Difference Between T-test and ANOVA

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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.

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 H₀: µ(x) = µ(y) against alternative hypothesis H₁: µ(x) ≠ µ(y), wherein µ(x) and µ(y) represents the population means. The degree of freedom of t-test is n₁ + n₂ – 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 (H₀) wherein all population means are the same, or alternative hypothesis (H₁) 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:

A hypothesis test that is used to compare the means of two populations is called 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.
Test Statistic for T-test is: Test Statistic for ANOVA is:

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