Likert scale; 1,2,3,4,5 or marks obtained in a mathematics test, the score obtained on an IQ test or the score obtained on an aptitude test.
2. Random Sampling
The sample of subjects should be randomly sampled from the population of interest.
The data come from a distribution that has one of those nice bell-shaped curves known as a normal distribution. Refer to Chapter 3: The Normal Distribution which provides both graphical and statistical methods for assessing normality of a sample or samples.
4. Sample Size
Fortunately, it has been shown that if the sample size is reasonably large, quite severe epartures from normality do not seem to affect the conclusions reached. Then again what is a reasonable sample size? It has been argued that as long as you have enough people in each group (typically greater or equal to 30 cases) and the groups are close to equal in size, you can be confident that the t-test will be a good, strong tool for getting the correct conclusions. Statisticians say that the t-test is a "robust" test. Departure from normality is most serious when sample sizes are small. As sample sizes increase, the sampling distribution of the mean approaches a normal distribution regardless of the shape of the original population.