```
tags:
- Mathematics/Statistics/Test
- Mathematics
aliases:
- Analysis of Variance
```

ANOVA (ANalysis Of VAriance) is a statistical technique used to compare the means of two or more groups. It helps determine if observed differences between group means are likely due to random chance or if they indicate a statistically significant effect of the variable being compared (independent variable) on the outcome variable (dependent variable).

- Types of ANOVA:
- One-way ANOVA: Comparing two or more groups
- Two-way ANOVA: Investigating the effects of two independent variables
- Repeated-measures ANOVA: Analyzing data where the same subjects are measured under different conditions

Notes:

- ANOVA is specifically designed to analyze the variability(variance) within and between groups. It partitions the total variance in the data to assess how much variance can be attributed to the groups themselves and how much is due to random error.
**F-Statistic:**The core output of ANOVA is the F-statistic, which compares the variance between groups to the variance within groups. A larger F-statistic suggests a greater influence of the independent variable on the dependent variable.- Often there is a strong correlation between a categorical variable and other variables, if the ANOVA test gives us a large F-test value and a small p-Value. End of transcript.
- ANOVA assumes normality of errors and Homogeneity of variance (equal variances across groups). Violations of these assumptions can affect the reliability of the results. It's crucial to check these assumptions before interpreting ANOVA results and consider alternative non-parametric tests if assumptions are not met.

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