# Difference Between T-Test and ANOVA with Proper Definition and Brief Explanation

There is a fine line of demarcation in the middle of the t-test. ANOVA, that is, when comparing the population means of only two groups, **t-test** is used, but when comparing means of more than two groups, **ANOVA** is preferred.

The 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 that the population from which the sample is drawn must be normally distributed, the homogeneity of the variance, the random sampling of the data, the independence of the observations, the measurement of the variable Dependent on the ratio or interval level, people often misunderstand two.

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

## Content: T-test Vs ANOVA

- Comparative graph
- Definition
- Key differences
- conclusion

### Comparative graph

Basis for comparison | T test | ANOVA |
---|---|---|

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

Test statistic |
(x ̄-µ) / (s / √n) | Variation between samples / Variation within the sample |

### Definition of T-Test

The t-test is described as the statistical test that examines whether the population means of two samples differ greatly from each other, using the t-distribution that is used when the standard deviation is unknown and the sample size is small. It is a tool to analyze if the two samples are drawn from the same population.

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

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

### Definition of ANOVA

Analysis of Variance (ANOVA) is a statistical method, commonly used in all situations in which a comparison is made between more than two population means, such as crop yield from multiple seed varieties. It is a vital analysis tool for the investigator that allows him to perform tests simultaneously. When we use ANOVA, the sample is assumed to be drawn from the normally distributed population and the variance of the population is equal.

In ANOVA, the total amount of variation in a data set is divided into two types, that is, the amount assigned at random and the amount assigned to particular causes. Its basic principle is to test the variations between the means of the population by evaluating the amount of variation within the group items, proportional to the amount of variation between the groups. Within the sample, the variance is due to unexplained random alteration, while a different treatment can cause a sample variance.

Using this technique, we test the null hypothesis (H _{0} ) where all the population means are equal, or the alternative hypothesis (H _{1} ) where 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:

- A hypothesis test that is used to compare the means of two populations is called a t-test. A statistical technique that is used to compare the means of more than two populations is known as Analysis of Variance or ANOVA.
- The test statistic for the T test is: The test statistic for ANOVA is:

### Conclusion

After reviewing the above points, it can be said that the 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 may increase if the t-test is used when we have to compare more than two means of the populations at the same time, that is why ANOVA is used