- 1). Define the mean of a population sample. The mean of a population sample is the sum of the scores in that sample divided by the number of members in the sample. This may be expressed mathematically as μ = Σ xi/n, where μ is the population mean, xi is the ith score in the sample and n is the number of members in the sample.
- 2). Define the standard deviation of a sample. A t-test measures scores in units of standard deviation, which may be represented mathematically as s = ( Σ ( xi - x )2 / ( n - 1 ) ) ^(1/2), where s is the standard deviation of the sample, xi is the ith element of the sample, x is the sample mean and n is the number of elements of the sample population.
- 3). Derive scores for the t-test. This is given by t = ( x - X ) / ( s / n^(1/2)), where t is the t-score, x is the mean of the sample, X is the mean of the population, s is the standard deviation of the sample and n is the number of members in the sample.
- 4). Learn the properties for the distribution of a t-test. A t-distribution has one less degree of freedom than the number of members in the sample. A t-distribution's mean is 0, and its variance is f / ( f - 2 ), where f is the number of degrees of freedom of the distribution. Note that this definition of variance means that the sample for a t-test must have at least four members.
- 5). Use a t-test when the standard deviation of the population is unknown. The sample size may be small so long as it has an approximately normal distribution.