Psychology 320: Psychological Statistics

Professor: Howard B. Lee

Lecture Notes

Week 13 : Chapter 10

Two Way ANOVA:

A separate null and alternative hypothesis is written for each IV. There is also a null hypothesis for the interaction. Therefore, in a two way ANOVA there are 3 null hypotheses. One for A effect, another for B effect and one for the interaction effect (A x B or AB).

A effect = "rows effect"
B effect = "column effect"
A x B effect = "rows x columns effect"

For A:
ho: u1 = u2 (this depends on the number of levels of A)
h1: There is at least one pair statistically different.

For B:
ho: u1 = u2 = ... (this depends on the number of levels for B)
h1: At least one pair of means is statistically different.

For AB:
ho: uAB = 0 (no interaction)
h1: uAB is not = 0 (there is a significant interaction)

4 Steps of Hypothesis Testing:

1. null hypothesis
2. alternative hypothesis
3. test statistic
4. decision rule

Since you have 3 null hypotheses and 3 alternative hypotheses, you have 3 test statistics and 3 decision rules!

The test statistics in a two way ANOVA is put in the form of an ANOVA summary table.

source	df	ss	ms	F (3 test statistics)
A (rows)	# levels of A - 1	ssA	ssA/dfA	msA/ms within
B (columns)	# levels of B - 1	ssB	ssB/dfB	msB/ms within
AB (rows x columns)	(dfA)(dfB)	ssAB	ssAB/dfAB	msAB/ms within
Within (error, residual)	N - (# levels of A)(# levels of B)	ss within	ss within/df within
Total	N - 1	ss total

The smallest number you can ever have with variance is zero. You should never see a value of less than zero. In ANOVAs, this holds true. There are no negative numbers!!!

The hardest part in constructing this table is the computing he SS.

Page 335:
3 different instructors: A, B, C/ 3 levels of one IV (column)
2 different teaching methods: discussion, lecture/ (row)

10 different people in each group.
Each subject/participant receives only one combination of A and B.
Every level of one IV is crossed with every level of the second IV. This is called a Factorial Design.
A "2 x 3 factorial design" means that there are 2 levels of IV1 (rows), 3 levels of IV2 (columns), and a total of 6 groups.
With a 4 x 3 factorial design you have 12 groups and 2 IVs.
With a 2 x 2 x 2 factorial design you have 3 IVs, and 7 null hypotheses.

What is the group number for?
The first level of IV # 1 combined with the 2nd level of IV # 2 = ?

Total ss = (SD)squared(N)
Enter in every value, find SD, square it, then multiply by N.
ssA
TA1 = 10 + 13 + 12 + 2 + .... + 12 +13 = 365.
(row 1 total)
TA2 = 18 + 15 + .... + 8 + 12 = 304.
(row 2 total)