What is Friedman's ANOVA Test ?

 What is Friedman's ANOVA Test ?







Friedman's ANOVA test is a non-parametric test used to compare the medians of multiple related samples. It is similar to the one-way analysis of variance (ANOVA), but it does not require the assumption of normality in the data.


Assumptions:

• Related samples (e.g., repeated measures)

• Ordinal or continuous data

• No outliers that could significantly affect the results

Procedure:

1. Calculate the ranks of all observations: For each subject, assign the ranks of their observations from 1 to k, where k is the number of treatments or conditions being compared. Ties are assigned the average of the ranks they would have received if they were not tied.

2. Calculate the test statistic: Friedman's test statistic (F) is calculated as:


F = (12N / k(k+1)) * Σ(Rj - R)^2


where:

• N is the number of subjects

• k is the number of treatments or conditions

• Rj is the sum of the ranks for treatment or condition j

• R is the overall mean rank

3. Determine the critical value: The critical value for Friedman's test is obtained from a chi-square distribution with (k-1) degrees of freedom.

4. Compare the test statistic to the critical value: If the test statistic is greater than the critical value, then the null hypothesis (that the medians of the treatments or conditions are equal) is rejected.


Interpretation:

• if the p-value is less than the significance level (usually 0.05), then the null hypothesis is rejected, and there is evidence that the medians of the treatments or conditions are different.

• If the p-value is greater than the significance level, then the null hypothesis is not rejected, and there is not enough evidence to conclude that the medians of the treatments or conditions are different.


Advantages:

• Non-parametric, so it does not require the assumption of normality.

• Can be used with ordinal or continuous data.

• Robust to outliers.


Disadvantages:

• Less powerful than the one-way ANOVA when the data is normally distributed.

• Can be sensitive to ties in the data.


Note: Friedman's ANOVA test is a special case of the Kruskal-Wallis test when the samples are related.

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