Anova

Anova is a statistical method used to analyze the differences among group means in a sample. The term "ANOVA" stands for "Analysis of Variance." It is a collection of statistical models and their associated procedures, which compare means by splitting the overall observed variance into different parts. ANOVA is widely used in various fields such as psychology, biology, education, and economics.

History

The ANOVA method was developed by the statistician Ronald Fisher in the early 20th century. Fisher introduced the technique in his 1925 book, "Statistical Methods for Research Workers," and it has since become a fundamental tool in the field of statistics.

Types of ANOVA

There are several types of ANOVA, each suited for different experimental designs and data structures:

• One-Way ANOVA: Used when comparing the means of three or more independent groups based on one factor.
• Two-Way ANOVA: Used when comparing the means based on two factors, which can be either independent or related.
• Repeated Measures ANOVA: Used when the same subjects are used for each treatment (i.e., repeated measurements).
• Multivariate ANOVA (MANOVA): Used when there are multiple dependent variables.

Assumptions

ANOVA relies on several key assumptions:

• Independence of observations.
• Normality of the residuals.
• Homogeneity of variances (homoscedasticity).

Applications

ANOVA is used in various research fields to test hypotheses about differences between group means. Some common applications include:

• Comparing the effectiveness of different medical treatments.
• Evaluating the impact of different teaching methods on student performance.
• Analyzing the effects of different fertilizers on crop yield.

Procedure

The basic steps in conducting an ANOVA include: 1. Formulating the null and alternative hypotheses. 2. Calculating the between-group and within-group variances. 3. Computing the F-statistic. 4. Comparing the F-statistic to the critical value from the F-distribution table. 5. Making a decision to reject or fail to reject the null hypothesis.

Related Pages

• Statistics
• Hypothesis testing
• Regression analysis
• Experimental design
• Ronald Fisher

See Also

• T-test
• Chi-squared test
• Non-parametric statistics