# When to Use T-Test vs. Z-Test

A hypothesis is an assumption of a scenario that is rejected or accepted based on the test result. There are two kinds of hypothesis testing method:

There are two types of tests in a parametric test – t-test, and z-test.

To a larger extent, both t-test and z-test are similar. Both are used to test a hypothesis to determine if there is a difference between two different population/sample groups. Let us first understand each of the tests. We later talk about when to use t-test and z-test, respectively.

## Basic Differences between t-test and z-test

 T-Test Z-Test A t-test analyses if the means of two datasets are different from each other when the standard deviation is unknown. A z-test analyses if the means of two datasets are different from each other when the standard deviation is known. It is based on Student’s t-distribution. It relies on the assumption that the sample means’ distribution is normal. When the data is plotted on a graph, it forms a symmetrical bell curve shape. However, the space is more in the tails and less in the center. When the data is plotted on a graph, it forms a bell-curve shape which is symmetrical. Population variance is unknown. Population variance is known. The sample size is small(n<30). The sample size should not be less than 5. The sample size is large (n>30).

## What is a t-test?

A t-test is a kind of a univariate hypothesis test. It compares the mean of two samples. A t-test assumes a sample’s normal distribution. It determines if the means of the two data sets differ from one another. T-value is the result that we derive out of a t-test.

The formula for calculating a t-value is:

t=xs∕n

x = sample mean

= population mean

s = sample standard deviation

n = sample size

There are three kinds of t-tests that we can perform:

• One-sample t-test
• Independent two-sample t-test/ unpaired two-sample t-test
• Paired sample t-test

### When to use a t-test?

• A T-test is conducted when the sample size is smaller than 30. The sample should not be lesser than 5.
• The data should be normally distributed, like in the case of a z-test. There is a slight difference in the bell curve.
• In the case of a t-test, the standard deviation of the population is assumed as unknown.
• A T-test is used when the data is assumed to be independent.
• We use a t-test when variance is homogeneous.
• We can perform a t-test when the sample sizes are equal.

## What is a z-test?

A z-test is a statistical tool that is used in the case of a large sample size. It lets us check if there are any differences in the two population means when we know the variances.

Z-score is the result that we derive out of a z-test. It is a conversion of individual scores into a standard form. A z-score signifies the number of standard deviations of a result from its mean.

The formula for calculating z-score is:

z=x-μ/n

x = observed value

= population mean

σ/n = standard deviation of population

If the z-score is lower than the critical value, we accept the null hypothesis.

There are four kinds of z-tests that we can perform:

• One-sample location test
• Two-sample location test
• Paired difference test
• Maximum likelihood estimate

### When to use a z-test?

• Z test is conducted when the sample size is larger than 30.
• The data should be normally distributed. It implies that it should form a symmetrical bell-curve shape when we plot the data on a graph. (clubdeportestolima.com.co)
• The data points need to be independent of one another. In simpler terms, one data point should not affect or relate to another data point.
• The data needs to be selected randomly from a population. It ensures an equal opportunity for each item to get selected.
• The sample sizes should be equal.
• In the case of the z-test, the standard deviation of the population is assumed as known.

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