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Group comparisons: Intro to factorial design

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Eg, before and after treatment (or pre/post) ... IV=viewing nature video. Level 1: test score pre-video. Level 2: test score post-video ... – PowerPoint PPT presentation

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Title: Group comparisons: Intro to factorial design


1
Group comparisonsIntro to factorial design
  • 3143/Josh Rodefer, Ph.D.

2
Previously (?)
  • Experimental design
  • Design Between vs Within
  • Compare 2 groups (t test different types)
  • Paired (within repeated measures)
  • Unpaired (between)
  • Control confounds
  • Extraneous variables (random vs systematic)
  • How to control or minimize?

3
Basic issues in experimental
  • What do you need for an experiment?
  • An independent variable (what the researcher
    varies minimally 2 groups)
  • Equal assignment to groups (lots of ways to do
    this)
  • Controlling extraneous variables (alternative
    explanations confounds)

4
Hypothesis testing 2 samples
  • Want to test relationship between the means
  • Use a t-test
  • Used when you have 2 levels of 1 IV
  • Dependent samples (1 sample, tested twice)
  • Independent samples (2 different samples)
  • aka Within- (dependent) and Between (independent)
    designs

5
Hypothesis testing 2 samples
  • Dependent samples (Within)
  • Eg, before and after treatment (or pre/post)
  • 20 people tested on attitude towards recycling
    after watching nature video
  • IVviewing nature video
  • Level 1 test score pre-video
  • Level 2 test score post-video
  • DV score on test
  • 2 samples, same people in each sample

6
Hypothesis testing 2 samples
  • Independent samples (between)
  • 2 scores are taken, but from different groups 2
    independent samples (random)
  • Eg, study effects of age on swearing
  • 20 ten yr olds and 20 fifteen yr olds, record
    swearing in 2 hr period
  • IVage
  • Level 1 10 yrs old
  • Level 2 15 yrs old

7
More than 2 groups ANOVA
  • Analysis of Variance
  • Tests the differences between treatment groups
    (conditions) to see if they are significant
  • Look at variance in DV, partition it into 2
    components
  • variance due to IV (good)
  • variance due to error (bad extraneous variables)
  • Asks if the ratio (IV variance/error variance)
    between the two types of variance is greater than
    would be expected due to chance (or equal or
    about 1.00)
  • F test examines this ratio

8
ANOVA when to use?
  • One IV at least 3 conditions
  • Between subjects One-way ANOVA
  • Eg, effect of psychiatric diagnosis (depression,
    panic, no disorder) on memory
  • Within subjects Repeated measures ANOVA
  • Eg, experiment where subjects experience all
    conditions example Stroop effect, colors/words
  • Two (or more) IVs
  • Factorial ANOVA
  • Effect of psychiatric diagnosis on Stroop effect
    multiple IVs

9
First One way ANOVA
  • One IV 3 (or more conditions)
  • Single test
  • Tests Null that all group means are equal
  • Alternative all group means are not equal
  • Null must be non-directional (vs t test
    directional)
  • Between subjects ANOVA
  • Analogous to independent samples t-test
  • (stats trivia In fact.if you have 2 independent
    groups, then Ft2)

10
One way ANOVA
  • Why not just perform 3 t-tests?
  • Psychiatric diagnosis memory example
  • Depression vs panic disorder
  • Depression vs no disorder
  • Panic disorder vs no disorder
  • Same thing, right?

11
One way ANOVA
  • Multiple tests result in an inflated alpha
  • Alpha for each test 0.05 (risk for Type I)
  • If you do 3 tests, then each is at 0.05 and they
    are additive
  • Thus, doing 3 t-test increases the
    experiment-wise Type I error rate from 0.05 to
    0.15 (not acceptable)
  • Must use ANOVA to test all combinations
    simultaneously, keeping alpha at 0.05

12
One way ANOVA
  • So, we can calculate the total variance and
    determine how much is due to IV and how much is
    error
  • F ratio variance due to IV /error variance
  • Variance due to IV is called MSB (Mean square
    between groups)
  • Variance due to extraneous variables or error is
    called MSW (Mean square within groups)
  • F test formula F MSB/MSW

13
ANOVA
  • Most data sets have both error variance and
    variance due to the IV (or, both between and
    within group variability)
  • We want to know if the between group variance is
    due to a true effect of the IV (is this effect
    real?)
  • FMSb/MSw
  • If F about 1, then no effect of IV
  • If F 1 then may have an effect of IV (need to
    look up value on F table, depends on critical F
    and df)

14
Factorial ANOVA 2 way designs
  • Have 2 (or more) IVs in the same experiment eg,
    test effects of gender and age on humor
  • IV gender (M/F)
  • IV age (10, 20, or 30 yrs old)
  • DV freq of laughing during comedy show
  • Why not conduct 2 separate experiments?
  • Gender on humor age on humor

15
Factorial ANOVA 2 way designs
  • Why do you want to look at 2 IVs?
  • More efficient study factor A then study factor
    Boryou could study them together
  • More interesting can see how things relate
    together
  • More representative of the real world

16
Factorial designs
  • Have 2 (or more) IVs
  • Each IV is called a factor
  • Each factor has at least 2 levels/conditions
  • The design must be complete each level of one IV
    must occur with each level of the other IV(s)
  • Described as 2x2 or 3x5 or2x3x4
  • Terminology Factors/Main effects levels cells
  • Can be experiment or quasi-experiment (whats
    quasi?)

