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ANOVA2 example1 with simple main effects.pdf

Y502 – Two-Way ANOVA 1

Two-Way Analysis of Variance

Betw een-Subjects Factors

group

counseling 8

individual

counseling 8

refused

counseling 8

female 12

male 12

GROUP

GENDER

Value Label N

Descriptive Statistics

Dependent Variable: LIFESATI

9.2500 .5000 4

13.2500 1.5000 4

11.2500 2.3755 8

5.0000 1.1547 4

11.2500 2.9861 4

8.1250 3.9438 8

5.0000 .8165 4

3.0000 .8165 4

4.0000 1.3093 8

6.4167 2.2344 12

9.1667 4.9696 12

7.7917 4.0215 24

GENDER

female

male

Total

female

male

Total

female

male

Total

female

male

Total

GROUP

group counseling

individual counseling

refused counseling

Total

Mean Std. Deviation N

Levene's Test of Equality of Error Variancesa

Dependent Variable: LIFESATI

3.939 5 18 .014

F df1 df2 Sig.

Tests the null hypothes is that the error variance of the

dependent variable is equal across groups.

Design: Intercept+GROUP+GENDER+GROUP

* GENDER

Y502 – Two-Way ANOVA 2

Tests of Be tw een-Subjects Effects

Dependent Variable: LIFESATI

329.708a 5 65.942 28.093 .000 .886

1457.042 1 1457.042 620.751 .000 .972

211.583 2 105.792 45.071 .000 .834

45.375 1 45.375 19.331 .000 .518

72.750 2 36.375 15.497 .000 .633

42.250 18 2.347

1829.000 24

371.958 23

Source

Corrected Model

Intercept

GROUP

GENDER

GROUP * GENDER

Error

Total

Corrected Total

Type III Sum

of Squares df Mean Square F Sig.

Partial Eta

Squared

R Squared = .886 (Adjusted R Squared = .855)a.

Estimated Marginal Means

1. GROUP

Dependent Variable: LIFESATI

11.250 .542 10.112 12.388

8.125 .542 6.987 9.263

4.000 .542 2.862 5.138

GROUP

group counseling

individual counseling

refused counseling

Mean Std. Error Low er Bound Upper Bound

95% Conf idence Interval

2. GENDER

Dependent Variable: LIFESATI

6.417 .442 5.487 7.346

9.167 .442 8.237 10.096

GENDER

female

male

Mean Std. Error Low er Bound Upper Bound

95% Conf idence Interval

3. GROUP * GENDER

Dependent Variable: LIFESATI

9.250 .766 7.641 10.859

13.250 .766 11.641 14.859

5.000 .766 3.391 6.609

11.250 .766 9.641 12.859

5.000 .766 3.391 6.609

3.000 .766 1.391 4.609

GENDER

female

male

female

male

female

male

GROUP

group counseling

individual counseling

refused counseling

Mean Std. Error Low er Bound Upper Bound

95% Conf idence Interval

Y502 – Two-Way ANOVA 3

Profile Plots

group counseling individual counseling

refused counseling

group

2.00

4.00

6.00

8.00

10.00

12.00

14.00

E s ti

m a te

d M

a rg

in a l M

e a n

gender

female

male

Estimated Marginal Means of lifesati

female male

gender

2.00

4.00

6.00

8.00

10.00

12.00

14.00

E s

ti m

a te

d M

a rg

in a

l M

e a

n s

group

group counseling

individual counseling

refused counseling

Estimated Marginal Means of lifesati

cars(1)(1).sav

Factorial ANOVA in SPSS.pdf

EDPSY 641: Factorial ANOVA in SPSS

Example of Two Way Factorial ANOVA

I am still looking for a car. However, I am now willing to consider buying a used (or as they like to call them “previously owned” car instead. I am curious about how the year the car was released as well as the make of the car impact the acceleration of the car.

I now have a situation for a Two way ANOVA because I have

1 Dependent Variable: Acceleration

2 Independent Variables:

 Country of Origin (3 levels) o American o European o Japanese

 Model Year (2 levels)

o Older than 1975 o Newer than 1975

Now that we have 2 IVs, we have the possibility to have 3 different types of effect:

 A main effect of Country of Origin  A main effect of Model Year  A Country of Origin*Model Year Interaction

Recall that the Assumptions for Factorial ANOVA are:

-Normality -Homogeneity of Variances -Indpendence -Scale of Measurement.

