There is a thin line of demarcation amidst t-test and ANOVA, i.e. when the population means of only two groups is to be compared, the **t-test** is used, but when means of more than two groups are to be compared, **ANOVA** is preferred.

T-test and Analysis of Variance abbreviated as ANOVA, are two parametric statistical techniques used to test the hypothesis. As these are based on the common assumption like the population from which sample is drawn should be normally distributed, homogeneity of variance, random sampling of data, independence of observations, measurement of the dependent variable on the ratio or interval level, people often misinterpret these two.

Here, is an article presented for you to understand the significant difference between t-test and ANOVA, have a look.

## Content: T-test Vs ANOVA

### Comparison Chart

Basis for Comparison | T-test | ANOVA |
---|---|---|

Meaning | T-test is a hypothesis test that is used to compare the means of two populations. | ANOVA is a statistical technique that is used to compare the means of more than two populations. |

Test statistic | (x ̄-µ)/(s/√n) | Between Sample Variance/Within Sample Variance |

### Definition of T-test

The t-test is described as the statistical test that examines whether the population means of two samples greatly differ from one another, using t-distribution which is used when the standard deviation is not known, and the sample size is small. It is a tool to analyse whether the two samples are drawn from the same population.

The test is based on t-statistic, which assumes that variable is normally distributed (symmetric bell-shaped distribution) and mean is known and population variance is calculated from the sample.

In t-test null hypothesis takes the form of H_{0}: µ(x) = µ(y) against alternative hypothesis H_{1}: µ(x) ≠ µ(y), wherein µ(x) and µ(y) represents the population means. The degree of freedom of t-test is n_{1} + n_{2} – 2

### Definition of ANOVA

Analysis of Variance (ANOVA) is a statistical method, commonly used in all those situations where a comparison is to be made between more than two population means like the yield of the crop from multiple seed varieties. It is a vital tool of analysis for the researcher that enables him to conduct test simultaneously. When we use ANOVA, it is assumed that the sample is drawn from the normally distributed population and the population variance is equal.

In ANOVA, the total amount of variation in a dataset is split into two types, i.e. the amount allocated to chance and amount assigned to particular causes. Its basic principle is to test the variances among population means by assessing the amount of variation within group items, proportionate to the amount of variation between groups. Within the sample, the variance is because of the random unexplained disturbance whereas different treatment may cause between sample variance.

With the use of this technique, we test, null hypothesis (H_{0}) wherein all population means are the same, or alternative hypothesis (H_{1}) wherein at least one population mean is different.

## Key Differences Between T-test and ANOVA

The significant differences between T-test and ANOVA are discussed in detail in the following points:

### Conclusion

After reviewing the above points, it can be said that t-test is a special type of ANOVA that can be used when we have only two populations to compare their means. Although the chances of errors might increase if t-test is used when we have to compare more than two means of the populations concurrently, that is why ANOVA is used

Isabella Ghement says

Nice post

Sophie M. says

It’s clear, and help a lot to remind the essential facts about these two analyses when you learned about them a long time ago.

Godwin says

This answer is so helpful for me…couldn’t have asked for more… Thanks

Manar Mizher says

Thanks for the valuable post.

It is clear now for me the difference between them.

Samuel says

Very invaluable! Thanks a lot.

Mike Tones says

If there are 5 different treatment applied to plots of a crop and you want to know which ones are different from each other, clearly you should use ANOVA. If one of those plots is a “control” and you are asking the question which of the treatments are significantly different from control, is it most appropriate to use ANOVA or to do multiple t-tests of each treatment in turn vs control? Thanks.

Ioannis Kamzolas says

Very clear explanation! Thanks a lot!

Bruce Berger says

This clears it up for me.- many thanks!

Sayo says

I have a test in two hours and I think you just saved my life so from the bottom of my heart, thank you

teecee says

On chapter two, experimental designs.. Thank for the help!

Maame says

Really appreciate the clear distinction you have drawn between the two tests. I am now really settled in my mind. Thanks

esmaeil says

Very invaluable! Thanks a lot.

Thanks for the valuable post.

Yumma Dorcas says

This is helpful. Thanks!