State the differences between ANOVA and t test?

1. ANOVA (Analysis of Variance) is used to compare the means of three or more groups, while t-test is used to compare the means of two groups.

2. ANOVA tests for overall differences among group means, while t-test compares the means of individual groups.

3. ANOVA provides an F-statistic and p-value to determine if there are significant differences among group means, while t-test provides a t-statistic and p-value to determine if there is a significant difference between two group means.

4. ANOVA assumes that the variances of the groups are equal, while t-test does not make this assumption.

5. ANOVA can be used to compare multiple groups simultaneously, while t-test can only compare two groups at a time.

6. ANOVA is more powerful than t-test when comparing multiple groups, as it can detect differences that t-test may miss.

ANOVA (Analysis of Variance)

- Compares the means of multiple groups (more than two)
- Evaluates whether there is a statistically significant difference between the means of those groups
- Assumes that the data are normally distributed and that the variances of the groups are equal

t-test

- Compares the means of two groups
- Evaluates whether there is a statistically significant difference between the means of those two groups
- Can be used for either independent or paired samples
- Can be used when the data are not normally distributed (e.g., t-test for unequal variances)

Key Differences

| Feature | ANOVA | t-test |
|---|---|---|
| Number of groups | Multiple (more than two) | Two |
| Assumptions | Assumes normal distribution and equal variances | Can be used for non-normal data and unequal variances (depending on the specific t-test used) |
| Purpose | Compares the means of multiple groups | Compares the means of two groups |