# Understand Difference Between Z-Test and T-Test

In statistics, hypothesis testing is a commonly used technique to make inferences about a population based on sample data. Two widely used methods for hypothesis testing are the Z test and the T-test. While both tests are used to assess the statistical significance of differences between sample means, there are some key differences between them. This article aims to explain the dissimilarities between the Z-test and T-test.

1. Population Standard Deviation Known and Unknown

The Z-test is appropriate when the “population standard deviation” is known, or when the sample size is large (typically considered as n > 30). On the other hand, the T-test is used when the population deviation standard is unknown, and the sample size is small to moderate (typically n < 30).

1. Distribution Assumption:

The Z-test assumes that the population follows a normal distribution, whereas the T-test assumes that the sample follows a normal distribution. When the sample size is large,  that the sample mean approximates a normal distribution, allowing the Z-test to be used.

1. Test Statistic:

The Z-test uses the Z-statistic, which is calculated as the difference between the sample mean and population mean, “standard deviation” of the population. On the other hand, the T-test uses the T-statistic, which is calculated as the difference between the sample mean and population mean, divided by the standard error of the sample mean.

1. Degrees of Freedom :

Degrees of freedom play a crucial role in hypothesis testing. In the Z-test, the degrees of freedom are not considered since the population deviation is known. However, in the T-test, the degrees of freedom are calculated based on the sample size and are used to determine the critical value from the t-distribution.

1. Use Cases:

The Z-test is commonly used in situations where  the population deviation is known. For example, it can be used in quality control processes or when comparing sample means from two large groups.

The T-test, on the other hand, is more versatile and is used when the sample size is small to moderate and the population deviation is unknown. It is widely applied in various fields, such as medicine, psychology, and social sciences, where sample sizes are often limited.

1. Statistical Software:

Both Z-test and T-test can be performed using statistical software such as R, Python, or Excel. However, the specific functions or procedures used may differ depending on the type of test and assumptions made.

Final words

The choice between the Z-test and T-test depends on the sample size, the availability of  population deviation, and the distribution assumption. If the population “standard deviation” is known , the Z-test is appropriate. On the other hand, if the population deviation is unknown or the sample size is small to moderate, the T-test should be used. Understanding these differences will enable researchers and practitioners to select the appropriate test for their specific hypothesis testing needs.