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T-Test Calculator


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What is a T-Test?

A t-test is a type of inferential statistical test that is used to determine the significant difference between the means of different groups of data. T-tests can be used to identify whether or not any differences in means could’ve happened by chance. T-tests are generally used with data that follows a normal distribution and possibly has unknown variances. 

In research, the t-test is generally used as a hypothesis testing tool that can reject or accept the alternative hypothesis. There are many different hypothesis testing tools including the Student’s T-Test, F test, Chi-square test, analysis of variance (ANOVA), and more.

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Understanding the T-Test

A t-test allows us to compare the mean values of two populations, or data sets, so that we can determine whether or not they came from the same population. When doing the math, we take a sample from each set of data and create a problem statement that assumes a null hypothesis that both the means are equal. Once we’ve calculated the means and compared them against each other (or against a standard value), we can determine whether the null hypothesis should be accepted or rejected. 

If both the means are not equal, the null hypothesis is rejected. This indicates that there is a significant difference between the means and therefore the difference in means is likely not due to chance. However, if the null hypothesis is accepted, the difference in means is not significant and are possibly due to chance.  

Types of T-Test

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There are three main types of t-test: 

  • One-Sample T-Test: The one-sample t-test involves comparing the mean of a single population to a known or pre-specified value. 
  • Independent Samples T-test: Also known as a two-sample t-test, an independent samples t-test is used to identify the difference in the means of two groups of data in 
  • Paired Sample T-Test: The paired sample t-test is used to determine the difference in the mean of a single population at two different time frames; this is generally before and after experimental intervention. 


T-Test Assumptions

The t-test makes the following assumptions about the data: 

  1. Assumption of Normality: It is assumed that when the data is plotted, it will result in a bell-shaped curve indicating normal distribution. 
  2. Assumption of Homogeneity of Variance: When the standard deviations of samples are (approximately) equal, equal variance exists. 
  3. Assumption of Independence: The observations in one sample are completely independent of the observations in the other.
  4. Assumption of Random Sampling: It is assumed that the data is gathered from a representative and randomly selected portion of the total target population. 

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Calculating T-Tests

You require three key data values to calculate a t-test:

  1. Difference Between Mean Values from Each Data Set
  2. Standard Deviation of Each Group
  3. The Number of Data Values of Each Group 

The t-test produces an outcome known as the t-value. This t-value is compared against a value obtained from the critical value table, also known as the T-Distribution Table. When compared, we can determine the effect of the chance alone on the difference, as well as whether the difference is outside or within the chance range. 

T-Distribution Table

The T-distribution table is available in two formats: 

  1. One-Tail Format: Used to assess cases where there is a fixed value or a range with a clear direction. 
  2. Two-Tails Format: Used for range-bound analysis. 


The t-test produces the following two outputs:

  1. T-Value: The ratio of the difference between the means of the sample sets and the variation between them. A large t-score indicates that the groups are different while a small t-score indicates that the groups are similar. 
  2. Degrees of Freedom: The values that have the freedom to vary and are integral to assess the validity and importance of the null hypothesis. 

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FAQs on T-Test Calculator

A t-test is an inferential statistical test that is used to determine the significant difference between the means of different groups of data.

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

  • One-Sample T-Test
  • Independent Samples T-test
  • Paired Samples T-Test

In statistics, the t-score refers to the ratio between two groups and the differences within them. The higher the t-score, the more difference there is between the groups. The smaller the t-score, the more similarity there is between the groups. 

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