So we should be sure to check Normality and Homogeneity of Variances along with our analysis.

EDPSY 641: Factorial ANOVA in SPSS

We can obtain descriptive statistics and a histogram from the Analyze- Descriptives-Frequencies menu…

Judging by the histogram and the skew/kurtosis statistics we can assume Normality.

And we can check Homogeneity of Variances at the time of running the analysis. So we can go ahead and set up our Factorial ANOVA

To run a Factorial ANOVA click Analyze → General Linear Model →Univariate

EDPSY 641: Factorial ANOVA in SPSS

Time to Accelerate is our Dependent Variable

Our Independent Variables: Country of Origin and Model Year go in the Fixed Factors Box

We will want thing from the Plots, Post Hoc and Options Menus..

Click on Plots

Here you can build your interaction plots.

You can put one variable on the horizontal (X) axis and represent the other as separate lines. If you have a 3rd variable you can make separate plots for the 3rd variable.

Whenever you input variables, though you must click add before you move on or the plot will not run.

Click Continue then Click Post Hoc.

EDPSY 641: Factorial ANOVA in SPSS

If we do NOT have a significant interaction we will want to look at some form of post hoc test for the main effects. If you want to use all pairwise comparisons you can run those at the time of running the Factorial ANOVA.

You must tell SPSS which variables you want to run post hoc’s on First: Click those over into the Post Hoc Tests for box.

Now it will allow you to choose whatever test you want.

Click Continue then Click Options

Here there are a variety of options you may want. Probably most important to grab would be:

1. Descriptive Statistics 2. Homogeneity Tests

Click Continue then Click OK to run the analysis.

EDPSY 641: Factorial ANOVA in SPSS

Univariate Analysis of Variance

Between-Subjects Factors Value Label N

1 American 253 2 European 73

Country of Origin

3 Japanese 79 0

1975 or older 188 Model_year

1 Newer than 1975 217

This indicates we have violated the assumption of homogeneity of variances

EDPSY 641: Factorial ANOVA in SPSS

We have a significant interaction so we skip the main effects and only interpret the interaction

Remember we also asked for post hoc tests just incase we needed them. But since our interaction was significant we can ignore them.

EDPSY 641: Factorial ANOVA in SPSS

Factorial ANOVA.pdf

EDPSY 642 – Factorial ANOVA 1

Factorial Analysis of Variance

Two-way analysis of variance examines differences between means on a dependent variable when there are two independent variables (or factors) with two or more levels. Two-way analysis of variance is part of a family of designs called factorial designs. Types of Factorial Designs • Crossed vs. Nested Designs

• Between Subjects vs. Within Subjects Designs

• Fixed Effects vs. Random Effects Designs

• Categorical and Continuous Independent Variables

• Three-Way, Four-Way, N-way Factorial Designs

EDPSY 642 – Factorial ANOVA 2

As in one-way ANOVA the independent variables are qualitative or nominal variables. The dependent variable should be measured on an interval or ratio-scale. Assumptions Independence - scores on the dependent measure are randomly and independently sampled. Normality - scores on the dependent measure come from a population where scores are normally distributed. Equality of Variance – the independent samples of scores come from populations with equal variances. Scale of Measurement – scores on the dependent variable are measured on an interval or ratio scale. In large sample, ANOVA is generally robust to violations of normality, and homogeneity of variance assumptions.

EDPSY 642 – Factorial ANOVA 3

ANOVA Main Effects and Interaction

A factorial ANOVA allows consideration of the effect of multiple independent variables on the dependent variables in the same study Main effect – the effect of a single variable on the

dependent variable Interaction – the combined effect of the independent

variables on the dependent variable. There is an interaction when the effect of one independent variable depends on the level of the other independent variable

Lets design a study testing the impact of counseling type and gender on life satisfaction. The Sources of Variability are:

- the main effect for “counseling type” - the main effect for “gender” - the interaction “counseling type*gender - error (everything left unaccounted for)

EDPSY 642 – Factorial ANOVA 4

Null Hypotheses - Null hypothesis for factor A:

