# T-Test vs. ANOVA

Main DifferenceThe main difference between T-Test and ANOVA (Analysis of Variance) Test is that T-Test is a specified statical test based on the student-t principal and is used to differentiate between two data sets from two population in the absence of variance. However, on the other hand, Analysis of Variance famously abbreviated as ANOVA is a generalized hypothetical technique to determine the difference between two or more population on the basis of variance.

## Difference Between T-Test and ANOVA

#### T-Test vs. ANOVA

The t-test is a hypothetical test which involves the differentiation of two data sets in which variance is not mentioned. It is usually used when the means of two populations are to be compared.

#### T-Test vs. ANOVA

Analysis of Variance (ANOVA) is a hypothetical test technique that is used to compare the means of more than two population by their variance.

#### T-Test vs. ANOVA

ANOVA is for more than two populations

#### T-Test vs. ANOVA

ANOVA facilitates a large sample size.

#### T-Test vs. ANOVA

The t-test is for the differentiation in two population samples.

#### T-Test vs. ANOVA

The t-test is worked with a small sample size.

#### T-Test vs. ANOVA

Variance is present in the ANOVA.

#### T-Test vs. ANOVA

Variance is absent in the T-Test.

#### T-Test vs. ANOVA

The t-test is based on student-T phenomenon.

#### T-Test vs. ANOVA

ANOVA is based on variance distribution equivalent to population distribution.

#### Anovanoun

a statistical method for making simultaneous comparisons between two or more means; a statistical method that yields values that can be tested to determine whether a significant relation exists between variables

## Comparison Chart

T-Test | ANOVA |

The t-test is a hypothetical test which involves the differentiation of two data sets in which variance is not mentioned. It is usually used when the means of two populations are to be compared. | Analysis of Variance (ANOVA) is a hypothetical test technique that is used to compare the means of more than two population by their variance. |

Applicability | |

In the absence of variance. | In the presence of variance. |

Limitations | |

The t-test is more of a specific kind of test. | ANOVA is a more of general kind of test. |

Test Statics | |

Based on Student T distribution. | Based on the general distribution. |

Conducted On | |

Small sample. | Large sample. |

Population Variance | |

In the T-Test based on the student-t phenomena, the population variance is unknown. | In the ANOVA along with the involvement of a large data sample, the population variance is known. |

Centered on | |

Statical T-test is based on the specific student-T distribution of data in the data sets. | Hypothetical ANOVA is based on the usual distribution of data in the data sets in the presence of variance in more than two populations. |

Independence | |

In T-test, all the data points are individually considered independent. | In ANOVA, all the sample observations are independent and are from more than two populations. |

### T-Test vs. ANOVA

T-Test based on the student-t distribution while as from the name of ANOVA Test (Analysis of Variance), it is clear that it is the test that is focused on the variance in the population. Other major difference between both of these statical and hypothetical test includes the size of the population. In ANOVA, the size of the sample is large and is from two or more populations, whereas in T-Test sample size is small and is from two different data sets of maximum two populations. Another thing that distinguishes these two famous tests is the population variance. In ANOVA population variance is known and is considered equal to the population distribution as a whole. On the other hand in the T-Test the population variance is unknown. Both can be used simultaneously to fulfill the required demands.

### What is a T-Test?

The t-test is a hypothetical test which involves the differentiation of two data sets in which variance is not mentioned. It is usually used when the means of two populations are to be compared. Statical T-test is based on the specific student-T distribution of data in the data sets. In T-test, all the data points are individually considered independent. In the T-Test based on the student-T phenomena, the population variance is unknown. In the T-Test based on student-t, the variance is absent, and data sets are compared in the absence of variance. The t-test is typically conducted on a small sample of data collected. In the Z-Test the two different data sets are compared from the large sample size of data in the presence of variance. A further type of Student –t-Test is paired T-test. In the paired T-test, the two data sets or the two data samples considered are dependent on each other in various ways, and their differentiation is tested by their dependency relation. The t-test is more of a specific kind of test in which only data sets of the population are differentiated on certain terms, and the small sample size is involved. We can state it as a special kind of ANOVA.

#### Expectations of T-test:

- In the T-Test based on student-t singularities, the sample values are taken and recorded precisely.
- In the T-Test as compare to Z-Test and other hypothetical tests, all data points are independent.
- The sample size is always small when it comes to T-Test.

### What is ANOVA?

Analysis of Variance (ANOVA) is a hypothetical test technique that is used to compare the means of more than two population on the basis of their variance. Hypothetical ANOVA is based on the usual distribution of data in the data sets in the presence of variance in more than two populations. In the ANOVA along with the involvement of a large data sample, the population variance is known. ANOVA is a more of general kind of test in which more than two populations can be differentiated, and the sample size is large, population variance is known and is considered equal to distributed population. ANOVA is applicable when two or more data sets of the population or the two or more populations are to be compared in the presence of variance.

ConclusionThe t-test is the statical test that is specified in nature when it comes to differentiating two data sets from two populations in the presence of variance. Whereas Analysis of Variance or ANOVA is a more of general hypothetical test that is used to differentiate data sets from two or more than two populations by variance.