Linear Multiple Regression This week, you have expanded on your knowledge of multiple regression to work with linear multiple regression. In this Application, you will perform a linear multiple regression analysis. Review Chapter 8 of the Field text for a description of the linear multiple regression and an example of conducting a linear multiple regression using PASW. Review Chapter 5 from the APA manual, "Displaying Results." Review the media resources demonstrating the linear multiple regression. The assignment: Complete Smart Alex's Task #5 on p. 355 to complete the linear multiple regression analysis using the Child Aggression.sav dataset from the Field text. However, use only the variables Aggression (DV), and test to see if Sibling Aggression is a mediator of the relationship between Parenting Style and Aggression or whether Sibling Aggression is a moderator of the relationship. You can follow the steps outlined on pp. 331–354 as a guide. Report your findings in APA format according to the guidelines in the PASW Application Assignment Guidelines handout. The final document should be 2–3 pages long. IMPORTANT: Additional Instructor Notes: 3rd edition of Field textbook: Chapter 7, Smart Alex's Task #3 on p. 262 using the Child Aggression.sav dataset. Use only the variables Aggression (DV), Sibling Aggression (mediator or moderator), and Parenting Style (IV).  4th edition of Field textbook: Chapter 8, Smart Alex's Task #5 on p. 355 using the Child Aggression.sav dataset. Use only the variables Aggression (DV), Sibling Aggression (mediator or moderator), and Parenting Style (IV).  The objective of the exercise is to conduct and interpret either (a) a regression analysis to see if Sibling Aggression is a mediator of the relationship between Parenting Style and Aggression, or (b) a regression analysis to see if Sibling Aggression is a moderator of the relationship between Parenting Style and Aggression. Do not submit both; choose to submit either the mediation analysis or the moderation. If you submit both I will only grade the first appearing analysis in the submitted assignment. So, I recommend that you study the tutorial (see below) as yourSupplemental Tutorial The tutorial contains two sections. Section 1 provides step-by-step graphic user interface (GUI) screencaptures for specifying the assignment in SPSS. If you follow the steps you will produce correct SPSS output. Section 2 presents and interprets output for a different set of variables, and includes a results write up guide, and sample APA style tables. IMPORTANT: Results Write Up Guide Begin the write up by describing the context of the research and the variables. If known, state how each variable was operationalized, for example: “Overall GPA was measured on the traditional 4-point scale from 0 (F) to 4 (A)”, or “Satisfaction was measured on a 5-point likert-type scale from 1 (not at all satisfied) to 5 (extremely satisfied).” Please pay attention to APA style for reporti ...

1. Linear Multiple Regression
This week, you have expanded on your knowledge of multiple
regression to work with linear multiple regression. In this
Application, you will perform a linear multiple regression
analysis.
Review Chapter 8 of the Field text for a description of the
linear multiple regression and an example of conducting a linear
multiple regression using PASW.
Review Chapter 5 from the APA manual, "Displaying Results."
Review the media resources demonstrating the linear multiple
regression.
The assignment:
Complete Smart Alex's Task #5 on p. 355 to complete the linear
multiple regression analysis using the Child Aggression.sav
dataset from the Field text. However, use only the variables
Aggression (DV), and test to see if Sibling Aggression is a
mediator of the relationship between Parenting Style and
Aggression or whether Sibling Aggression is a moderator of the
relationship.
You can follow the steps outlined on pp. 331–354 as a guide.
Report your findings in APA format according to the guidelines
in the PASW Application Assignment Guidelines handout. The
final document should be 2–3 pages long.
IMPORTANT: Additional Instructor Notes:
3rd edition of Field textbook:
Chapter 7, Smart Alex's Task #3 on p. 262 using the Child
Aggression.sav dataset. Use only the variables Aggression

2. (DV), Sibling Aggression (mediator or moderator), and
Parenting Style (IV).
4th edition of Field textbook:
Chapter 8, Smart Alex's Task #5 on p. 355 using the Child
Aggression.sav dataset. Use only the variables Aggression
(DV), Sibling Aggression (mediator or moderator), and
Parenting Style (IV).
The objective of the exercise is to conduct and interpret either
(a) a regression analysis to see if Sibling Aggression is a
mediator of the relationship between Parenting Style and
Aggression, or (b) a regression analysis to see if Sibling
Aggression is a moderator of the relationship between Parenting
Style and Aggression. Do not submit both; choose to submit
either the mediation analysis or the moderation. If you submit
both I will only grade the first appearing analysis in the
submitted assignment.
So, I recommend that you study the tutorial (see below) as
yourSupplemental Tutorial
The tutorial contains two sections. Section 1 provides step-by-
step graphic user interface (GUI) screencaptures for specifying
the assignment in SPSS. If you follow the steps you will
produce correct SPSS output. Section 2 presents and interprets
output for a different set of variables, and includes a results
write up guide, and sample APA style tables.
IMPORTANT: Results Write Up Guide
Begin the write up by describing the context of the research and
the variables. If known, state how each variable was
operationalized, for example: “Overall GPA was measured on
the traditional 4-point scale from 0 (F) to 4 (A)”, or
“Satisfaction was measured on a 5-point likert-type scale from 1
(not at all satisfied) to 5 (extremely satisfied).” Please pay
attention to APA style for reporting scale anchors (see p. 91 and
p. 105 in the 6th edition of the APA Manual).
Report descriptive statistics such as minimum, maximum,

