# The T-Test

The t-test is an analysis to see if two different sample groups are statistically different from one another. From the immediate data we gather, it may be possible to infer that there are differences between the groups, but this might not represent a true difference in the real population and the results were merely arrived on by chance.

The t-test helps us to determine the probability that we got these results by chance by analysing the sizes of the sample and the degrees of freedom. Generally, if the t-test determines that there is a less than 5% chance of getting the observed differences by chance, then we can say we found a statistically significant difference between the two groups.

During the class, we applied the t-test to a sample of people who were measuring their anxiety levels with and without a mindfulness app, with the null hypothesis that the groups would not show a statistically significant difference in anxiety levels. Through the application of Robson’s ‘T-test Recipe’, I found that the difference between the two groups was 2.47%, which is less than the 5% difference that denotes it to be statistically significant.

Therefore, from this t-test, we could reject the null hypothesis that suggested that the mindfulness app would have no effect on anxiety levels and instead determine that they did have an effect. However, if a second sample was taken there would be a completely different statistical result proving the relationship between anxiety levels and mindfulness app use. Would we still be as confident that the independent variable effected the dependent variable?

In deriving these difference in means, assumptions must be made about the populations from which they are drawn – that they all have the same variance within the data. It is possible to test for these assumptions on a particular set of scores, for example, through the use of a chi-square. This can assess how the sample t-distribution is when compares to a normal distribution. The results are significant if they are below 5%. When a chi-square was used on the t-test data, I got 3.8%, meaning that both the t-test and the chi-square confirmed that there was a causal link between the use of the app and reported levels of anxiety in the sample.

I found this a difficult concept to relate and reflect upon – how can human behaviour be boiled down to such analysable data predetermined through statistics? It made for a large amount of reading around the subject in an attempt to understand how the t-test could be used to analyse experimental data and provide useful insights into the sampled responses.

However, the benefits of such a test are obvious, as it would be impossible to test the whole a whole population for a certain behaviour, so smaller samples need to be tested with confidence. The t-test appears robust when confronted with non-homogenous variance within a sample or with considerable variation in its results, making it ideal in a randomised sample of a population.

Author: Megan Venn-Wycherley