Who can help me with my t test? When should I use t test? These are some of the questions that are asked by researchers and statistical analysts. Here at Assignmentgiant.com we shall answer the question, but first let’s begin by understanding the concept of t-test. A t test is a statistical test that is used when comparing the means of two groups. It is used when hypothesis testing to establish if a process or treatment actually has an impact on the population of interest. Through it, you can determine if two groups are different from one another.

## Application of t test: example

You want to understand the difference in knee cost surgeries for the same person in two different public hospitals. You will test the difference between these two hospitals using a t test and null and alternative hypotheses.

- Null hypothesis (
*H*_{0}) is that the true difference between the hospital costs is zero - Alternative hypothesis (H
_{a}) is that the true difference between the hospital costs is different from zero.

## When Should I use a T test?

A t-test can only be used when comparing the means of two groups (that is pairwise comparison). If you want to compare more than two groups or you want to carry on multiple pairwise comparison then use ANOVA test or the post-hoc test.

The t-test is a parametric test of difference. This is because it makes the same assumptions regarding your data just as the other parametric tests. The assumptions includes:

- The data are independent.
- The data are normally distributed or approximately distributed
- The data have same degree of variance within each group that is compared. There is homogeneity of variance.

In case the data does not meet the assumptions, then you can consider using the non-parametric alternatives to the t test. A good example of non-parametric alternative that would apply is the Wilcoxon Signed-Rank test for data using the unequal variances.

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## Which type of t test should I use?

Before applying the t test, it is necessary to understand the right types of t test to use. Two sets of considerations or criterion are important. First, find out whether the groups being compared are from a single population or they are from two different populations. Also find out whether you want to test the difference in a given direction.

**Should I use One-sample, two sample, or paired t test?**

Perform a paired t test if the groups are from a single population. The groups are measuring before and after an experimental treatment. This is a within-subjects design.

Perform two-sample t test if the groups come from two different populations (two different varieties or people from two different countries). This is also referred to as the independent t test. This is the between-subjects design.

Perform one-sample t test if there is one group being compared against a standard value. For instance, comparing the performance of a student to the mean score mark of 50%.

**One-tailed t test Vs. Two-tailed t-test**

If your concern is whether the two populations are different from one another, then do two-tailed t test.

If your concern is to find out if one population mean is greater than or less than the other then do one-tailed t test.

## Example of t test

In your test of whether the knee surgery costs differ by hospitals:

Your observations are derived from two separate populations (different types of hospitals) so you perform a two-sample t test.

You do not consider the direction of the difference, only whether there is a difference, so you choose a two-tailed t test.