## Hypothesis Testing and Design of Experiments

##### Outlier Testing

##### t-test

##### ANOVA

ANOVA (analysis of variance) is a statistical tool for testing homogeneity based on differences in different groups.

ANOVA is a method of analyzing the variance of a dataset and dividing the variance into groups according to their sources of variation.

ANOVA is based on the principle that the total amount of difference in a data set can be divided into two types: random and specific causes.

Population uses ANOVA to analyze the variation within each sample and compare it to the between-sample variation to determine the difference between sample means.

Two assumptions are made when performing ANOVA. The first is that the sample was drawn from a normal population, and the second is that all factors other than what is being tested are controlled for.

**One-way ANOVA:**One-way ANOVA is a shortcut method that considers one factor and observes the effect on the sample.It is a commonly used technique because it is more convenient.

This step is performed if the sample mean and/or the mean of sample means are not integer values.

The drawback of one-way ANOVA is that it cannot determine which particular groups are different from each other, but at least he can determine that two groups are different. One-way ANOVA analyzes at least three groups because the t-test can be used to determine the difference between two groups. Therefore, the t-test can be performed instead of the F-test, greatly reducing the time and effort required. The relationship between ANOVA and t-test can be described as $F=t^2$.

**Two-way ANOVA:**The Two Way ANOVA technique is used when a given data set falls into two different independent factors.Here, the measurements are made separately for each factor, so the measurements may or may not be repeated.

The main purpose of two-way ANOVA is to determine whether there is a relationship between independent and dependent factors. This technique helps determine whether the effect of an independent factor on a dependent factor is influenced by other independent factors.