Download presentation
Presentation is loading. Please wait.
Published byAlan Walton Modified over 9 years ago
1
Psychology 202a Advanced Psychological Statistics November 24, 2015
2
The plan for today A priori contrasts in SAS Orthogonal contrasts Contrast coding The Eysenck ANOVA example Helmert contrasts Introduction to power
3
A priori contrasts A contrast is a question about a linear combination of means. Example: Shorthand notation: 1/2 1/2 -1 Equivalent: 1 1 -2 Another question that might interest us is 1 -1 0.
4
Contrasts (continued) Once a contrast is specified, its sum of squares is calculated: Contrasts always have 1 df, so the sum of squares is a mean square. Division by the error mean square provides an F statistic that tests the contrast.
5
Contrasts (continued) Illustration in SAS. Any set of contrasts defined in advance may be tested, dividing the alpha among them. However, this particular set has a special property: orthogonality. If the contrasts are orthogonal and specified in advance, there is no need for an adjustment to alpha.
6
Checking for orthogonality Multiply the corresponding coefficients of each pair of contrasts. If the products sum to zero, the pair is orthogonal. Here, we are considering (1, 1, -2) and (1, -1, 0). (1×1) + (1×-1) + (-2×0) = 0, so the pair is orthogonal.
7
Why is orthogonality special? Contrast coding Illustration in SAS So orthogonal contrasts divide the model sum of squares into exhaustive and mutually exclusive partitions. A more complicated example (Eysenck memory experiment)
8
Introducing power In the world of hypothesis testing, one of two things is true: –The null hypothesis may be true; or –The null hypothesis may be false. In the world of hypothesis testing, one of two outcomes will occur: –The null hypothesis may be rejected; or –The null hypothesis may be retained.
9
Consider that in tabular form: H 0 TrueH 0 False H 0 Rejected H 0 Retained
10
Consider that in tabular form: H 0 TrueH 0 False H 0 RejectedGreat! H 0 Retained
11
Consider that in tabular form: H 0 TrueH 0 False H 0 RejectedGreat! H 0 RetainedNo problem.
12
Consider that in tabular form: H 0 TrueH 0 False H 0 RejectedType I errorGreat! H 0 RetainedNo problem
13
Consider that in tabular form: H 0 TrueH 0 False H 0 RejectedType I errorGreat! H 0 RetainedNo problemType II error
14
Consider that in tabular form: H 0 TrueH 0 False H 0 Rejected Type I error (p = Great! H 0 RetainedNo problemType II error
15
Consider that in tabular form: H 0 TrueH 0 False H 0 Rejected Type I error (p = Great! H 0 RetainedNo problem Type II error (p =
16
What is power? In that scenario, power = 1 – In other words, power is the probability that we will avoid a Type II error, given that the null hypothesis is actually false.
Similar presentations
© 2025 SlidePlayer.com. Inc.
All rights reserved.