BS141 Lecture 4 - Comparing Multiple Samples

Why are multiple t-tests not suitable for comparing more than two groups

Increase # of tests and inflate chance of false positives, reducing detection power

What is the multiple testing problem

As # of groups increases, # of stats tests increases

What happens to detection power with multiple testing

It decreases making real differences harder to detect

What statistical method is used to compare three or more means

ANOVA or Analysis of Variance

What key statistical concept is ANOVA based on

Variance and its additivity

What does variance additivity mean

If distributions are independent, variance of their sum = sum of their variances

What two variances are compared in ANOVA

Variance within groups and variance between groups

What does variance within groups measure

The combined variability of measurements inside each group

What does variance between groups measure

The variability of group means around the overall mean

If all samples come from the same population how should the two variances compare

They should be approximately equal

What happens when group means are far apart

Variance between groups becomes much larger than variance within groups

What is the F statistic

The ratio of variance between groups to variance within groups

When the null hypothesis is true what distribution does the F statistic follow

The F distribution

How many degrees of freedom define an F distribution

2 - 1 btwn groups, 1 w/in groups

What is the null hypothesis in one way ANOVA

All group means are equal

What is the alternative hypothesis in one way ANOVA

At least one group mean is different

What type of samples are required for one way ANOVA

k independent samples

What are the main steps of a one way ANOVA

Collect data compute within group variance compute between group variance calculate F compare to F distribution

How is sample variance calculated

Sum of squares divided by degrees of freedom

What are degrees of freedom for a group with three measurements

Two

What are the main components of an ANOVA table

Sum of squares degrees of freedom mean square and F value

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What sources of variance are considered in two way ANOVA

Variance between rows variance between columns and variance within groups

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