Student's t-test

Student's t-test

File:T-test.png

Illustration of a t-test

The Student's t-test is a statistical hypothesis test used to determine if there is a significant difference between the means of two groups. It was developed by William Sealy Gosset, who published under the pseudonym "Student" in 1908.

Purpose

The purpose of the t-test is to compare the means of two groups and determine if the difference between them is statistically significant. It is commonly used in scientific research to analyze experimental data and make inferences about population parameters.

Assumptions

The t-test assumes that the data is normally distributed and that the variances of the two groups being compared are equal. Additionally, it assumes that the observations within each group are independent of each other.

Types of t-tests

There are three main types of t-tests:

1. Independent samples t-test: This test is used when comparing the means of two independent groups. For example, it can be used to compare the test scores of students who received a specific intervention versus those who did not.

2. Paired samples t-test: This test is used when comparing the means of two related groups. For example, it can be used to compare the before and after test scores of students who received a specific intervention.

3. One-sample t-test: This test is used when comparing the mean of a single group to a known population mean. For example, it can be used to determine if the average height of a sample of students is significantly different from the average height of the general population.

Calculation

The t-test calculates a t-value, which is then compared to a critical value from the t-distribution to determine statistical significance. The formula for calculating the t-value depends on the type of t-test being used.

Interpretation

If the calculated t-value is greater than the critical value, it indicates that there is a significant difference between the means of the two groups being compared. Conversely, if the calculated t-value is less than the critical value, it suggests that there is not a significant difference.

Limitations

The t-test has some limitations. It assumes that the data is normally distributed and that the variances are equal, which may not always be the case. Additionally, it is sensitive to outliers and can be influenced by small sample sizes.

Conclusion

The Student's t-test is a widely used statistical test for comparing the means of two groups. It provides a way to determine if the observed difference between the groups is statistically significant. However, it is important to consider the assumptions and limitations of the t-test when interpreting the results.

See also

• Hypothesis testing
• Statistical significance
• P-value