3. mean, and standard deviation for each metric variable. For
nominal variables, report percentage for each level of the
variable, for example: “Of the total sample (N = 150) there were
40 (26.7%) males and 110 (73.3%) females.” Keep in mind that
a sentence that includes information in parentheticals must still
be a sentence (and make sense) if the parentheticals are
removed. For example: “Of the total sample there were 40 males
and 110 females.”
State the purpose of the analysis or provide the guiding
research question(s). If you use research questions, do not craft
them such that they can be answered with a yes or no. Instead,
craft them so that they will have a quantitative answer. For
example: “What is the strength and direction of relationship
between X and Y?” or “What is the difference in group means
on X between males and females?”
Present null and alternative hypothesis sets applicable to the
analysis. For the mediation analysis, following Baron and
Kenny (1986), there would be three hypothesis sets: (a) DV on
IV, (b) mediator on IV, and (c) DV on mediator while
controlling for IV. For the moderation analysis there would be
four sets of hypotheses, one each for IV, moderator, and
interaction, and one combined effect. Where appropriate, be
careful to note within a hypotheses while “controlling for” or
“holding constant” the effects of the other predictors.
State assumptions or other considerations for the analysis, and
report the actual statistical result for relevant tests. For this
course, the only regression consideration that needs to be
presented and discussed is for multicollinearity. Even if
violated, you must still report and interpret the remaining
results.
Report and interpret the overall regression results. Report and

4. interpret the results of each predictor. Be sure to include the
actual statistical results in text—examples were provided within
the annotated output section of this tutorial. Don’t forget to
interpret the results (e.g., as IQ increased, overall GPA was
predicted to increase; based on semipartial correlations,
variable x was the most important predictor of y; 56% of the
effect of parental involvement on GPA was indirect through the
mediating variable of attention span; etc.). Draw conclusions
about rejecting or failing to reject each null. If needed,
summarize the results (without statistics) in a concluding
sentence or paragraph. If there is a mediated or moderated
effect, you should briefly discuss why it would make sense that
the relationship between the IV and DV was affected by the
mediator or moderator.
Provide APA style tables appropriate to the analysis. Do not
use SPSS output, it is not in APA style. Example APA tables
are shown in the next section using the results from the example
output in this tutorial. Although one would typically not
duplicate information in text and tables, it is important to
demonstrate competence in both ways of reporting the results;
so, you cannot just provide tables, you must also report the
relevant statistical results within the textual write up.
Shampoo Blog
The market for shampoo a wide market and is something
that will always be in demand. It’s one of the first things I use
when I wake up and one of the last things I use before going to
sleep at night. Shampoo is something all college students need,
no one wants to be that person or be friends with someone who
either looks like they walked through a blizzard or took grease

5. from under a car and rubbed it through their hair. Along with
the disgusting look, the odor can make a person wish they didn't
have a sense of smell.
A trip to Walmart showed about 40 different types of
shampoo ranging in price, smell, and for men and women. The
first thing that caught my eye was the bright colors on all of the
bottles ranging from all ends of the color spectrum such
as green, aqua, pink, and orange. The pink and orange bottles
were little kids shampoo which is a smart tactic, if a kid is
shopping with their parent and see the bright color they are
more likely to want to get that than a dull brown or black
colored bottle. All of them either seemed to have a bright bottle,
label, or both. All of these colors represent freshness and
healing power which might be something someone is looking
for when buying a new type of shampoo. A company can use
this saying it will fix your damaged hair. Companies can use a
shade of blue, which is often used, to represent health,
tranquility, and softness.
The language on the bottles are also a very tactical
strategy for trying to sell a product. As I was skimming the
aisle words such as “Silky Smooth”, “Hydrate”, and
“Moisturize” caught my eye and were plastered across almost
every bottle. All these words are very appealing when buying
shampoo because you want your hair to look as good as it can,
if it’s dried out and crusty then you might as well not even use
the shampoo. Along with these words were pictures of people
on the bottles with thick, smooth, a great looking hair. Another
image on a few bottles was a picture of a beach giving the
impression that the shampoo is fresh like the outdoors. One of
the brands that specifically did this was Old Spice. A few of
their bottles had a beach on them representing freshness and
some had a forrest on them to market towards the outdoors
group.
Shampoo companies market their products much like
almost any other company would with their products. They do
things to catch the eye such as using bright colors, using

6. attractive language, and displaying “feel good” images on the
bottle all to make the product appear more clean and fresh. The
companies that do this the best include all of these aspects then
develop their product even more on top of these.
New Professor Note for Week 7 Assignment:
Results Write Up Guide
Begin the write up by describing the context of the research and
the variables. If known, state how each variable was
operationalized, for example: “Overall GPA was measured on
the traditional 4-point scale from 0 (F) to 4 (A)”, or
“Satisfaction was measured on a 5-point likert-type scale from 1
(not at all satisfied) to 5 (extremely satisfied).” Please pay
attention to APA style for reporting scale anchors (see p. 91 and
p. 105 in the 6th edition of the APA Manual).
Report descriptive statistics such as minimum, maximum, mean,
and standard deviation for each metric variable. For nominal
variables, report percentage for each level of the variable, for
example: “Of the total sample (N = 150) there were 40 (26.7%)
males and 110 (73.3%) females.” Keep in mind that a sentence
that includes information in parentheticals must still be a
sentence (and make sense) if the parentheticals are removed.
For example: “Of the total sample there were 40 males and 110
females.”
State the purpose of the analysis or provide the guiding research
question(s). If you use research questions, do not craft them
such that they can be answered with a yes or no. Instead, craft
them so that they will have a quantitative answer. For example:
“What is the strength and direction of relationship between X
and Y?” or “What is the difference in group means on X
between males and females?”

