Unit 3 Outline

1
Unit 3 Outline

• Day 1 Introduce F
• Return Tests (20)
• Power (20)
• Matching variance with data, ranking Fs (20)
• SPSS Example (15) up to F value
• Day 2 Clean-up F Practice F in class
• Finish SPSS Example (10)
• Post-hoc, alternative outcomes, practical
  significance (15)
• Explain where F comes from (15)
• Hypothesis Testing Steps
• ANOVA Example 2 (20)
• Practice conducting ANOVAs and writing up. (Dep.
  Therapies)
• Homework Explain.Write up 1 ANOVA outcome
  (Typing) two outcomes.
• Day 3 Write-ups Fs, Team Events
• Review Homework (10)
• Understanding F ratio curves on graph paper
  (15)
• Pick the stat (20)
• Regression Review (30)
• Day 4 Practice test selection write-ups

2
Lecture Overview on ANOVA

• Review
• hypothesis testing inferential statistics
• z-test, t-test, independent dependent t-test
• New Stuff
• Power Ability to reject Ho
• ANOVA
• Analysis of Variance
• Done with 3 or more groups
• Playground Exercise
• Complete SPSS Example

3
Power

• Review Hypothesis Testing Errors
• Wrongly rejecting Ho Chance of Type I error a
• Wrongly retaining Ho Chance of Type II error ß
• Power
• Opposite of ß
• Power 1- ß
• Ability to reject Ho (when Ho should be
  rejected).
• Researchers want Power!
• Want ability to reject Ho Show you were right
  to suspect a difference.
• Want to show IV affects your DV.

4
Error Areas

• a area (where we reject the Ho, and we shouldnt)
• beyond tcritical
• under Ho

• ß area (where we retain the Ho, and we shouldnt)
• inside tcritical
• under Ha

Ho µ55
Ha µgt55
5
Increasing Power

• 1 Increase Treatment Increase difference
  between groups (µs)

6
Examples of increasing power

• Rat Study IVCaffeine Level DVAmt. Food
  Found
• Therapy Study IVTherapy (drug, talk,
  drugtalk, or control) DV Improvement

• 1 Increase Treatment Effect
• (Increase BG differences)
• Rat study
• 0,3,or 6 mg
• 0,10,or 20 mg
• Therapy study
• 10 therapy sessions
• 1 therapy session

• 2 Decrease Sampling Error
• (Decrease WG differences)
• Rat study
• Different strains of rats
• Same strain of rat
• Rats allowed to eat freely
• Rats all unfed for 24 hours
• Therapy study
• Diff. types of Therapy
• Same type of Therapy

7
1-Way ANOVA

• ANOVA
• Analysis of Variance
• 1-way means 1 Independent Variable (IV)
• Purpose
• ANOVA allows hypothesis testing with 3 sample
  means
• Imagine study on interventions to help frosh make
  friends
• Three IV levels Standard courses, interactive
  courses, clustered courses.

• ANOVA uses F-test
• Strategy Compare variability within group to
  variability between groups.
• F is ratio between two values

8
ANOVA Playground
(Download from Website)
9
Matching Exercise
10
Playground Exercises

• Do the following and record what happens to F

Make the means (approximately) 2, 4, and 6 without changing the WG variability.
Now double the WG variability, trying to keep the means about the same (2,4,6).
Now change the means to approximately 6, 4, 2.
Now change the means to approximately 12, 7, and, 2.

• Play with the following
• Make F as big as possible.
• Make F as close to 1 as possible.

11
Draw Conclusions from Playground

• What does a large F mean?
• What two things will make F large?

12
Partitioning Variance

• Partition
• fancy word for divide up
• ANOVA partitions variance (MS means variance)
• Types of variance
• Total variance MSWG MSBG
• MSWG sampling error (background noise)
• MSBG sampling error treatment (includes
  effect of Independent Variable)

• If just error ? F tends toward 1.0
• If treatment effect? F gets larger

13
Example of 1-way ANOVA

• Studying effect of caffeine on productivity
• Does caffeine help or hurt?
• IV Level of Caffeine 0, 10, 20 mg
• DV Number of Food Pellets Found

0 mg 10 mg 20 mg
2 3 1 4 2 1 2 3 1 2 4 4 4 4 5 5
Number of Food Pellets Found
14
SPSS Data Entry
IV
DV
Label levels of IV so output is easier to read.
15
SPSS Analysis

• Go to Analyze, Compare Means, select One-way
  ANOVA

Put DV here.
Put IV here.
16
SPSS Analysis, Part 2
Select this to get descriptive statistics like
sample means standard deviations.
Alpha level still set to .05, just like it was
with t-tests.
Gives you a line graph of the sample means
Conducts after the fact test to compare all
pairs of sample means.
17
SPSS Output
Sample means from 3 groups, plus mean amount of
food found overall.
Source of Variation Table
18
Where does F come from?

• MSWG SSWG/dfWG Sum of Squares / degrees of
  freedom
• MSBG SSBG/dfBG Sum of Squares / degrees of
  freedom
• Degrees of freedom
• dfWG NT K (Total of
  subjects - of groups)
• dfBG K-1 ( of groups
  1)
• dfTOTAL NT 1 (Total of subjects
  1)
• Expectations
• If I give you df and SS, you can calculate F
• You dont have to get any SS by hand.

