What is t-test?

History and Definition

The objective of any statistical test is to determine the likelihood of a value in a sample, given that the null hypothesis is true. A t-test is typically used in case of small samples and when the test statistic of the population follows a normal distribution.

A t-test is when the test statistic follows a t-distribution, and you want to statistically test whether the null hypothesis is true. It was originally developed by W S Gossett in 1908 to monitor the stout quality while working in a brewery. A t-test (also known as Student’s t-test) is often used to test if two samples are statistically different from each other. A t-test does this by comparing the means of both samples.

There are two types of t-tests – one sample and two samples. The one sample t-test is used to test the null hypothesis that the mean of the population is equal to a certain value, while the two sample t-test is used to compare the mean values of both samples. The two sample t-tests may be conducted on independent samples, paired samples or overlapping samples.


Say, a sofa manufacturer wants to find out how much weight his sofa chair can handle before it breaks. He chooses a sample of 3 sofa chairs that he is ready to subject to extreme weight tests so he might claim that his sofas can handle up to 800 pounds of weight. Since the test is ultimately going to break each sofa that he tests, he is unwilling to suffer any more damaged sofas; on the other hand even a sample of 3 sofas is relatively small to be able to claim that all his sofas can handle 800 pounds of weight. In such a scenario, he would conduct a one sample t-test with the null hypothesis that average weight that a sofa chair can handle is 800 pounds. Depending on his t-test result, he shall be able to determine whether all sofas in his factory actually have a capacity of 800 pounds or not.

In another scenario, say we want to test the hypothesis that plastic chairs of company X have a different weight handling capacity than wooden chairs of company Y. We will measure the weight handling capacity of the two different and random samples of chairs – of companies X and Y. We will then conduct an independent two sample t-test to find out whether our null hypothesis is valid (that there is really no difference in their weight bearing capacity) or not.

Let’s take an example where you are insurance service provider and want to find out customer preference to various insurance products for introducing newer insurance plans. You can study the available insurance sales data and conduct a t-test to check the normality of the data; and provide a set of attributes that drive the customers to purchase insurance products; and rank them in order of preference. This would help you better understand the customer’s preference of insurance products and develop new insurance products to cater to different target segments.

Benefits and Practical Usage of t-tests

A t-test is widely used where we have only small samples available. Further, where population variance in unknown and has to be estimated from the sample itself, the t-test may be most appropriate.

A t-test is of special importance in industries where quality testing of products is done by subjecting them to stress tests or by destroying the products – like checking of cars for ability to withstand accidents. It would be extremely costly and unwise to subject a large sample of cars to such tests; hence t-tests prove extremely useful here. Another important use of t-tests is in the medical industry where the paired t-tests are used widely to study the impact of a particular treatment on a sample of patients before and after the medication.

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