7. Present null and alternative hypothesis sets applicable to the
analysis. For the mediation analysis, following Baron and
Kenny (1986), there would be three hypothesis sets: (a) DV on
IV, (b) mediator on IV, and (c) DV on mediator while
controlling for IV. For the moderation analysis there would be
four sets of hypotheses, one each for IV, moderator, and
interaction, and one combined effect. Where appropriate, be
careful to note within a hypotheses while “controlling for” or
“holding constant” the effects of the other predictors.
State assumptions or other considerations for the analysis, and
report the actual statistical result for relevant tests. For this
course, the only regression consideration that needs to be
presented and discussed is for multicollinearity. Even if
violated, you must still report and interpret the remaining
results.
dsus4data/Album Sales.sav
dsus4data/Angry Pigs.sav
dsus4data/Angry Real.sav
dsus4data/Attitude.sav
dsus4data/Band Personality.sav
dsus4data/Beckham (1929).sav
dsus4data/BeerGogglesLighting.sav

8. __MACOSX/dsus4data/._BeerGogglesLighting.sav
dsus4data/Bernard et al. (2012).sav
dsus4data/Big Hairy Spider.sav
dsus4data/BigBrother.sav
__MACOSX/dsus4data/._BigBrother.sav
dsus4data/Board & Fritzon 2005.sav
dsus4data/Burnout.sav
__MACOSX/dsus4data/._Burnout.sav
dsus4data/Bushtucker.sav
__MACOSX/dsus4data/._Bushtucker.sav
dsus4data/Cat Regression.sav
dsus4data/Cats and Dogs.sav
dsus4data/Cats Weight.sav
dsus4data/Cats.sav
dsus4data/Catterplot.sav
dsus4data/Chamorro-Premuzic.sav
__MACOSX/dsus4data/._Chamorro-Premuzic.sav
dsus4data/Chat-Up Lines.sav

9. __MACOSX/dsus4data/._Chat-Up Lines.sav
dsus4data/Chick Flick (Mixed).sav
__MACOSX/dsus4data/._Chick Flick (Mixed).sav
dsus4data/chicken.sav
__MACOSX/dsus4data/._chicken.sav
dsus4data/ChickFlick.sav
dsus4data/Child Aggression.sav
__MACOSX/dsus4data/._Child Aggression.sav
dsus4data/CIr.sav
dsus4data/CIr.sps
*****************************************************
*******.
* Author: Andy Field, University of Sussex, UK .
*****************************************************
*******.
MATRIX.
GET n /VARIABLES = n
/MISSING=OMIT.
GET r /VARIABLES = r
/MISSING=OMIT.
COMPUTE z = 0.5*(ln((1+r)/(1-r))).
COMPUTE SEz = 1/sqrt(n-3).
COMPUTE zscore = z/SEz.
COMPUTE sigz = 2*(1-cdfnorm(abs(zscore))).
COMPUTE zrupper = z + (1.96*SEz).
COMPUTE zrlower = z - (1.96*SEz).

10. COMPUTE rlower =(exp(zrlower/0.5)-1)/(1+exp(zrlower/0.5)).
COMPUTE rupper =(exp(zrupper/0.5)-1)/(1+exp(zrupper/0.5)).
COMPUTE zCI = {r, rlower, rupper, zscore, sigz}.
print "*** 95% Confidence interval for r ***".
print zCI /TITLE = " r 95% Lower 95% Upper
z Sig".
END MATRIX.
__MACOSX/dsus4data/._CIr.sps
dsus4data/Coldwell et al. (2006).sav
dsus4data/condom.sav
__MACOSX/dsus4data/._condom.sav
dsus4data/Contrast.sav
__MACOSX/dsus4data/._Contrast.sav
dsus4data/Cosmetic Surgery.sav
dsus4data/Coulrophobia.sav
__MACOSX/dsus4data/._Coulrophobia.sav
dsus4data/Çetinkaya & Domjan (2006).sav
__MACOSX/dsus4data/._Çetinkaya & Domjan (2006).sav
dsus4data/Daniels (2012).sav

11. dsus4data/DarkLord.sav
__MACOSX/dsus4data/._DarkLord.sav
dsus4data/Davey(2003).sav
__MACOSX/dsus4data/._Davey(2003).sav
dsus4data/Depression.sav
__MACOSX/dsus4data/._Depression.sav
dsus4data/DepressionSyntax.SPS
MANOVA
before after BY treat(0 4)
/WSFACTORS time (2)
/CONTRAST (time)=special(1 1, 1 -1)
/CONTRAST (treat)=special (1 1 1 1 1, -4 1 1 1 1, 0 -3 1 1 1, 0
0 1 1 -2, 0 0 1 -1 0)
/CINTERVAL JOINT(.95) MULTIVARIATE(BONFER)
/METHOD UNIQUE
/ERROR WITHIN+RESIDUAL
/PRINT TRANSFORM HOMOGENEITY(BARTLETT
COCHRAN BOXM)
SIGNIF( UNIV MULT AVERF HF GG )

12. PARAM( ESTIM EFSIZE).
__MACOSX/dsus4data/._DepressionSyntax.SPS
dsus4data/DFBeta.sav
dsus4data/Diet.sav
dsus4data/Differences between dependent r.sps
*****************************************************
*******.
* Author: Andy Field, University of Sussex, UK .
*****************************************************
*******.
MATRIX.
GET rxy /VARIABLES = rxy.
GET rzy /VARIABLES = rzy.
GET rxz /VARIABLES = rxz.
GET n /VARIABLES = n.
COMPUTE diff = rxy-rzy.
COMPUTE ttest = diff*(sqrt(((n-3)*(1+rxz))&/(2*(1 - rxy**2 -
rxz**2 - rzy**2 + (2*rxy)*rxz*rzy)))).
COMPUTE sigt = tcdf(ttest,(n-3)).
COMPUTE output = {diff, ttest, sigt}.
print "*** Tests of Differences between Dependent Correlation
Coefficiants ***".
print output /TITLE = " Difference t Sig".
END MATRIX.
__MACOSX/dsus4data/._Differences between dependent r.sps

13. dsus4data/Display.SAV
__MACOSX/dsus4data/._Display.SAV
dsus4data/DownloadFestival.sav
dsus4data/Drug.sav
dsus4data/Dummy.sav
__MACOSX/dsus4data/._Dummy.sav
dsus4data/Eastenders.sav
__MACOSX/dsus4data/._Eastenders.sav
dsus4data/Eel.sav
dsus4data/Elephant Football.sav
dsus4data/Escape From Inside.sav
__MACOSX/dsus4data/._Escape From Inside.sav
dsus4data/EssayMarks.sav
__MACOSX/dsus4data/._EssayMarks.sav
dsus4data/Exam Anxiety.sav
dsus4data/Facebook.sav
__MACOSX/dsus4data/._Facebook.sav
dsus4data/Field (2006).sav