€

H0 :µ1 = µ2 = µ3 =… = µ j [there is no difference between the different levels of A]

- Null hypothesis for factor B:

€

H0 :µ1 = µ2 = µ3 =… = µk [there is no difference between the different levels of B]

- Null Hypothesis for interaction:

€

H0 : all(µ jk −µ j . −µk . + µ) = 0 [there is no difference between the interaction cell means that cannot be explained by the effect of A or the effect of B]

2 Independent Variables: 2-Way ANOVA Counseling Type: 3 levels Gender: 2 levels

Independent Variables

Dependent Variable: Life Satisfaction Group Counseling

males females

Individual Counseling

males females

Refused Counseling

males females

EDPSY 642 – Factorial ANOVA 5

Partitioning the Sums of Squares

SStotal Total Variability

SSwithin SSBetween Within-Groups Between-Groups Variability Variability SSA SSB SSA*B Variability Variability Variability due to A due to B due to A*B

Interaction

EDPSY 642 – Factorial ANOVA 6

Interpretation of Main Effect and Interaction If significant interaction:

⇒DO NOT interpret main effects

⇒plot interaction ⇒conduct tests of simple effects

⇒conduct multiple comparisons for interaction

A significant interaction means that at least one of the cell means is significantly different from the other ones – that is the effect of one factor (A) is different at different levels of the other factor (B).

If non-significant interaction: ⇒ interpret significant main effects ⇒conduct post hoc comparisons (e.g., Scheffé if more than two means involved) If significant results also report measures of association

€

(η2, ω 2 )and effect sizes.

EDPSY 642 – Factorial ANOVA 7

Tests of Simple Effects

A simple effect is defined as the effect of one factor at one level of the other factor. Tests of simple effects allow us to determine if we see the same differences for one factor at each level of the other factor. Each Simple Effect is calculated as a sum of squares

€

SSsimple effect = n X jk − X j .( )∑ 2

We simply calculate the SS using only the data for one factor. Example from Howell (2007) Eysenck Data

Condition

Age

Counting Rhyming Adjective Imagery Intention Mean Older 7.0 6.9 11.0 13.4 12.0 10.06 Younger 6.5 7.6 14.8 17.6 19.3 13.16 Mean 6.75 7.25 12.9 15.5 15.65 11.61

Source df SS MS F Age (A) 1 240.25 240.25 29.94* Condition (C) 4 1514.94 378.735 47.19* A*C 4 190.30 47.575 5.93* Error 90 722.30 8.026 Total 99 2667.79 cell means n = 10

EDPSY 642 – Factorial ANOVA 8

Simple Effects calculations: Conditions at each Age SSCondition at OLD = 10 x [(7.0 – 10.06)2 + (6.9-10.06)2 + … + (12.0-10.06)2] = 351.52 SSC at YOUNG = 10 x [6.5 – 13.16)2 + (7.6 – 13.16)2 + … + (19.3 – 13.16)2 = 1353.72 Age at each Condition SSAge at Counting = 10 x [(7.0 - 6.75)2 + (6.5 – 6.75)2] = 1.25 SSA at Rhyming = 10 x [(6.9 - 7.25)2 + (7.6 – 7.25)2] = 2.45 SSA at Adjective = 10 x [(11.0 – 12.9)2 + (14.8 – 12.9)2] = 72.2 SSA at Imagery = 10 x [(13.4 – 15.5)2 + (17.6 – 15.5)2] = 88.2 SSA at Intention = 10 x[(12.0 – 15.65)2 + (19.3 – 15.65)2] = 266.45

* p < .05

€

MS = SS df

€

F = MS MSE

Source df SS MS F Conditions C at Old 4 351.52 87.88 10.95* C at Young 4 1353.72 338.43 42.15* Age A at Counting 1 1.25 1.25 .155 A at Rhyming 1 2.45 2.45 .305 A at Adjective 1 72.2 72.2 9.00* A at Imagery 1 88.2 88.2 10.99* A at Intentional 1 266.45 266.45 33.2* Error 90 722.30 8.03

Same error term and df from the ANOVA

EDPSY 642 – Factorial ANOVA 9

Interpretation: There are significant differences between memory conditions for both Older and Younger participants. However, differences did not seem to be present for the lower level memory tasks but were present at the higher level memory tasks. Since we just had two levels of Age, we can simply compare the means at each significant condition to see the nature of the differences. This is a relatively simple procedure for teasing apart interaction effects for factorial ANOVA. However, to use this procedure and be thorough, many tests are necessary which can seriously inflate the type I error rate. (Think about what would be necessary if there were 3 IVS or 5 levels for each IV????) Issue: If you test too many simple effects you either raise the familywise error rate to unacceptable levels or you control the familywise error rate at some reasonable level but lose power for each simple effect you test. Don’t calculate a contrast or simple effect unless you plan to discuss it when you write up the results!

