Analysis of Variance: ANOVA

Group 1: control group/ no ind. Var.

Group 2: low level of the ind. Var.

Group 3: high level of the ind var.

If you evaluated the differences using a t test:

group 1 vs. group 2

group 2 vs. group 3

group 1 vs. group 3

What is the probability of a type one error somewhere in this analysis?

Type One error: rejecting the null when there really isn’t any effect of the independent variable.

Reject the null

The probability of a type one error in a single comparison is whatever the probability of a random event is.

P < .05 or 5% of the time

Probability over three comparisons:

type one error in comparison one

or

comparison two

or

comparison three

Probability of type one error:

.05 + .05 + .05 = .15

or

15% of the time

This inflation of the type one error rate is known as:

Experimentwise error rate

To hold down the experimentwise error rate we perform an analysis of variance (ANOVA) instead of multiple t tests.

variance between groups

F = ---------------------------------------

variance within groups

Var. between : how much each group mean differs from all other group means.

Var. within: how much individuals within the groups vary from each other.

What causes variability between:

treatment + random events

independent variable

confounding factors

What causes variability within:

Random events (individual differences)

treatment + random events

F = ------------------------------------------------

random events

When the only thing that has caused the groups to differ is random events,

F should be a value very close to 1

S

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variance

Sum of squares (SS)

Degrees of freedom (df)

In ANOVA:

Variance is known as the mean square

(MS)

Sum of Squares

Variance = -------------------------------

degrees of freedom

MSSS

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Where K represents the number of groups

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