14. __MACOSX/dsus4data/._Field (2006).sav
dsus4data/Field&Hole.sav
__MACOSX/dsus4data/._Field&Hole.sav
dsus4data/fugazi.sav
__MACOSX/dsus4data/._fugazi.sav
dsus4data/Gallup et al.sav
__MACOSX/dsus4data/._Gallup et al.sav
dsus4data/Gelman & Weakliem (2009).sav
dsus4data/GlastonburyDummy.sav
dsus4data/GlastonburyFestival.sav
__MACOSX/dsus4data/._GlastonburyFestival.sav
dsus4data/GlastonburyFestivalRegression.sav
__MACOSX/dsus4data/._GlastonburyFestivalRegression.sav
dsus4data/Goat or Dog.sav
dsus4data/goggles.sav
dsus4data/GogglesRegression.sav
__MACOSX/dsus4data/._GogglesRegression.sav
dsus4data/GogglesSimpleEffects.SPS

15. glm Attractiveness by gender alcohol
/emmeans = tables(gender*alcohol)compare(gender).
__MACOSX/dsus4data/._GogglesSimpleEffects.SPS
dsus4data/grades.sav
__MACOSX/dsus4data/._grades.sav
dsus4data/Gueguen (2012).sav
dsus4data/Handlebars.sav
__MACOSX/dsus4data/._Handlebars.sav
dsus4data/HangoverCure.sav
dsus4data/Hiccups.sav
__MACOSX/dsus4data/._Hiccups.sav
dsus4data/Hill et al. (2007).sav
__MACOSX/dsus4data/._Hill et al. (2007).sav
dsus4data/HonestyLab.sav
dsus4data/Honeymoon Period Restructured.sav
__MACOSX/dsus4data/._Honeymoon Period Restructured.sav
dsus4data/Honeymoon Period.sav
__MACOSX/dsus4data/._Honeymoon Period.sav
dsus4data/Horoscope.sav

16. __MACOSX/dsus4data/._Horoscope.sav
dsus4data/Independent r.sav
__MACOSX/dsus4data/._Independent r.sav
dsus4data/Independent t from means.sps
COMPUTE df = n1+n2-2.
COMPUTE Diff = x1-x2.
COMPUTE poolvar = (((n1-1)*(sd1 ** 2))+((n2-1)*(sd2 **
2)))/df.
COMPUTE poolsd = sqrt((((n1-1)*(sd1 ** 2))+((n2-1)*(sd2 **
2)))/(n1+n2)).
Compute SE = sqrt(poolvar*((1/n1)+(1/n2))).
COMPUTE CI_Upper = Diff+(idf.t(0.975, df)*SE).
Compute CI_Lower = Diff-(idf.t(0.975, df)*SE).
COMPUTE d = Diff/poolsd.
COMPUTE t_test = Diff/SE.
COMPUTE t_sig = 2*(1-(CDF.T(abs(t_test),df))).
Variable labels Diff 'Difference between Means (X1-X2)'.
Variable labels SE 'Standard Error of Difference between
means'.
Variable labels poolsd 'Pooled SD'.
Variable labels d 'Effect Size (d)'.
Variable labels t_test 't statistic'.
Variable labels t_sig 'Significance (2-tailed)'.
Variable labels CI_Upper '95% Confidence Interval (Upper)'.
Variable labels CI_Lower '95% Confidence Interval (Lower)'.
Formats t_sig(F8.5).
EXECUTE .
SUMMARIZE
/TABLES= x1 x2 Diff CI_Lower CI_Upper df t_test t_sig d
/FORMAT=VALIDLIST NOCASENUM TOTAL LIMIT=100
/TITLE='T-test'

17. /MISSING=VARIABLE
/CELLS=NONE.
__MACOSX/dsus4data/._Independent t from means.sps
dsus4data/Infidelity.sav
__MACOSX/dsus4data/._Infidelity.sav
dsus4data/Invisibility Baseline.sav
dsus4data/Invisibility RM.sav
dsus4data/Invisibility.sav
dsus4data/Jiminy Cricket.sav
dsus4data/Johns et al. (2012).sav
dsus4data/Lacourse et al. (2001) Females.sav
__MACOSX/dsus4data/._Lacourse et al. (2001) Females.sav
dsus4data/Lambert et al. (2012).sav
dsus4data/LooksOrPersonality.sav
__MACOSX/dsus4data/._LooksOrPersonality.sav
dsus4data/lying.sav
dsus4data/Marzillier & Davey (2005).sav
__MACOSX/dsus4data/._Marzillier & Davey (2005).sav

18. dsus4data/Massar et al. (2011).sav
dsus4data/Matthews et al. (2007).sav
dsus4data/McNulty et al. (2008).sav
dsus4data/MenLikeDogs.sav
__MACOSX/dsus4data/._MenLikeDogs.sav
dsus4data/Method Of Teaching.sav
__MACOSX/dsus4data/._Method Of Teaching.sav
dsus4data/Miller et al. (2007).sav
__MACOSX/dsus4data/._Miller et al. (2007).sav
dsus4data/MixedAttitude.sav
__MACOSX/dsus4data/._MixedAttitude.sav
dsus4data/Murder.sav
dsus4data/Muris et al (2008).sav
__MACOSX/dsus4data/._Muris et al (2008).sav
dsus4data/Nichols & Nicki (2004).sav
__MACOSX/dsus4data/._Nichols & Nicki (2004).sav
dsus4data/OCD.sav
dsus4data/Ong et al. (2011).sav

19. dsus4data/Outliers (Percentage of Z-sc.textClipping
__MACOSX/dsus4data/._Outliers (Percentage of Z-
sc.textClipping
dsus4data/Oxoby (2008) MOA.sav
dsus4data/Oxoby (2008) Offers.sav
dsus4data/PBCorr.SAV
dsus4data/Penalty.sav
dsus4data/Penis.sav
__MACOSX/dsus4data/._Penis.sav
dsus4data/Perham & Sykora (2012).sav
dsus4data/Piff et al. (2012) Pedestrian.sav
dsus4data/Piff et al. (2012) Vehicle.sav
dsus4data/ProfilePicture.sav
dsus4data/psychology.sav
__MACOSX/dsus4data/._psychology.sav
dsus4data/pubs.sav
__MACOSX/dsus4data/._pubs.sav
dsus4data/RecodeGlastonburyData.SPS
DO IF (1-SYSMIS(change)).
RECODE music (3=1)(ELSE = 0) INTO Crusty.

