Independent Samples T-Test Independent Samples T-Test

Independent Samples T-Test

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What is a T-Test?

Before we can delve into understanding what the independent samples t-test is, let’s go over what a T-Test is and why it’s used. 

A t-test is a statistical test that is used to compare the means of different datasets to identify the significant difference between them. In research, t-tests are generally used as a hypothesis testing tool that researchers use to test assumptions made on different populations. 

There are three main types of t-tests, namely:

  1. Independent Samples T-Test: Used to compare the means of two groups
  2. Paired Sample T-Test: Used to compare the means of the same group at different periods of times
  3. One-Sample T-Test: Used to test the mean of a single group against a known mean

Within this article, we will specifically explore the independent samples t-test. 

Independent Samples T-Test Independent Samples T-Test

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What is an Independent Samples T-Test?

Independent Samples T-Test Independent Samples T-Test

The independent samples t-test, also known as the two-samples t-test or the unpaired samples t-test, is the most commonly used form of the t-test. It is used to compare the means of two sets of data. When the independent samples t-test is used to compare two samples from the same population, the means of both are generally identical. However, when used to compare samples taken from different populations, the means of the samples often differ. This test, therefore, helps researchers determine whether or not there is a difference in the mean of two samples, as well as the extent of the difference between them. 

When is the Independent Samples T-Test Used

The independent samples t-test is used to test the statistical differences between the means of two groups. There are other tests that can also be used to do so, such as the z-test. The z-test is a statistical test used to compare the means of two data sets, however, unlike the t-test, it requires information about the population mean or standard deviation. This makes the t-test applicable to more situations as it doesn’t require as much information as the z-test does. 

The t-test, therefore, is used in situations where:

  • There are two independent samples
  • Information on the population mean or standard deviation is not available

Assumptions for the Independent Samples T-Test

The independent samples t-test makes the following assumptions:

  • Assumption of Independence: There must be two data sets that are not connected with each other, and are therefore independent.  
  • Assumption of Homogeneity of Variance: The variances of the dependent variable must be equal. 
  • Assumption of Normality: The sampling distribution of the mean across samples must be normal and therefore must fit the bell curve. The dependent variable must, therefore, be (approximately) normally distributed and must be measured on a continuous scale.

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Null and Alternative Hypothesis in an Independent Samples T-Test

Generally, the null hypothesis for an independent samples t-test is that the two populations are equal. Therefore;

 H0:u1=u2

However, researchers are normally trying to reject the null hypothesis and accept the alternative hypothesis, which states that the population means are not equal;

 H0:u1u2

In order to reject or accept the alternative hypothesis, we must set a significance level known as alpha (). The value of alpha is usually set at 0.o5. 

Your p-value indicates the probability that your null hypothesis is true. If your p-value is less than your selected alpha level, the null hypothesis is rejected and the alternative hypothesis is accepted. However, if your p-value is more than your selected alpha level, the null hypothesis is accepted and the alternative hypothesis is rejected. 

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FAQs on Independent Samples T-Test

An independent samples t-test is an inferential statistical test that is used to compare the means of two unrelated sets of data.

There are three main types of t-test used in hypothesis testing, namely;

  • Independent samples t-test
  • Paired sample t-test
  • One sample t-test

An independent samples t-test is a statistical test that is used to compare the means of two different data sets.

The independent samples t-test is used when we want to compare the means of two different data sets, without having information on the population mean or standard deviation.

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