## What assumptions are made when conducting a t-test?

The common assumptions made when doing a t-test include those regarding the scale of measurement, random sampling, normality of data distribution, adequacy of sample size and equality of variance in standard deviation.

## The T-test

The t-test was developed by a chemist working for the Guinness brewing company as a simple way to measure the consistent quality of stout. It was further developed and adapted, and now refers to any test of a statistical hypothesis in which the statistic being tested for is expected to correspond to a t-distribution if the null hypothesis is supported.

A t-distribution is basically any continuous probability distribution that arises from an estimation of the mean of a normally distributed population using a small sample size and an unknown standard deviation for the population. The null hypothesis is the default assumption that no relationship exists between two different measured phenomena.

## T-test Assumptions

The first assumption made regarding t-tests concerns the scale of measurement. The assumption for a t-test is that the scale of measurement applied to the data collected follows a continuous or ordinal scale, such as the scores for an IQ test.

The second assumption made is that of a simple random sample, that the data is collected from a representative, randomly selected portion of the total population.

The third assumption is that the data, when plotted, results in a normal distribution, bell-shaped distribution curve.

The fourth assumption is that a reasonably large sample size is used. A larger sample size means that the distribution of results should approach a normal bell-shaped curve.

The final assumption is homogeneity of variance. Homogeneous, or equal, variance exists when the standard deviations of samples are approximately equal.