EDPSY 642 – Factorial ANOVA 10

Multiple Comparison Procedures for Interactions Tests of simple effects are not terribly efficient. If you want to be thorough you have to do many different tests, which can inflate your type 1 error rate substantially. They are also essentially atheoretical. One does not require any theory or hypotheses of any kind to work from a simple main effects design. This is fine if your study is truly exploratory. However if you do have a theoretical framework or solid hypotheses to work from, it may be best to take a more targeted approach. All of the a priori multiple comparison procedures discussed as follow- up to the One Way ANOVA can still be used!

• Bonferroni • Scheffe* • Dunn-Sidak • Etc.. (if you remember… there are MANY)

*Depending on the number of IVs and number of levels of each IV, Scheffe can often be overly conservative. Probably the best place to start with proper interpretation of any interaction is to plot it!

EDPSY 642 – Factorial ANOVA 11

Differences in Independence as a factor of birth order and gender… Firstborn Middle Born Last Born Composite Males

73.15 79.87

s Y n

93.18 62.90

s Y n

41.11 07.72

s Y n

09.17 40.83

s Y n

Females

03.17 14.85

s Y n

49.15 86.71

s Y n

17.20 94.77

s Y n

24.18 30.79

s Y n

46.84 38 =

Y n ij

24.81 24

Y n ij

10.75 31 =

Y n ij

Source df F Sig Birth Order 2 3.97 0.022 Gender 1 1.32 0.254 Birth Order x Gender 2 3.74 0.028 Error 87 MSE = 277.91

First Born

Middle Born

Last Born

Birth Order

M ea

n S

co re

Males Females

EDPSY 642 – Factorial ANOVA 12

A significant interaction, remember, means that the effect of one independent variable, on the dependent variable differs at different levels of the other independent variable(s). So in terms of this example, there is a difference(s) in the effect of birth order on relationship beliefs between genders. OR, the effect of birth order is different for men and women. (I think the plot describes this beautifully!) It is now our job to determine the nature of these differences. Recall:

Bonferroni (a priori) tcrit n – 2df, number of contrasts being tested

Scheffe Fcrit (1, n - k) for a priori Fcrit (k - 1)Fα(k – 1, n – k) for post hoc

Keep in mind: When choosing appropriate contrasts there is no one absolute correct solution. Sometimes you have to get creative!

€

F = Ψ 2

MSe w 2

n j

∑

€

t = Ψ

MSe w 2

n j

∑

EDPSY 642 – Factorial ANOVA 13

One Option: Are males always higher than females? We know the answer is a resounding “NO”. But the question remains, which males aren’t? H1: µfirst born males > µfirst born females

H2: µsecond born males > µsecond born females

H3: µlast born males > µlast born females

€

H1 : t = (1)87.79+ (−1)85.14

277.91 (1) 2

19 + (−1)2

19 #

$ %

' (

= 2.65 5.41

= .489

€

H2 : t = (1)90.62+ (−1)(71.86)

277.91 (1) 2

12 + (−1)2

12 #

$ %

' (

= 18.76 6.81

= 2.75

€

H2 : t = (1)72.02+ (−1)(77.94)

277.91 (1) 2

15 + (−1)2

16 #

$ %

' (

= −5.87 4.90

= −1.20

EDPSY 642 – Factorial ANOVA 14

What patterns do we see for birth order?

