T-Test

T-Test is a type of inferential statistical test that is used to determine if there is a significant difference between the means of two groups. The T-Test is based on the Student's t-distribution, which is a probability distribution that is used to estimate population parameters when the sample size is small and/or when the population variance is unknown.

Overview

The T-Test was developed by William Sealy Gosset, who published under the pseudonym "Student". There are three main types of T-Test:

• Independent samples t-test: This is used when the data collected is from two independent groups. For example, comparing the mean scores of two different groups of students.
• Paired samples t-test: This is used when the data collected is from the same group at two different times (or under two different conditions). For example, comparing the mean scores of students before and after a teaching intervention.
• One-sample t-test: This is used when the data collected is from a single group that is compared to a known population mean. For example, comparing the mean score of a group of students to the known population mean.

Assumptions

The T-Test assumes that the data is normally distributed, the samples are independent, and the variances of the populations are equal (this is known as the assumption of homogeneity of variance). If these assumptions are not met, the results of the T-Test may not be valid.

Calculation

The formula for the T-Test depends on the type of T-Test being conducted. However, all T-Tests are calculated using the means and standard deviations of the groups being compared. The basic formula for a one-sample T-Test is:

t = (X̄ - μ) / (s/√n)

where X̄ is the sample mean, μ is the population mean, s is the standard deviation of the sample, and n is the sample size.

Interpretation

The result of a T-Test is a t-value and a p-value. The t-value represents the difference between the means divided by the standard error, and the p-value represents the probability that the observed data could have occurred under the null hypothesis. If the p-value is less than the chosen significance level (usually 0.05), then the null hypothesis is rejected and the difference between the means is considered statistically significant.

See also

• Z-test
• F-test
• Analysis of variance