20. RECODE music (2=1)(ELSE = 0) INTO Metaller.
RECODE music (1=1)(ELSE = 0) INTO Indie_Kid.
END IF.
VARIABLE LABELS Crusty 'No Affiliation vs. Crusty'.
VARIABLE LABELS Metaller 'No Affiliation vs. Metaller'.
VARIABLE LABELS Indie_Kid 'No Affiliation vs. Indie Kid'.
VARIABLE LEVEL Crusty Metaller Indie_Kid (Nominal).
FORMATS Crusty Metaller Indie_Kid (F1.0).
EXECUTE.
__MACOSX/dsus4data/._RecodeGlastonburyData.SPS
dsus4data/RovingEye.sav
dsus4data/Sage Editors Can't Play Football.sav
__MACOSX/dsus4data/._Sage Editors Can't Play Football.sav
dsus4data/SAQ (Item 3 Reversed).sav
dsus4data/SAQ.sav
dsus4data/Schützwohl(2008).sav
dsus4data/Shopping Exercise.sav
dsus4data/SimpleEffectsAttitude.sps
DATASET ACTIVATE DataSet2.
GLM beerpos beerneg beerneut winepos wineneg wineneut
waterpos waterneg waterneut
/WSFACTOR=Drink 3 Imagery 3
/EMMEANS = TABLES(Drink*Imagery) COMPARE(Imagery).

21. dsus4data/Sing or Guitar.sav
dsus4data/Sonnentag (2012).sav
dsus4data/Soya.sav
dsus4data/SPSSExam.sav
__MACOSX/dsus4data/._SPSSExam.sav
dsus4data/Stalker.sav
dsus4data/Superhero.sav
dsus4data/Supermodel.sav
__MACOSX/dsus4data/._Supermodel.sav
dsus4data/Tablets.sav
dsus4data/Tea Makes You Brainy 15.sav
dsus4data/Tea Makes You Brainy 716.sav
dsus4data/Teach.sav
__MACOSX/dsus4data/._Teach.sav
dsus4data/Text Messages.sav
__MACOSX/dsus4data/._Text Messages.sav
dsus4data/The Biggest Liar.sav

22. dsus4data/TOSSE-R.sav
__MACOSX/dsus4data/._TOSSE-R.sav
dsus4data/Transformations.SPS
COMPUTE logday1 = LG10(day1 + 1) .
COMPUTE logday2 = LG10(day2 + 1) .
COMPUTE logday3 = LG10(day3 + 1) .
COMPUTE sqrtday1 = SQRT(day1).
COMPUTE sqrtday2 = SQRT(day2).
COMPUTE sqrtday3 = SQRT(day3).
COMPUTE recday1 = 1/(day1+1).
COMPUTE recday2 = 1/(day2+1).
COMPUTE recday3 = 1/(day3+1).
EXECUTE .
__MACOSX/dsus4data/._Transformations.SPS
dsus4data/Tuk et al. (2011).sav
dsus4data/Tumour.sav

23. dsus4data/TutorMarks.sav
__MACOSX/dsus4data/._TutorMarks.sav
dsus4data/Viagra.sav
dsus4data/ViagraCovariate.sav
__MACOSX/dsus4data/._ViagraCovariate.sav
dsus4data/ViagraCovariateContrasts.sav
__MACOSX/dsus4data/._ViagraCovariateContrasts.sav
dsus4data/ViagraCovariateDummy.sav
dsus4data/Video Game Graphs.sav
dsus4data/Video Games.sav
dsus4data/Wii.sav
dsus4data/Williams.sav
__MACOSX/dsus4data/._Williams.sav
dsus4data/Zibarras et al. (2008).sav
© Charles T. Diebold, Ph.D., 7/16/13, 10/11/13. All Rights
Reserved. Page 1 of 25
Mediation and Moderation Tutorial:

24. RSCH-8250 Advanced Quantitative Reasoning
Charles T. Diebold, Ph.D.
July 16, 2013 (Revised October 11, 2013)
How to cite this document:
Diebold, C. T. (2013, October 11). Mediation and moderation
tutorial: RSCH-8250 advanced quantitative
reasoning. Available from [email protected]
Table of Contents
Assignment and Tutorial Introduction
...............................................................................................
..................... 2
Section 1: SPSS Specification of the Assignment
.............................................................................................. .
... 2
Descriptive Statistics
...............................................................................................
............................................ 2
Mediation Analysis
...............................................................................................
.............................................. 4
Moderation Analysis
...............................................................................................
............................................ 6
Section 2: Annotated Example SPSS Output, Write Up Guide,

25. and Sample APA Tables .................................. 11
Mediation Framework: Conceptual and Analytic
.............................................................................................
11
Example Mediation Analysis
...............................................................................................
............................. 13
Example Moderation Analysis
...............................................................................................
........................... 17
Results Write Up Guide
...............................................................................................
..................................... 22
Example APA Tables
...............................................................................................
......................................... 23
References and Recommended Reading
...............................................................................................
................ 25
© Charles T. Diebold, Ph.D., 7/16/13, 10/11/13. All Rights
Reserved. Page 2 of 25
Mediation and Moderation Tutorial:
RSCH-8250 Advanced Quantitative Reasoning
Assignment and Tutorial Introduction

