The T-Test (also called "Student's T-Test") is probably the most widely used statistical test of all times, and certainly the most widely known. It is simple, straightforward, easy to use, and adaptable to a broad range of situations. No statistical toolbox should ever be without it. Some statistical tools (e.g. average, standard deviation, etc) are descriptive statistical tools, designed to describe the data you have, but they do not allow you to generalize beyond that. The T-Test is an inferential statistical tool: it allows you to make inferences or predictions about the population you have surveyed, beyond the data you have obtained.

Sometimes in a fieldwork it is only possible to collect small samples (10-30 values) due to limitations of available individuals or of time: the T-Test allows you to reliably compare the two entire populations from which the samples are taken. It can tell you if the two samples (given as numerical non-ranked data) are truly significant (in which case the two entire populations are truly different), or if the differences between the two samples simply occurred by chance (in which case you cannot draw a conclusion as to the similarity/dissimilarity of the two entire populations).

The T-Test is a value comparing the difference betwen the means and the "standard error of the differences between means" and uses the variance (=squared standard deviation) (see the video below). The T-Test value is given by the formula above where x is the mean of each sample (use only the

Limitations of the T-Test:

Sometimes in a fieldwork it is only possible to collect small samples (10-30 values) due to limitations of available individuals or of time: the T-Test allows you to reliably compare the two entire populations from which the samples are taken. It can tell you if the two samples (given as numerical non-ranked data) are truly significant (in which case the two entire populations are truly different), or if the differences between the two samples simply occurred by chance (in which case you cannot draw a conclusion as to the similarity/dissimilarity of the two entire populations).

The T-Test is a value comparing the difference betwen the means and the "standard error of the differences between means" and uses the variance (=squared standard deviation) (see the video below). The T-Test value is given by the formula above where x is the mean of each sample (use only the

*positive*value of the difference), s is standard deviation of each sample and n is number of values in each sample.Limitations of the T-Test:

- If one sample has more than 30 values, use the Comparison of Two Means
- If the sample is NOT normally distributed, or for ordinal (=ranked) data, use the Mann Whitney U-Test.

Three methods are possible to perform the T-Test:

- VERY SIMPLE: you can use an online calculator to perform a T-Test which will tell you directly whether the two entire populations are truly different, based on the means of your samples
- SIMPLE: you can use this calculator to paste in your data: the calculator will tell you directly the probability that the null hypothesis is true with 95% certainty. Therefore, probability that is must be rejected is 1 - p (x 100 for a %)
- LONG: you can follow a step-by-step method on how to perform the T-Test. First calculate the T-value using the formula shown on top of this page (or the corresponding Excel formula). You then need to calculate the degrees of freedom of the table, decide on a level of certainty and look up the corresponding critical values of the T-Test to interpret the result. If the T-value of your table is higher than the critical T-value you have found, you can therefore reject the Null Hypothesis and assert, with the certainty level selected, that there is indeed a significant difference between the two sets of data