Psychology 320: Psychological Statistics

Professor: Howard B. Lee

Lecture Notes

Week 12 : Chapter 10

Multiple comparisons with Scheffe and Tukey :

Group 1	Group 2	Group 3	Group 4
m1 = 13.4	m2 = 18.47	m3 = 10.36	m4 = 20.50
n = 15	n = 15	n = 14	n = 10

* Remember that for absolute values you must ignore the sign of the resulting subtraction.

D12 = /M1 - M2/ = /13.4 - 18.47/ = 5.07
D13 = /M1 - M3/ = /13.4 - 10.36/ = 3.04
D14 = /M1 - M4/ = 13.4 - 20.50/ = 7.1*
D23 = /M2 - M3/ = /18.47 - 10.36/ = 8.11*
D24 = /M2 - M4/ = /18.47 - 20.50/ = 2.03
D34 = /M3 - M4/ = /10.36 - 20.50/ = 10.14*

The "*" means that the number is significant.
To determine which absolute mean differences are significant, develop the Tukey critical value. Refer to page 318, top of page in your book.

If n1 = n2 = n3 = n4 = 15, then n = 15, but this is not the case.

The following are not equal "n"s:
n1 = 15
n2 = 15
n3 = 14
n4 = 10
To handle this, compute Nh (the harmonic mean) using formula on page 318.

MSW = 32.1 from ANOVA table.

This says that if any D value is > or = 5.8884, then those means are statistically different (significant).
There is a significant difference between 1 and 4, 2 and 3, and 3 and 4.
Therapy in group 4 is the best therapy.

The Scheffe test is the most conservative. If there is a difference shown here, then all other multiple comparisons tests will find the same thing (for ex.Tukey).

Two Way ANOVA:

With Two Way ANOVA you are studying two independent variables at the same time.

Ex.
A = 1st IV = sex differences
B = 2nd IV = test anxiety
(* the IVs are non-manipulated, the levels of IV pre-exist)
AB = "interaction"

Dosages--->high, low (these are manipulated IVs).
Type of instruction--->clean, ambiguous (these are also manipulated IVs).

Ex. A classic study in Psychology: (1 IV)
Large lecture classroom.
Instruct class that they will get a "guest speaker".
Pass out a description of the speaker (2 different forms). One form said that the speaker's personality was "cold". The other form said that the speaker's personality was "warm".
Asked students after the lecture for their opinion of the speaker.
Just by varying (manipulating) one word the outcome was changed.

ANOVA Summary Table:

Verbally stated conclusions...

For A:

• ho: There is no difference between the words "cold" and "warm" on attitude response.
  
• h1: There is a difference between the words "cold" and "warm" on attitude response.
  

For B:

• ho: There is no difference in attitude responses between males and females.
  
• h1: There is a difference in attitude responses between males and females.
  

For AB:

• ho: There is no interaction effect.
  
• h1: There is an interaction effect.
  

Ex. An interaction effect is where males would get "cold" form and give a more positive attitude than males who get "warm" form and females would get "cold" form give a more negative response than females who get "warm" form.

---

source	df	ss	ms	F
A effect
B effect
AB effect
Error (within/residual)
Total