## Difference Between Z Test vs T-Test

Z-tests and t-tests are the two statistical methods that involve data analysis which has applications in science, business, and many other disciplines. The t-test can be referred to a univariate hypothesis test that is based on t-statistic, wherein the mean i.e. the average is known, and population variance i.e. standard deviation is approximated from the sample. On the other hand, Z-test, also a univariate test which is based on a standard normal distribution. In this article, we discuss the key differences between Z Test vs T test

### Use of the Z Test

Z-tests, as mentioned earlier, are the statistical calculations which can be used to compare population averages to a sample’s. The z-test will tell you how far, in standard deviations terms, a data point is from the average of a data set. A z-test will do a comparison of a sample to a defined population that is typically used for dealing with problems relating to large samples (i.e. n > 30). Mostly, they are very useful when the standard deviation is known.

### Use of T-Test

T-tests are also calculations which can be used to test a hypothesis, but they are very useful when we need to determine if there is a statistically significant comparison between the 2 independent sample groups. In other words, a t-test asks whether the comparison between the averages of 2 groups is unlikely to have occurred due to random chance. Usually, t-tests are more appropriate when you are dealing with problems with a limited sample size (i.e. n < 30).

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### Z Test vs T Test Infographics

Here we provide you with the top 5 difference you must know.

### Key Differences

- One of the most important conditions for conducting t-test is that population standard deviation or the variance is unknown. Conversely, population variance as stated above should be assumed to be known or be known in case of a z-test.
- The t-test as mentioned earlier is based on Student’s t-distribution. On the contrary, the z-test depends upon the assumption, that the distribution of sample means will be normal. Both the normal distribution and student’s t-distribution appears the same, as both are bell-shaped and symmetrical. However, they differ in one of the cases that in at-distribution, there is lesser space in the center and more in their tails.
- Z-test is used as given in the above table when the sample size is large, which is n > 30, and t-test is appropriate when the size of the sample is not big which is small, i.e. that n < 30.

### Head to Head Comparison

Basis |
Z Test |
T-Test |
||

Basic Definition |
Z-test is kind of hypothesis test which ascertains if the averages of the 2 datasets are different from each other when standard deviation or variance is given. | The t-test can be referred to a kind of parametric test that is applied to an identity, how the averages of 2 sets of data differ from each other when the standard deviation or variance is not given. | ||

Population Variance |
The Population variance or standard deviation is known here. | The Population variance or standard deviation is unknown here. | ||

Sample Size |
The Sample size is large | Here the Sample Size is small. | ||

Key Assumptions |
1) All data points are independent. 2) Normal Distribution for Z, with an average zero and variance = 1. | 1) All data points are not dependent. 2) Sample values are to be recorded and taken accurately |
||

Based upon (a type of Distribution) |
Z test is based on Normal distribution. | A t-test is based on Student-t distribution. |

### Conclusion

By and to the larger extent, both these tests are almost similar, but the comparison comes only to their conditions for their application, meaning that t-test is more appropriate and applicable when the size of the sample is not more than thirty units. However, if it is greater than thirty units, one should use z-test. Similarly, there are also other conditions, which will make it clear that which test is to be performed in a situation.

Well, there are also different test like f test, two-tailed vs single tailed, etc., statisticians must be careful while applying them after analyzing the situation and then deciding which one to use. Below is a sample chart for what we discussed above.

### Recommended Articles

This has been a guide to them Z Test vs T-Test. Here we discuss the top 5 differences along with infographics and comparison table. You may also have a look at the following articles –

- Excel Z Test
- What is Hypothesis Testing?
- Formula of F-Test
- Logical Test in Excel (AND, OR, IF)
- How to do F-Test in Excel?

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