€

H4 :µ3M < µ1M + µ2M

H5: µ1M < µ2M

€

H6 :µ1F > µ2F + µ3F

H7: µ3F > µ2F

€

H4 : t = (1)87.79+ (1)90.62+ (−2)72.07

277.91 (1) 2

19 + (1)2

12 + (−2)2

15 #

$ %

' (

= 34.27 10.57

= 3.242

€

H5 : t = (−1)87.79+ (1)90.62

277.91 (1) 2

19 + (−1)2

12 #

$ %

' (

= 2.83 6.14

= .461

€

H6 : t = (2)85.14+ (−1)71.86+ (−1)77.94

277.91 (2) 2

19 + (−1)2

12 + (−1)2

16 #

$ %

' (

= 20.48 9.95

= 2.05

€

H7 : t = (−1)71.86+ (1)77.94

277.91 (−1) 2

12 + (1)2

16 #

$ %

' (

= 6.08 6.36

= .955

Lets say we did ALL of these comparisons: tcrit Bonferroni (7 comparisons, 90df) = 2.76 Lets say we did only the first 3 comparisons: tcrit Bonferroni (3 comparisons, 90df) = 2.44 Power considerations!!!!!

Factorial ANOVA(1).pdf

EDPSY 642 – Factorial ANOVA 1

Factorial Analysis of Variance

• Between Subjects vs. Within Subjects Designs

• Fixed Effects vs. Random Effects Designs

• Categorical and Continuous Independent Variables

• Three-Way, Four-Way, N-way Factorial Designs

EDPSY 642 – Factorial ANOVA 2

EDPSY 642 – Factorial ANOVA 3

ANOVA Main Effects and Interaction

A factorial ANOVA allows consideration of the effect of multiple independent variables on the dependent variables in the same study Main effect – the effect of a single variable on the

dependent variable Interaction – the combined effect of the independent

variables on the dependent variable. There is an interaction when the effect of one independent variable depends on the level of the other independent variable

Lets design a study testing the impact of counseling type and gender on life satisfaction. The Sources of Variability are:

- the main effect for “counseling type” - the main effect for “gender” - the interaction “counseling type*gender - error (everything left unaccounted for)

EDPSY 642 – Factorial ANOVA 4

Null Hypotheses - Null hypothesis for factor A:

€

H0 :µ1 = µ2 = µ3 =… = µ j [there is no difference between the different levels of A]

- Null hypothesis for factor B:

€

H0 :µ1 = µ2 = µ3 =… = µk [there is no difference between the different levels of B]

- Null Hypothesis for interaction:

€

H0 : all(µ jk −µ j . −µk . + µ) = 0 [there is no difference between the interaction cell means that cannot be explained by the effect of A or the effect of B]

2 Independent Variables: 2-Way ANOVA Counseling Type: 3 levels Gender: 2 levels

Independent Variables

Dependent Variable: Life Satisfaction Group Counseling

males females

Individual Counseling

males females

Refused Counseling

males females

EDPSY 642 – Factorial ANOVA 5

Partitioning the Sums of Squares

SStotal Total Variability

SSwithin SSBetween Within-Groups Between-Groups Variability Variability SSA SSB SSA*B Variability Variability Variability due to A due to B due to A*B

Interaction

EDPSY 642 – Factorial ANOVA 6

Interpretation of Main Effect and Interaction If significant interaction:

⇒DO NOT interpret main effects

⇒plot interaction ⇒conduct tests of simple effects

⇒conduct multiple comparisons for interaction

€

(η2, ω 2 )and effect sizes.

EDPSY 642 – Factorial ANOVA 7

Tests of Simple Effects

€

SSsimple effect = n X jk − X j .( )∑ 2

We simply calculate the SS using only the data for one factor. Example from Howell (2007) Eysenck Data

Condition

Age

Counting Rhyming Adjective Imagery Intention Mean Older 7.0 6.9 11.0 13.4 12.0 10.06 Younger 6.5 7.6 14.8 17.6 19.3 13.16 Mean 6.75 7.25 12.9 15.5 15.65 11.61

Source df SS MS F Age (A) 1 240.25 240.25 29.94* Condition (C) 4 1514.94 378.735 47.19* A*C 4 190.30 47.575 5.93* Error 90 722.30 8.026 Total 99 2667.79 cell means n = 10

EDPSY 642 – Factorial ANOVA 8

* p < .05

€

MS = SS df

€

F = MS MSE

Same error term and df from the ANOVA

EDPSY 642 – Factorial ANOVA 9

EDPSY 642 – Factorial ANOVA 10

• Bonferroni • Scheffe* • Dunn-Sidak • Etc.. (if you remember… there are MANY)

