PSYC 333 Lecture Notes - Lecture 4: F-Test, Histogram, Multiple Comparisons Problem
7 May 2018
School
Department
Course
Professor
PSYC 305 – STATISTICS FOR EXPER DESIGN, WINTER 2018
Lecture 4: One-Way ANOVA II
Midterm Exam will be on MARCH 1ST, Thursday, from 11:40 am to 12:30 pm.
One-Way ANOVA
Purpose:to test whether the means of k (≥ 2) populations significantly differ.
• H0: μ1 =μ2···=μk
• H1: Not all μ’s are the same (at least one of the means is different)
(not all of these means are the same is all you can say (don’t say “ALL of them are different
from one another”)
Example: One-Way ANOVA
A statistics classroom is divided into three rows: front, middle, and back.
The instructor noticed that the further the students were from him, the more likely they
were to miss class or use an instant messenger during class.
He wanted to see if the students further away did worse on the exams.
A random sample of the students in each row was taken.
The scores for those students on the mid-term exam were recorded:
• Front: 82, 83, 97, 93, 55, 67, 53
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PSYC 305 – STATISTICS FOR EXPER DESIGN, WINTER 2018
• Middle: 83, 78, 68, 61, 77, 54, 69, 51, 63
• Back: 38, 59, 55, 66, 45, 52, 52, 61
DV = Exam score
Factor (IV) = Class row
Three levels: front, middle, & back
• H0: μ1 =μ2=μ3
• H1: Not all μ’s are the same
This is the basic one-way ANOVA table
Source
SS
df
MS
F
Between
1901
2
950.5
5.9
Within
3386
21
161.2
Total
5288
23
• In this example, the critical value for α = .05 is 3.47 with df(B) = 2 and df(W) =
21. F(.05, 2, 21) = 3.47
• The null hypothesis may be rejected because your F value (5.9) > 3.47.
• We may thus conclude that where students sit in the stat. class has a significant
effect on their mid-term exam scores (F (2, 21) = 5.9, p < .05). Also this effect is
large (ω = .54).
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PSYC 305 – STATISTICS FOR EXPER DESIGN, WINTER 2018
When the null hypothesis is rejected in ANOVA, it suggests that there is at least one
pair of group means is different.
Then, we may want to know which pairs of group means are significantly different.
μ1 ≠ μ2
μ1 ≠ μ3 μ2
≠ μ3
• F-test gives a global effect of the independent variable (factor) on the dependent
variable (omnibus or overall test)
▪ doesn’t tell which pairs of means are different. We need to perform post hoc
comparison tests to determine this.
▪ Post hoc (a posteriori/unplanned) comparisons Decided upon after the
experimentUsed if three or more means were compared
so if K =3
Ho: M1=M2=M3 (F— Reject) — then need to apply POST HOC
then look at each pair of two means at a time (So here we have K=3 (So # of pairs = (K
x (K-1) / 2
So…
Ho: M1=M2
Ho: M1=M3
Ho: M2=M3
so 3 null hypotheses, and apply Post hoc tests for each pair.
Post Hoc Comparisons
We will focus on two post-hoc comparison tests:
Scheffé
Tukey’s Honestly Significant Difference (HSD) test
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find more resources at oneclass.com
Document Summary
Midterm exam will be on march 1st, thursday, from 11:40 am to 12:30 pm. A statistics classroom is divided into three rows: front, middle, and back. The instructor noticed that the further the students were from him, the more likely they were to miss class or use an instant messenger during class. He wanted to see if the students further away did worse on the exams. A random sample of the students in each row was taken. The scores for those students on the mid-term exam were recorded: front: 82, 83, 97, 93, 55, 67, 53. Psyc 305 statistics for exper design, winter 2018: middle: 83, 78, 68, 61, 77, 54, 69, 51, 63, back: 38, 59, 55, 66, 45, 52, 52, 61. Three levels: front, middle, & back: h0: 1 = 2= 3, h1: not all "s are the same. Also this effect is large ( = . 54).
