The analysis of variance (ANOVA) methods of this chapter require the F distribution
The F distribution has the following properties:
One way analysis of variance (ANOVA) is a method of testing the equality of three or more population means by analyzing sample variances. One way analysis of variance is used with data categorized with one factor (or treatment), so there is one characteristic used to separate the sample data into different categories
Understand that a small p-value (
When we conclude that there is sufficient evidence to reject the claim of equal population means, we cannot conclude from ANOVA that any particular mean is different from the others
Test statistic for One-way ANOVA: F = variance between samples / variance within samples
When testing for equality of 3 or more populations, use analysis of variance. Using multiple hypothesis tests with 2 samples at a time could adversely affect the significance level
How to calculate the test statistic F with equal sample sizes n:
Degrees of freedom (using k = number of samples and n = sample size), numerator degrees of freedom = k -1 and denominator degrees of freedom = k(n-1)
The F test statistic is very sensitive to sample means, even though it is obtained through 2 different estimates of the common population variance
One way to reduce the effect of the extraneous factors in an experiment is to use a completely randomized design (each sample value is given the same chance of belonging to the different factor groups) or rigorously controlled design (sample values are carefully chosen so that all other factors have no variability)
Two informal methods for comparing means:
Range tests allow us to identify subsets of means that are not significantly different from each other
Multiple comparison tests use pairs of means and make adjustments to overcome the problem of having a significance level that increases as the number of individual tests increases. Examples include the Bonferroni Multiple Comparison test.
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