26. This tutorial is intended to assist RSCH-8250 students in
completing the Week 7 application assignment. I
recommend that you use this tutorial as your first line of
instruction; then, if you have time, view Dr.
Morrow’s video or capitalize on other resources noted in the
classroom.
3rd edition of Field textbook:
Chapter 7 in the Field textbook, Smart Alex's Task #3 on p. 262
(as modified below).
4th edition of Field textbook:
Chapter 8 in the Field textbook, Smart Alex's Task #5 on p. 355
(as modified below).
The exercise uses the Child Aggression.sav SPSS datafile. The
objective of the exercise is to conduct and
interpret a mediation analysis or a moderation analysis using the
following three variables:
DV: Aggression, which is a measure of the younger sibling’s
aggression
IV: Parenting_Style, with higher scores indicating “bad”
parenting
M: Sibling_Aggression, which is a measure of the older
sibling’s aggression. This is the mediator in the
mediation analysis, and the moderator in the moderation
analysis (in the real world, mediation and
moderation require different theoretical or empirical rationale
and expected outcome; so, you would do
one or the other but not both for the same variable as done in
this assignment for sibling aggression).
The tutorial contains two sections. Section 1 provides step-by-

27. step graphic user interface (GUI) screencaptures
for specifying the assignment in SPSS. If you follow the steps
you will produce correct SPSS output. Section 2
presents and interprets output for a different set of variables,
and includes a results write up guide, and sample
APA style tables (the variables and data in Section 2 are “made
up” and do not reflect real research).
Section 1: SPSS Specification of the Assignment
Descriptive Statistics
Open the datafile, the Variable View screencapture is shown
below. There are six variables in the datafile, but
we are only interested in the three variables described above.
© Charles T. Diebold, Ph.D., 7/16/13, 10/11/13. All Rights
Reserved. Page 3 of 25
The Descriptives dialogue box appears (below left). Select the
three variables of interest and move into the
Variable(s) box (below right).
Click the OK button, which will produce output with the

28. minimum, maximum, mean, and standard deviation
values for each variable. In addition to providing descriptive
statistic information for the write up of results, the
means for parenting style and sibling aggression will be needed
in order to create centered versions of these
variables for the moderation analysis.
© Charles T. Diebold, Ph.D., 7/16/13, 10/11/13. All Rights
Reserved. Page 4 of 25
Mediation Analysis
The mediation analysis requires two separate regressions. In the
first, sequentially regress aggression (DV) on
parenting style (IV) and sibling aggression (Mediator). In the
second, regress sibling aggression on parenting
style. The reasons and focus of the two regressions are
demonstrated in the annotated example section of this
tutorial.
below.
The Linear Regression dialogue
box appears (below left). We
want to predict aggression, so it
is the dependent variable; click
on it to highlight, then click the
arrow next to the Dependent
box, which will move aggression
into the box.

29. Next, move the independent
variable, parenting style, into the
Independent(s) box (below left).
Click the “Next” button (below
left), which opens a blank
Independent(s) box (i.e., Block
2). Move the mediator, sibling
aggression, into the Block 2
Independent(s) box (below
right).
Below the Independent(s) box for both Block 1 and Block 2 is
the word “Method” and a dropdown box with
different ways to specify the entry of the predictors. For this
assignment, leave it as “Enter”.
© Charles T. Diebold, Ph.D., 7/16/13, 10/11/13. All Rights
Reserved. Page 5 of 25
In the Linear Regression dialogue box (see previous
screencaptures), there is a column of buttons along the upper
right. Click the “Statistics” button; a new dialogue box will
appear. Click the boxes so that checkmarks appear for each
of the elements as shown at left.
For the purposes of this assignment, there is no need to
examine the dialogue boxes for Plots, Save, Options, or
Bootstrap. Even though Field discusses some regression
diagnostics, use and understanding of these are (except for
multicollinearity) beyond the level of this course.

30. So, once you have specified the statistics at left click the
Continue button, which will return you to the Linear
Regression dialogue, in which clicking the OK button will
run the first regression analysis and produce adequate output
for the assignment. Example output is shown and interpreted
in Section 2 of this tutorial.
previously shown for the first regression. The
Linear Regression dialogue will likely still have the
specifications from the first regression (below left). To
clear and start fresh, click the “Reset” button. Move sibling
aggression into the Dependent box and parenting
style into the Independent(s) box. There is no need for any
further specifications. Clicking the OK button will
run the second regression analysis and produce adequate output
for the assignment. Example output is shown
and interpreted in Section 2 of this tutorial.
© Charles T. Diebold, Ph.D., 7/16/13, 10/11/13. All Rights
Reserved. Page 6 of 25
Moderation Analysis
The moderation analysis requires a standard regression of
aggression (DV) on parenting style (IV), sibling
aggression (moderator), and the interaction of parenting style
and sibling aggression (some people do a
sequential regression, but such is not necessary [Hayes, 2013]).
However, parenting style and aggression need

31. to be “centered” and the interaction term will then be the cross-
product (i.e., multiplication) of the centered
versions of the two variables (the reason for centering is
discussed in the annotated example in Section 2 of this
tutorial).
Centering and creation of the interaction variable are
demonstrated in two ways: (a) using SPSS syntax, and (b)
using SPSS GUI. Use either the syntax or GUI approach.
First, though, we need to know the mean values for parenting
style and sibling aggression. From the descriptive
statistics procedure you will find the following:
Variable Mean
Parenting style .0000
Sibling aggression .0083
Centering causes the mean of a variable to become zero.
Because the parenting style mean is already zero and
the sibling aggression is near zero, this is not a very good
example (but see the annotated example in Section 2
for what tends to happen in the real world and why centering is
important for moderation analysis). There is no
need to center parenting style, but even though just slightly off,
you should center sibling aggression to
demonstrate mastery of the technical skill.
Using SPSS syntax to center and create interaction. Go to