EDPSY 642 – Factorial ANOVA 11

Differences in Independence as a factor of birth order and gender… Firstborn Middle Born Last Born Composite Males

73.15 79.87

s Y n

93.18 62.90

s Y n

41.11 07.72

s Y n

09.17 40.83

s Y n

Females

03.17 14.85

s Y n

49.15 86.71

s Y n

17.20 94.77

s Y n

24.18 30.79

s Y n

46.84 38 =

Y n ij

24.81 24

Y n ij

10.75 31 =

Y n ij

Source df F Sig Birth Order 2 3.97 0.022 Gender 1 1.32 0.254 Birth Order x Gender 2 3.74 0.028 Error 87 MSE = 277.91

First Born

Middle Born

Last Born

Birth Order

M ea

n S

co re

Males Females

EDPSY 642 – Factorial ANOVA 12

Bonferroni (a priori) tcrit n – 2df, number of contrasts being tested

Scheffe Fcrit (1, n - k) for a priori Fcrit (k - 1)Fα(k – 1, n – k) for post hoc

Keep in mind: When choosing appropriate contrasts there is no one absolute correct solution. Sometimes you have to get creative!

€

F = Ψ 2

MSe w 2

n j

∑

€

t = Ψ

MSe w 2

n j

∑

EDPSY 642 – Factorial ANOVA 13

One Option: Are males always higher than females? We know the answer is a resounding “NO”. But the question remains, which males aren’t? H1: µfirst born males > µfirst born females

H2: µsecond born males > µsecond born females

H3: µlast born males > µlast born females

€

H1 : t = (1)87.79+ (−1)85.14

277.91 (1) 2

19 + (−1)2

19 #

$ %

' (

= 2.65 5.41

= .489

€

H2 : t = (1)90.62+ (−1)(71.86)

277.91 (1) 2

12 + (−1)2

12 #

$ %

' (

= 18.76 6.81

= 2.75

€

H2 : t = (1)72.02+ (−1)(77.94)

277.91 (1) 2

15 + (−1)2

16 #

$ %

' (

= −5.87 4.90

= −1.20

EDPSY 642 – Factorial ANOVA 14

What patterns do we see for birth order?

€

H4 :µ3M < µ1M + µ2M

H5: µ1M < µ2M

€

H6 :µ1F > µ2F + µ3F

H7: µ3F > µ2F

€

H4 : t = (1)87.79+ (1)90.62+ (−2)72.07

277.91 (1) 2

19 + (1)2

12 + (−2)2

15 #

$ %

' (

= 34.27 10.57

= 3.242

€

H5 : t = (−1)87.79+ (1)90.62

277.91 (1) 2

19 + (−1)2

12 #

$ %

' (

= 2.83 6.14

= .461

€

H6 : t = (2)85.14+ (−1)71.86+ (−1)77.94

277.91 (2) 2

19 + (−1)2

12 + (−1)2

16 #

$ %

' (

= 20.48 9.95

= 2.05

€

H7 : t = (−1)71.86+ (1)77.94

277.91 (−1) 2

12 + (1)2

16 #

$ %

' (

= 6.08 6.36

= .955

Goggles_Simple Effects EX.pdf

Factorial ANOVA: Beer Goggles Example

Goggles_Simple Effects EX(1).pdf

Factorial ANOVA: Beer Goggles Example

ONLINE_EDPS Project 3(2).pdf

Assignment 3: Factorial ANOVA

Assignment 3: Data Analysis using Factorial ANOVA (25pts Total) Using the Therapy.sav SPSS file: 1. You are a faculty member in a Counseling Psychology department and your main

research interests involve gender differences in the efficacy of therapeutic treatments for stalking. Recently, you have been working mostly with two newly emerging treatments we will call Therapy 1 and Therapy 2. You collect data on 50 individuals who have been diagnosed with moderate to severe stalking tendencies. You want to know how gender and therapy type (therapy) impact the efficacy of stalking treatment post therapy (post_therapy). However, you are most interested in whether there are gender differences in the efficacy of the different therapies. a. Describe the sample. [5]

i. How many males? Females? ii. How many individuals receiving each therapy? iii. Describe typical performance. Present means/standard deviations for

each group.

