Using a t-test


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A t-test is a statistical technique to compare the means of two groups sharing the same features or relation. It is nothing but a tool used to test hypotheses formulated on an assumption about a population.

Using a t-test t-test

In this article, we will explicitly discuss when to use t-test and what are scenarios that will want you to choose t-test as the best fitting option to deal with your data.

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When to use t-test?

A t-test is used when the mean and standard deviation of the population parameters are not known. 

  • Independent sample t-test is used when you have to compare means of two groups.
  • Paired sample t-test is used when you have to compare the means of the same group but at different time intervals.
  • And one sample t-test is used when you have to compare a mean of a group against a sample mean. 

t-test is a statistical tool that tests the hypotheses that are made based on some assumptions on certain populations. To do so, it uses t-statistics, t-distribution table and to determine the statistical significance of the difference, degrees of freedom is used. 

The score for t-statistics or test statistics is calculated as:

t = (x1 — x2) / (σ / √n1 + σ / √n2), 

Where, x1 = mean of sample 1, x2 = mean of sample 2, n1 = size of sample 1, n2 = size of sample 2

t-test is hence used in most of the data analysis fields which affect directly on businesses, science, and much more. It uses some calculations to test out a theory made against certain population, whose sample can be drawn to experiment for the conclusion. The result of the t-test will end up either accepting or rejecting the formulated hypothesis.

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The main purpose of t-test statistics is to see whether there is a significant difference between the means and standard deviations of two unrelated, independent sample groups. Depending on the results, the test then determines whether the difference between the means of two independent sample groups is occurred due to a random chance. 

The first thing you need to check before thinking of applying t-test to the sample data is: the sample size of both the population sample should be less than 30

That is n<30 where n denotes the sample size of a population sample. 

Apart from the above mentioned requirements, if you are going to use t-test for your data, the following assumptions should be satisfied:

  • The scale of measurement applied to the data collected should follow a continuous or ordinal scale. Example: Height of students.
  • The sample made from the population is the best representative of the entire population. 
  • The data should be normally distributed.
  • When we plot the data on the graph, the line connecting the points should look like a bell. 
  • The variance is homogeneous/equal along with the standard deviations. 

When your data satisfies all the above assumptions and requirements, you can say t-test is a best hypotheses testing tool for your study. 

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