When to use t-test vs. z-test
WHEN TO USE T-TEST VS. 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.
In this article we will have an in-depth understanding of:
Basic differences between a t-test and a z-test
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.
s = sample standard deviation
n = sample size
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.
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.
σ/ = standard deviation of population
If the z-score is lower than the critical value, we accept the null hypothesis.
Maximum likelihood estimate
When to use a z-test?
Z test is conducted when the sample size is larger than 30.
In the case of the z-test, the standard deviation of the population is assumed as known.