32. © Charles T. Diebold, Ph.D., 7/16/13, 10/11/13. All Rights
Reserved. Page 7 of 25
An empty syntax window will open (below left). Type the
following into the syntax editor (below right). Text in
ALL CAPS, though not necessary to be in all caps, are SPSS
commands. Text in lowercase font are variable
names that already exist or that you are creating. For example,
sib_agg_centered is the name I made up for the
new centered variable; however, sibling_aggression is the
existing name of the original variable.
COMPUTE sib_agg_centered = sibling_aggression - .0083.
FREQ sib_agg_centered/FORMAT=NOTABLE/STA=MIN MAX
MEAN.
COMPUTE interaction = parenting_style*sib_agg_centered.
EXECUTE.
After typing in the syntax, click “Run”; this will open the
dropdown options shown below. Click “All”.
© Charles T. Diebold, Ph.D., 7/16/13, 10/11/13. All Rights
Reserved. Page 8 of 25
As shown at left in the frequencies output for the centered
version of sibling
aggression, the mean is now zero as expected.

33. The Variable View of the Child Aggression.sav datafile now
includes the two
additional variables that were created. If you want, you can
click into the Label
cell for each of these and type in a label such as shown in the
second screen
below.
Statistics
sib_agg_centered
N
Valid 666
Missing 0
Mean .0000
Minimum -1.44
Maximum 1.10
© Charles T. Diebold, Ph.D., 7/16/13, 10/11/13. All Rights
Reserved. Page 9 of 25
Using SPSS GUI to center and create interaction. Go to
Transf

34. A Compute Variable dialogue
box opens. At the upper left
type the name of the new
variable you are creating in the
box under “Target Variable”.
Here I typed sib_agg_centered.
Select the Sibling_Aggression
variable and click the arrow
button next to the “Numeric
Expression” box, then type “-
.0083” but without the quote
marks. In its entirety it should
appear as follows:
Sibling_Aggression - .0083
Click the OK button, which will create the new variable.
Repeat the process to create the new interaction variable. That
before. Type the name of the new variable, for example
“interaction” (but without the quotes) in the Target
Variable box. Select the sib_agg_centered variable and move to
the Numeric Expression box, type *, then select
and move the parenting_style variable into the box. In its
entirety, the Numeric Expression box should contain:
Sib_agg_centered*Parenting_Style
Click the OK button, which will create the new variable.

35. © Charles T. Diebold, Ph.D., 7/16/13, 10/11/13. All Rights
Reserved. Page 10 of 25
Using SPSS GUI for moderation regression. Now that the
variables have been centered and the interaction
term created, we can run the regression to test for moderation.
Following Hayes (2013), who demonstrated that
the commonly used sequential regression approach is not
necessary, a standard regression is used to enter all
three variables simultaneously.
In the Linear Regression dialogue, move the
aggression variable to the Dependent box and move parenting
style (which was already centered), the centered
version of sibling aggression, and the interaction term to the
Independent(s) box.
Next to “Method” leave as “Enter”.
Click the Statistics button and set up as shown below right.
Then click the OK button to run the analysis.
Example output is demonstrated and interpreted in the next
section, which also demonstrates how to
descriptively probe the interaction if statistically significant.
© Charles T. Diebold, Ph.D., 7/16/13, 10/11/13. All Rights
Reserved. Page 11 of 25

36. Section 2: Annotated Example SPSS Output, Write Up Guide,
and Sample APA Tables
The example output shown below uses variables different from
the Week 7 assignment. The purpose is to
explain key elements of the output, point out what to focus on,
and demonstrate how to interpret and report the
results in APA statistical style. First, though, I present a
conceptual and analytic framework for understanding
mediation.
Mediation Framework: Conceptual and Analytic
A simple mediation analysis consists of three variables: IV
(predictor), DV (outcome), and the Mediator.
In classic mediation1
, the predictor and mediator are known (or expected) to
correlate with the outcome, and the
predictor is known (or expected) to correlate with the mediator.
The generic research question is: To what
extent is the effect of the predictor on the outcome transmitted
by the mediator?
That is, in classic mediation, the predictor is not thought to
cause the outcome. Instead, the predictor is thought
to cause the mediator, which in turn causes the outcome.
Because of this, the mediator should be something
amenable to change (i.e., not something such as sex). As well,
as a causal model, the predictor should
temporally precede the mediator, and both should temporally
precede the outcome or, at least, it should be

37. logically plausible to think of the predictor as causing the
mediator that, in turn, causes the outcome.
A generic path diagram of a simple mediation model is shown in
Figure 1. The model can be analyzed using
structural equation modeling software such as AMOS, or as a
series of two multiple regressions, which is the
procedure used in this demonstration. The outcome variable
(DV) should be quantitative. The mediator and
predictor (IV) can be quantitative or a true dichotomous
variable.
As depicted in Figure 1, path c is the total bivariate effect of the
IV on the DV (i.e., the simple correlation),
which is partitioned into a direct effect on the DV while
controlling for the mediator (c’) and an indirect effect
on the DV through the mediator (ab). As a partitioning of the
total effect between the IV and the DV, it
mathematically follows that:
(1) βc = βYX = rYX, the correlation between IV and DV
(2) βc = βc’ + βaβb
(3) βc’ ÷ c = direct effect proportion
(4) βaβb ÷ c = indirect effect proportion
Each of these are demonstrated with actual output and the Sobel
test is used to test for a statistically significant
indirect (i.e., mediated) effect.
1 I follow MacKinnon (2008) in using the term mediation to
refer to the classic case of a causal chain among the variables in

