What is the difference between T-test and ANOVA?

T-test and ANOVA are two models of statistical analysis. Understanding the difference between T-test and ANOVA will make it easier to carry out research. Let’s find out:

**What is the T-test?**

The T-test is also known as the student’s T-test and it is typically used to compare the means between two groups. It helps to see if the means are different from each other.

It is only applicable where two sets are to be compared when a random assignment has been given.

For the testing to take place, here are some of the conditions that need to be met. They include:

- Population data need to be distributed
- Mean is supposed to be known
- Population variance needs to be calculated.

A test null hypothesis is represented as H0: µ(x) = µ(y) against alternative hypothesis H1: µ(x) ≠ µ(y). Where µ(x) and µ(y) represents the population means. The degree of freedom of the t-test is n_{1} + n_{2} – 2.

**What is ANOVA?**

ANOVA is a statistical model used to make a comparison between two or more population means. It is a statistical tool that helps the researcher to make the test simultaneously.

The total amount of variation in a data set is normally split into the amount allocated to chance and amount assigned to particular causes.

The core function is to test the variances among population means by assessing the amount of variation within group items.

**Comparison Chart: T-test Vs ANOVA**

Basic Terms |
T-test |
ANOVA |

Meaning | Typically used when determining whether two averages or means are the same or different. | Typically used when comparing three or more averages or means. |

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

Accuracy | Prone to errors | Tend to be quite accurate |

Groups | Not more than two | Can be two or more |

**Core Difference between T-test and ANOVA In Point Form **

- T-test comparison is based on two groups only while ANOVA two or more groups
- The T-test is prone to making more errors while ANOVA tend to be quite accurate
- ANOVA has four types such as One-Way Anova, Multifactor Anova, Variance Components Analysis, and General Linear Models while the T-test has two types such as Independent Measures T-test and Matched Pair T-test.
- The test statistic formula for T-test is (x ̄-µ)/(s/√n) while that of ANOVA is s
^{2}b/s^{2}

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**Comparison Video**

**Summary**

Generally, the T-test is a special type of ANOVA where only two sets of data are supposed to be compared. Understanding the core difference between T-test and ANOVA is quite important is statistical analysis.

**More Sources and References **