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Analysis Variance

One Way Anova

Repeated Measures Anova

Definition

Basic Assumption

Adv of ANOVA vs T-test

F= Between-grp variability Within-grp variability

method used to compare the means of several groups of observations ( more than 2)

F-test is used to test the null hypothesis that the means of all the groups of observations are equal.

Eg. we might measure the height of 10-year-old girls in five different countries and wish to test whether the mean height of 10-year-old females is the same in all five countries.

One Way” signifies that there is a single independent variable whose effect on a dependent variable is under study eg.in the comparison of means between different ethnic groups.

1. The samples come from normally distributed populations with the same standard deviation

2. Groups being compared are composed of randomly sample subjects.

3. The populations from which the groups are drawn are assumed to have equal variance.

4. The subjects in the grps have been independently sampled.

1. Tedious to use T-test to compare many groups

2. Reduce risk of a Type 1 error

A significant F test does not tell us which pairs of means are significantly different from one another need additional analyses. Multiple comparison tests used are: Fisher’s Least Significant Difference (LSD) test Duncan ‘s test. Tukey’s honestly significant difference (HSD) test etc

If the grp means are all equal ;

When the grp means in a sample are different, the differences can be attributable to two factors:

F=MSB / MSW

1) no between grp variability

2) F = 0

3) Acceptance of Null Hypothesis.

1) Sampling Error.

2) The effect of the independent variable

If F value in a test is larger than your F statistic, you can reject the null hypothesis.

F value = variance of the group means (Mean Square Between) / mean of the within group variances (Mean Squared Within)

Reject the null when your p value is smaller than your alpha level.

You should not reject the null if your critical f value is smaller than your F Value, unless you also have a small p-value.

Crtical F value for alpha = table for F distribution