19
SPSS Output Post Hoc Test
No Sig. Diff. Between 0 10mg
Rats at 20 mg found significantly more food than
rats on 0 or 10 mg of caffeine.
20
SPSS Output Practical Significance

• ?2 (eta squared)
• Effect size statistic indicates of variance
  explained
• Measures impact of IV on DV
• We can explain 68 of the variance in how much
  food a rat finds if we know the level of caffeine.

21
Hypothesis Testing Steps

• Comparison cf. three sample means.
• Hypothesis Ho µ1 µ2 µ3 Ha Not all
  µs equal
• Set-up a .05 , dfbg K-1 2, dfwg NT-K
  16-313, Fcrit 3.80
• Fobt 13.653
• Reject Ho.
• The hypothesis was largely supported. Rats found
  sig. more food on 20mg of caffeine (M4.33) than
  on 0mg (M2.40) or 10mg (M1.80), F(2,13)
  13.653, p lt.05. Caffeine has a large effect on
  food finding behavior, accounting for about 68
  of the variance, ?2 .6775.

22
F-table
df Between Groups
df Within Groups
23
Lab 8 1-way ANOVA

• TV Problem The hypothesis was supported. Light
  TV users provided more community service (M
  6.13) than did moderate users (M 4.00), who
  provided more than heavy users (M 1.75),
  F(2,21) 15.963, p .05. TV accounts for about
  60 of the variance in community service, ?2
  .6032.

24
Follow-up Questions

• Q1 Variance within group? MSwg 2.399
• Q2 Variance between groups? MSbg38.292
• Q3 Replacing heavy scores with 4,5,4,5,6,5,4,3
  would decrease the difference between groups
  because the heavy users would then difference
  less from the other groups.
• Q4 Decreasing between group differences
  (decreasing treatment) would decrease F.

25
Problem 2 Post Hoc Explanation
26
Problem 2 Post Hoc Explanation
27
Problem 2

• The hypothesis was supported. People commuting 0
  minutes participated significantly more (M3.4
  hours) than people commuting 45 (M1.2) or 60
  minutes (M1.6), F (3,16) 7.256, p.05.
  Commuting accounted for a large amount of
  variance in community involvement, ?2 .5764.

28
Follow-up Questions

• Q1 Variance within group? MSwg .650
• Q2 Variance between groups? MSbg4.717
• Q3 Replacing 30 minute commuting scores with
  1,4,1,4,3 would increase the within group
  variability.
• Q4 Increasing sampling error would decrease F.

29
Review Partitioning

• Study Does alcohol affect reaction time?

• Identify the treatment effect in this case.
• Explain how sampling error might arise.

No Alcohol 2 Beers 4 Beers
10 15 20
20 25 15
15 30 30
10 20 40
14 23 26
Sample Means
30
One-Way ANOVA

• Part 2!!

31
Review Partitioning

• Study Does alcohol affect reaction time?

• What accounts for variability within groups?
• What accounts for variability between groups?
• Whats the Formula for F?

No Alcohol 2 Beers 4 Beers
10 15 20
20 25 15
15 30 30
10 20 40
32
Review Partitioning

• If the alcohol content of the beers is not held
  constant, what happens?
• error increases
• error decreases
• treatment effect increases
• treatment effect decreases

• Study Does alcohol affect reaction time?

No Alcohol 2 Beers 4 Beers
10 15 20
20 25 15
15 30 30
10 20 40

• If the alcohol content of the beers is not held
  constant, what happens to F?
• increases
• decreases
• neither

33
Hypothesis Testing Steps

• Comparison cf. three sample means.
• Hypothesis Ho µ1 µ2 µ3 Ha Not all
  µs equal
• Set-up a .05 , dfbgK-13-12,
  dfwgNT-K12-39, Fcrit 4.26
• now do one-way ANOVA on SPSS

34
SPSS Output - Charts
35
SPSS Output - Graphs
36
Hypothesis Testing Steps

• Comparison cf. three sample means.
• Hypothesis Ho µ1 µ2 µ3 Ha Not all
  µs equal
• Set-up a .05 , dfbgK-13-12,
  dfwgNT-K12-39, Fcrit 4.26
• Fobt 2.633
• Retain Ho.
• The hypothesis was not supported. The reaction
  times following no alcohol (M13.75), two beers
  (M22.50), and four beers (M26.25) did not
  differ significantly, F(2,9) 2.633, n.s..

37
Numb. of Words Recalled Dataset A
4 8 12
5 9 10
4 9 11
5 8 12

• Bet. Group Varib L M H
• MSbg _______
• With. Group Varib L M H
• MSwg _______

38
Numb. of Words Recalled Dataset B
8 4 10
9 5 12
9 5 11
8 4 12

• Bet. Group Varib L M H
• MSbg _______
• With. Group Varib L M H
• MSwg _______

39
Numb. of Words Recalled Dataset C
7 3 9
10 6 13
7 6 10
10 3 13

• Bet. Group Varib L M H
• MSbg _______
• With. Group Varib L M H
• MSwg _______

40
Numb. of Words Recalled Dataset D
7 6 7
10 8 7
7 6 12
10 10 12

• Bet. Group Varib L M H
• MSbg _______
• With. Group Varib L M H
• MSwg _______

41
Numb. of Words Recalled Dataset E
7 6 7
10 8 7
7 6 12
10 10 12
7 6 7
10 8 7
7 6 12
10 10 12

• Bet. Group Varib L M H
• MSbg _______
• With. Group Varib L M H
• MSwg _______

42
Numb. of Words Recalled Dataset F

• Bet. Group Varib L M H
• MSbg _______
• With. Group Varib L M H
• MSwg _______