17
Factorial designs
  • Example examine effect of sleep and caffeine on
    reaction time study
  • IV-1 Sleep 2 hrs vs 8 hrs
  • IV-2 Caffeine zero (water) vs 3 Cokes
  • DV computer game reaction time
  • Both IVs are between subjects variables

18
Factorial design
  • Randomly select subject for each condition equal
    cell sizes
  • 2 IVs test for 3 effects
  • 2 Main effects (effects of sleep and caffeine)
  • 1 interaction (interaction of sleep caffeine)
  • Thus, 3 null hypotheses, 3 alternative
    hypotheses, and 3 F tests

19
Factorial designs
  • Main effect
  • The effect of one factor (IV) collapsed across
    levels of the other factor (IV) (ie, you ignore
    the other IV)
  • Test one main effect for each factor (IV)
  • Need to analyze statistics to check for
    significance

20
Factorial design Main effect graphic
8 hrs
2 hrs
0 Cokes
3 Cokes
Did different amounts of sleep have an effect?
Mean of 2 hrs
Mean of 8 hrs
21
Factorial design Main effect graphic
8 hrs
2 hrs
0 Cokes
Mean of 0 Cokes
3 Cokes
Mean of 3 Cokes
Did different quantities of Coca-cola have an
effect?
22
Post hoc tests
  • Post hoc means after the fact
  • Tests that are performed after finding a
    significant effect (sig F value)
  • ANOVAs tell you if there is a difference, but
    they dont tell you where it is
  • Post hoc tests answer that question

23
Post hoc tests
  • Would you need a follow up post hoc test after a
    significant t-test?
  • Would you need to follow up a significant F-test
    where there are 3 levels of the IV with a post
    hoc test (say, for the sleep experiment you used
    2, 4 or 8 hrs of sleep as three different levels
    of the IV).

24
Post hoc tests
  • So, need to use post hoc tests when
  • You have 3 or more means
  • You have a significant difference with a
    general/omnibus test (F test)
  • Post hoc tests (pairwise comparisons) examine all
    possible combinations of means

25
Post hoc tests
  • Many types Tukeys HSD (honestly significant
    difference), Bonferroni, Scheffes,
    Kruskal-Wallis, Dunnetts
  • Each tests pairwise hypotheses
  • Each calculates a particular statistic that
    resembles a t-test (but it isnt that simple)

26
Post hoc tests
  • Consider the 3 level IV, where you find a
    significant F value
  • Next need to assess all possible pairwise
    comparison
  • Mean 1 /diff mean 2
  • Mean 1 /diff mean 3
  • Mean 2 /diff mean 3
  • Compute pairwise comparison for each
    testascertain where the difference(s) are
    statistically significant

27
Next time
  • More factorials interactions

28
Previously -- 2nd Lecture
  • Experimental design (Between vs Within)
  • Compare 2 groups (paired vs unpaired)
  • Control confounds (random vs systematic)
  • ANOVAs (3 or more groups)
  • Do overall F tests
  • Pairwise compartions (post hoc tests)
  • (like t tests done after significant F tells
    you where the difference is that is, which two
    means are significantly different from each other)

29
ANOVA when to use?
  • One IV at least 3 conditions
  • Between subjects One-way ANOVA
  • Eg, effect of psychiatric diagnosis (depression,
    panic, no disorder) on memory
  • Within subjects Repeated measures ANOVA
  • Eg, experiment where subjects experience all
    conditions example Stroop effect, colors/words
  • Two (or more) IVs
  • Factorial ANOVA
  • Effect of psychiatric diagnosis on Stroop effect
    multiple IVs

30
Factorial designs
  • Have 2 (or more) IVs
  • Each IV is called a factor
  • Each factor has at least 2 levels/conditions
  • The design must be complete (sometimes called
    completely crossed) each level of one IV must
    occur with each level of the other IV(s)
  • Described as 2x2 or 3x5 or2x3x4
  • Can be experiment or quasi-experiment

31
Factorial designs
  • Example examine effect of sleep and caffeine on
    reaction time study
  • IV-1 Sleep 2 hrs vs 8 hrs
  • IV-2 Caffeine zero (water) vs 3 Cokes
  • DV computer game number correct
  • Both IVs are between subjects variables

32
Factorial design
  • Randomly select subject for each condition equal
    cell sizes
  • 2 IVs test for 3 effects
  • 2 Main effects (effects of sleep and caffeine)
  • 1 interaction (interaction of sleep caffeine)
  • Thus, 3 null hypotheses, 3 alternative
    hypotheses, and 3 F tests

