Inferential Statistics

T-tests

A t-test is a type of inferential statistic used to determine if there is a significant difference between the means of two small groups, which may be related in certain features. It is mostly used when the data-sets follow a normal distribution and may have unknown variances. A t-test is used as a hypothesis testing tool, which allows testing of an assumption applicable to a population. For example, we might want to test whether men and women smoke cigarettes with the same average frequency.

There are many different types of statistical tests which can be applied to sampling. In this package, we concentrate on two of them : the t-test for independent samples and the t-test for dependent samples.

The Independent Samples t-test, compares two unique samples of data in order to determine whether there is statistical evidence that the associated population means are significantly different. The data must meet the following requirements:

1. Two independent values that are categorical e.g. gender (male/female) or transport method (car/train).
2. Multiple values that are numeric e.g. age, distance.
3. Each unique sample must consist of a pair, e.g. male, 50 years old.
4. There should be no relationship between the subjects in each sample-set.
5. The number of samples in each group should be more or less the same but it is not a requirement that they be identical.

The purpose of this test, is to determine if there is a statistical variation between the two samples. For example, if 100 people in a sample drive to work and 100 people take a train, we could measure whether statistically, the time taken to work is the same. This would measure whether or not the mode of travel determines the length of time it takes to arrive at work. The Independent Samples t-test, compares two samples of data from the same source in order to determine whether there is statistical evidence that an associated intervention is significantly different. The data must meet the following requirements:

1. One population group with two unique tests before and after an intervention, eg heartrate before and after strenuous exercise.
2. Multiple value-pairs that are numeric e.g. weight before and after a diet regime.
3. There should be a relationship between the measurements in each sample-set, i.e. before and after an intervention.

Purpose of t-test

For a small sample (e.g. up to 30 data-sets), we would want to measure whether or not there is a relationship between the two groups to a specific statistical measurement. Example : consider that a drug manufacturer wants to test a newly invented medication. The standard procedure would be to treat the drug on one group of patients and giving a placebo to another group, called the control group. The placebo given to the control group is a substance of no intended therapeutic value and serves as a benchmark to measure how the other group, which is given the actual drug, responds. The t-test will then measure whether or not the two groups have statistically different responses, i.e. the medication has or has not some medical impact.