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• ### 1 ANOVA

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• #### When can one use ANOVA?

- The OV is quantitative
- The PV is categorical, so has two or more categories (0,2 or 4 beers predict if something will happen)
- participants differ from each other (different test groups do not have the same participants)
- population is normally distributed
- populations must have the same variance
• #### Variance testing can distinguish two tests, which two?

Variance testing within groups
Variance testing between groups (this is the one that says the most)
• #### What does the F-test tell (ANOVA)?

Variance between sample means / variance within the samples

Variance between sample means = mean sum of squares of the model / Degrees of Freedom (number of groups - 1)

Variance within the samples = Mean square residuals / Degrees of Freedom (number of participants - number of groups)
• #### When is there effect from a PV on an OV?

When the explained variance (between groups) is large relative to the unexplained variance (within groups) --> High F score
• #### What is a Brown-Forsyth or Welch test?

It is a criterion that tells if ANOVA can be done P > 0.05
• #### What happens with R2 when there is only one PV?

Than R2 becomes eta2
• #### A T-test cannot be done to test for statistical evidence because there are used more than 2 groups to test (3x40N). Why can one not do multiple t-tests on these groups to find evidence?

Because of alpha inflation (type 1 error)

To test with 3 groups, three t-tests have to be done.

1-0.95 = 0.05
1-0.95^3 = 0.14
• #### What are the two criteria for planned contrast tets?

1. Sum of the weights must be 0
2. If multiple contrasts are done (so multiple hypotheses are tested) they must be orthogonal. This means that the multiplied comparison of the tetst must be 0.

Example: H1 = group 2 > group 3 --> 0, 1, -1
H2 = group 1 > rest --> 1, -0.5, -0,5

multiplied comparison:
0*1 = 0
1*-0.5 = -0,5
-1*-0.5 = 0.5

These added up is 0, so they are orthogonal!
• #### What does the Levene probability tell?

If the significance is >0.05, than equal variances can be assumed.
• #### What is a post hoc test?

Statistical test afterwards to check the reliability of the earlier tetst done.
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