33
Factorial designs
  • Main effect
  • The effect of one factor (IV) collapsed across
    levels of the other factor (IV) (ie, you ignore
    the other IV)
  • Test one main effect for each factor (IV)

34
Factorial designs
  • Interactions are a way to qualify findings
  • Revisit coke and sleep study

8 hrs
2 hrs
0 Cokes
3 Cokes
35
Factorial Design
  • Calculate cell means and plot

2 hrs
8 hrs
0 Cokes
3 Cokes
36
Factorial Design
  • Calculate cell means and plot

2 hrs
8 hrs
0 Cokes
3 Cokes
What does the parallel shift suggest to you?
37
Factorial Design
  • Calculate cell means and plot

2 hrs
8 hrs
0 Cokes
3 Cokes
38
Factorial Design
  • Calculate cell means and plot

2 hrs
8 hrs
0 Cokes
3 Cokes
Spreading interaction (aka ordinal) usually at
least one main effect
39
Factorial Design
  • Calculate cell means and plot

2 hrs
8 hrs
0 Cokes
3 Cokes
But what about if we plotted this differently?
40
Factorial Design
  • Calculate cell means and plot

2 hrs
8 hrs
0 Cokes
3 Cokes
41
Factorial Design
  • Calculate cell means and plot

2 hrs
8 hrs
0 Cokes
3 Cokes
Cross-over interaction (aka disordinal) opposite
effects of IV1 at different levels of IV2
usually no main effects, but still can have
interaction (!)
42
Interactions
  • So look at main effects
  • Look for interactions
  • Graphing things helps
  • parallel lines no interactions
  • crossing or close to crossing lines interaction
  • But ultimately you need stats and p values to
    make judgement about significance

43
Factorials
  • So with 2 Independent variables you can have
    multiple types of designs
  • Both IV are within
  • Both IV are between
  • One IV is within and one IV is between
  • Also can have 1 true IV, and 1 quasi-IV
    (sometimes called mixed or experi-corr)
  • Lets you consider unmanipulated factors like
    subject variables (sex, age, diagnoses, etc.)
  • The more correlational something is, the more
    external validity (and less internal validity)
    you have

44
Within designs
  • Simple 2 group comparison or ANOVA, doesnt
    matter.
  • Limitations?
  • How to fix?

45
Counter balancing schemes
  • Reverse order of group presentation (AB vs BA)
    but remember ANOVA usually have more conditions
  • Gets complicated quickly.
  • Consider a within subjects design IV that has 4
    levels, how many different orders of conditions?

46
Counter balancing schemes
  • Reverse order of group presentation (AB vs BA)
    but remember ANOVA usually have more conditions
  • Gets complicated quickly.
  • Consider a within subjects design IV that has 4
    levels, how many different orders of conditions?
  • ABCD

47
Counter balancing schemes
  • Reverse order of group presentation (AB vs BA)
    but remember ANOVA usually have more conditions
  • Gets complicated quickly.
  • Consider a within subjects design IV that has 4
    levels, how many different orders of conditions?
  • ABCD, ABDC,

48
Counter balancing schemes
  • Reverse order of group presentation (AB vs BA)
    but remember ANOVA usually have more conditions
  • Gets complicated quickly.
  • Consider a within subjects design IV that has 4
    levels, how many different orders of conditions?
  • ABCD, ABDC, ACBD,

49
Counter balancing schemes
  • Reverse order of group presentation (AB vs BA)
    but remember ANOVA usually have more conditions
  • Gets complicated quickly.
  • Consider a within subjects design IV that has 4
    levels, how many different orders of conditions?
  • ABCD, ABDC, ACBD, ACDB, ADBC, ADCB
  • BCDA, BCAD, BDAC, BDCA, BACD, BADC
  • CDAB, CDBA, CABD, CADB, CBAD, CBDA
  • DABC, DACB, DBAC, DBCA, DCAB, DCBA

50
Counterbalancing
  • Too confusingmore simple way is a Latin Square
    design
  • Number conditions number of orders
  • Each condition appears at each position only once

C
D
A
B
1st condition
2nd condition
3rd condition
4th condition
51
Fancy control groups
  • Might be possible that the IV isnt all that is
    involved in a particular effect
  • Other factors (timing, duration, pairing with
    other events) may be critical
  • How to control? A Yoked control group
  • The yoked control subject is paired directly with
    an experimental subject (matching of experiences
    in a way)

52
Summary
  • How many IVs?
  • 1 IV, 2 group/levels t-test
  • Paired (subjects serve in both conditions) vs
    Unpaired (different subjects in both conditions)
  • 1 IV, 2 groups/levels one-way ANOVA
  • 2 IV two-way ANOVA (factorial design)
  • Do subjects serve in only one condition?
  • Yes between-subjects design (aka independent)
  • No within-subjects design (aka repeated
    measures, aor dependent)
  • Yes and No mixed between/within combo design
  • Main effects (did the IV have an effect?)
    interactions (was the effect dependent upon
    different levels of the other IV?)
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