A T-test is a statistical tool that is used for hypothesis testing to compare the mean of two sets of observed data and find out the rate of difference between them.

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It falls within the ambit of inferential statistics, the branch that is concerned with making predictions and generalisations regarding a given population by picking up a sample of that population.

Unlike in Z-test, the sample size in a T-test should be less than 30, and the standard deviation should be unknown.

**Origin of T-test**

A T-test was conducted for the first time by William Sealy Gosset, an English statistician, chemist and brewer. While working for a brewing company called Guinness, he applied the t-test to observe the consistent character of the stout.

Eventually, this test was upgraded with its current connotation referring to any hypothesis test whose data variables follows a t-distribution (a bell-shaped curve with weighty tails) if the null hypothesis proves to be accurate.

**When can a T-test be conducted?**

A T-test has to adhere to the following conditions for a standard interpretation and validation.

- The sets of observed data should not be more than two.
- The data should be sampled randomly.
- The sample size must not be more than 30.
- The data variables must be independent.
- The data variables must reflect an approximately normal distribution.
- The variance needs to be unknown and homogenous.
- The outcome of the scale of measurement applied to the collected data must follow a continuous line.

**Which kind of T-test is most suitable?**

The choice of a type of T-test will primarily depend on two things:

- Whether the collected data sets belong to the same population or two different populations.
- The intention of the conductor of the test to examine the difference in a particular direction.

Based on the **nature of the sample population**, a T-test may be classified into three types.

**One Sample T-test:**It entails comparing the mean of a single data set with a known mean or standard value.**Paired Sample T-test:**It involves comparing the mean of a single set of observed data at different intervals, say, before and after an experiment.**Independent Samples T-test:**Also known as**Two-Samples T-test,**it entails comparing two different sets of observed data and their averages.

Based on the **test conductor’s** **intention to examine the difference in a particular direction**, a T-test may be classified into the following two types.

**One-tailed T-test:**It is used to find out whether a population average is less or greater than the other population mean.**Two-tailed T-test:**It is used to find out whether there is a difference between two sets of data or not.

**How to conduct a T-test?**

A T-test measures the real difference between the means of two sample groups by employing the **ratio of the difference in sample group means over the pooled standard error of both sample groups**.

The following formula can be used to run a two-sample or student’s t-test:

Here,

**t =**value of the T-test**x1**Means of the two sample groups_{ and }x2 =**s2 =**Pooled Standard Error of the two sample groups**n1 and n2**= Number of Observations in each sample group

To find out if the computed t-value is more than that of the t-value expected by chance, one has to employ a critical value chart and compare the calculated t-value with the critical t-value.

If the computed t-value is indeed higher, it implies that the null hypothesis is rejected. Accordingly, one can conclude that the sample groups are indeed different.

**What is t-score?**

A t-score or t-value is a number that represents the extent of difference between the averages of two sets of observed data.

A higher t-score implies that the sample groups are different. In contrast, a smaller t-score means that there are similarities between the sample groups.

**Advantages of T-test**

The following are some notable advantages of the T-test:

- It is one of the
**most straightforward and versatile tools**for comparing two sets of data. - The output of the independent variables is
**easy to interpret**. - It requires a small sample size. Consequently,
**data collection is relatively more comfortable**under a t-test. - It is used for finding out whether two sets of sample data belong to the same population or not. Consequently, it helps in
**obtaining the source of data.**

**Disadvantages of T-test**

As a tool for hypothesis testing, T-test is quite conservative. The following are some significant limitations of the T-test.

- Only
**two sets of sample data can be compared**using a T-test. - The assumption of
**the sample data being random is not always right.** - Even though a T-test can help in finding out the source of a given set of data,
**environmental factors can significantly affect its outcomes**and make the results unreliable.

**References**

- https://www.ncbi.nlm.nih.gov/pmc/articles/pmc4667138/
- https://scholarworks.umass.edu/cgi/viewcontent.cgi?article=1307&context=pare
- https://onlinelibrary.wiley.com/doi/abs/10.1002/bimj.4710280202