b. Check Assumptions for this Analysis. [4] i. Name each assumptions ii. For each assumption, tell me if the assumption is met AND what

evidence you based your decision on.

c. Run this analysis in SPSS. [4] Your output should include (but not be restricted to):

i. Descriptive Statistics ii. Estimates of Effect Size iii. Plot of the interaction

d. Interpret your results so far. Look at your main effects and interaction(s). What

do you know at this point? [2]

e. Follow-‐up tests. In order to follow up on your results, you decide to test the following two hypotheses using Bonferroni contrasts.

Hypothesis 1: Therapy 1 was more effective for males than females. Hypothesis 2: Therapy 2 was more effective for females than males.

i. Compute the t-‐value for Hypothesis 1 [2] ii. Compute the t-‐value for Hypothesis 2. [2] iii. What is the Bonferroni critical value for this situation? [2] iv. Is Hypothesis 1 significant? What does this mean? [2] v. Is Hypothesis 2 significant? What does this mean? [2]

Therapy(1)(1).sav

Using SPSS to help compute Tests of Simple Effects.pdf

Using SPSS to help compute Tests of Simple Effects: Part 1: The intuitive way: Step 1: Using the Split file. Because tests of simple effects are essentially a set of one-‐way ANOVAs for one independent variable… each one run at only one level of the other independent variable… our goal will be to first split one of our independent variables. This will be accomplished with a split file.

Go to Data -> Split File

We want to split one of our independent variables so that we can compare each level individually. -‐Click compare groups -‐Click one of the IVs into the Groups based on box. -‐Click OK

You have not run any analyses yet! So you will not have anything in your output at this point except for a syntax statement telling you that you implemented a split file. You will know the split file worked if you check the lower right hand column of your data file. It will say Split By Origin to indicate that your split file is on and comparing groups on origin.

NOW we will run our first set of simple effects. Simple Effects are just one-‐way ANOVAs so just go to analyze -> compare means -> one way ANOVA

Our dependent variable is time to accelerate. Since we split our file for country of origin we can now easily find simple effects for model year:

“Is there an effect of model year for American cars… European cars… Japanese cars?”

The sum of squares between will be the sum of squares for the simple effects of Origin at Model Year!

The df, MS and F will not be correct for the simple effects though as they are not using the correct error. You will have to compute those yourself.

Now that we have the simple effects for Model Year AT Origin we need to get the simple effects for Origin at Model Year. To do this we need to:

1. Change our split file to Model Year 2. Run a one-‐way ANOVA for Origin

These Sums of Squares Between are the Sums of Squares for the Simple effects for Model Year at Origin! (Recall our Original Factorial ANOVA results from your example on blackboard)

To get the significance tests, now, we need to form our table and enter the sum of squares from the SPSS output. Source Sum of Squares df Mean Square F

American 194.102 1 194.102 28.04 European 6.363 1 6.363 .919

Model Year at

Japanese .002 1 .002 .0002

Old 224.407 2 112.204 16.21 Origin at New 50.524 2 25.262 3.649

Error 2768.774 400 6.922

Part 2: The harder way using SPSS syntax. This method will do all of the simple effects for you (with the correct F values). However, it is not intuitive, and sometimes difficult to set up. Step 1. Set up your Factorial ANOVA but do not hit OK to run the model. Step 2. Hit PASTE

This will open up a syntax window. It has pasted the SPSS syntax for everything you just asked SPSS to run. IF you highlight this and hit the blue arrow it will run the analysis you requested. BUT FIRST… Step 3. Delete the period at the end of the syntax!!

Now SPSS knows to expect more in this command. Step 4. Adding to the SPSS syntax. Add the following commands to the syntax: /emmeans = tables(origin*model_year) compare(origin) /emmeans =tables(model_year*origin) compare(model_year).

Its not elegant and will report some redundant information, however it will give you all the simple effects (it’s the best way I’ve found so far to organize it easily) Step 4: Highlight the output and hit the blue arrow to run the analysis. In addition to your analysis you will now have the following new boxes:

Simple Effects: Origin at Model_Year

Simple Effects : Model_Year at Origin