38. which the
direct relationship between the IV and DV is statistically
significantly reduced. Three related models that are not subject
matter of this
demonstration include: (a) covariate, in which the relationship
between IV and DV is not substantially changed; (b) suppressor,
in
which the relationship between IV and DV is significantly
increased; and (c) distorter, in which the relationship between
IV and DV is
significantly reversed.
© Charles T. Diebold, Ph.D., 7/16/13, 10/11/13. All Rights
Reserved. Page 12 of 25
Figure 1. Generic path diagram of a simple mediation model.
Path a is the result of regressing the Mediator on the IV. Paths b
and c’
result from regressing the DV simultaneously on the IV and
Mediator. Path c, which is for comparison purposes only,
represents the
simple regression of the DV on the IV.
Figure 2. Path diagram with generic coefficient notation. Outer
notations are unstandardized B coefficients and their standard
errors
(SEB) from the regression outputs, and inner notations are the
standardized beta (β) coefficients. Path a and Path b B

39. coefficients and
standard errors are needed for the Sobel test of statistically
significant mediation. All four β coefficients are needed to
calculate the
proportions of direct and indirect effects.
© Charles T. Diebold, Ph.D., 7/16/13, 10/11/13. All Rights
Reserved. Page 13 of 25
Steps in analyzing a classic mediation model. Two separate
regressions are all that is needed for a 3-variable
mediation analysis.
Regression 1: Using a sequential regression, regress the DV on
the IV (Block 1) and Mediator (Block 2).
Step 1a: Examine the correlation matrix. Each of the following
is required if following the conservative
Baron and Kenny (1986) approach (alternative approaches are
beyond the scope of this course):
• IV needs to be statistically significantly correlated with the
DV (if it is not, there is no relationship to
be mediated). The correlation between IV and DV represents the
total effect, Path βc in the model.
• IV needs to be statistically significantly correlated with the

40. Mediator (if it is not, the IV effect on the
DV cannot be transmitted through the Mediator).
Step 1b: Examine the regression coefficients output:
• Mediator coefficient, while controlling for IV, needs to be
statistically significant. If not, there is no
mediation. If statistically significant, the mediator’s B, SEB,
and β values are needed for Path b in
the model.
• IV’s β value, whether statistically significant or not, is needed
for Path c’ in the model in order to
calculate the direct effect proportion. The IV’s B and SEB
values are only for descriptive
comparison.
Regression 2: Regress Mediator on IV
• This provides the B, SEB, and β coefficients for Path a.
If Path b is significant and Path c’ is not, the IV effect on the
DV is said to be completely mediated. If both
paths are significant there may or may not be partial mediation.
An easy to conduct Sobel test can be used to
determine if the indirect (i.e., mediated) effect is statistically
significant. There are other more powerful ways to
test the mediation effect, but such are beyond the scope of this
course.
Example Mediation Analysis
Descriptive statistics. For the example output, the DV is overall
grade point average (GPA) of 9th grade
students. The IV is parental involvement in student’s education
(PARENT_INV) and the mediator is a measure

41. of a student’s attention span (ATTENTION). The research
question is: To what extent is the effect of parental
involvement on overall GPA mediated by attention span? That
is, the supposition is not that parental
involvement directly influences GPA, but that parental
involvement influences a student’s attention span that
then accounts for overall GPA.
As shown in the descriptive statistics output (from the
DESCRIPTIVES procedure in SPSS), data had been
collected on 216 individuals. The minimum, maximum, mean,
and standard deviation of each variable are
provided. Reporting on the operationalization of each variable
and the observed values in the sample give the
reader insight into the variable being analyzed. For example:
“Attention was measured for 9th grade students in
minutes on three separate occasions for three separate tasks.
Attention span was the average of these and ranged
from 13.04 to 40.54 minutes with a mean of 19.76 (SD = 4.46).”
Descriptive Statistics
N Minimum Maximum Mean Std. Deviation
GPA 216 .25 4.00 2.4386 .84507
PARENT_INV 216 55.00 137.00 102.3542 12.55762
ATTENTION 216 13.04 40.54 19.7605 4.45536
Valid N (listwise) 216
© Charles T. Diebold, Ph.D., 7/16/13, 10/11/13. All Rights
Reserved. Page 14 of 25

42. Regression 1. The correlation between parental involvement
(IV) and overall GPA (DV) was statistically
significantly correlated, r(214) = .446, p < .001. Also
statistically significant was the correlation between parent
involvement and attention span (mediator), r(214) = .622, p <
.001. These satisfy Baron and Kenny’s (1986)
first two conditions for a mediation analysis.
Correlations
GPA PARENT_INV ATTENTION
Pearson Correlation
GPA 1.000 .446 .523
PARENT_INV .446 1.000 .622
ATTENTION .523 .622 1.000
Sig. (1-tailed)
GPA . .000 .000
PARENT_INV .000 . .000
ATTENTION .000 .000 .
N
GPA 216 216 216
PARENT_INV 216 216 216
ATTENTION 216 216 216

43. Baron and Kenny’s third condition that the relationship between
mediator (attention span) and DV (overall
GPA) be statistically significant while controlling for the IV
(parental involvement) was also satisfied, t(213) =
5.47, p < .008. With VIF value below 2.0, there was no
evidence of collinearity between parental involvement
and attention span, so each coefficient’s significance values are
considered valid. The B, SEB, and β values
highlighted for attention span constitute the coefficients needed
for Path b in the mediation model. The β value
highlighted for parental involvement is needed to calculate the
direct effect; the B and SEB are for reference.
Coefficientsa
Model Unstandardized Coefficients Standardized
Coefficients
t Sig.
B Std. Error Beta
1
(Constant) -.633 .425 -1.492 .137
PARENT_INV .030 .004 .446 7.289 .000
2
(Constant) -.418 .400 -1.043 .298
PARENT_INV .013 .005 .197 2.679 .008
ATTENTION .076 .014 .401 5.465 .000

44. Model 95.0% Confidence Interval for B Correlations
Collinearity Statistics
Lower Bound Upper Bound Zero-order Partial Part Tolerance
VIF
1
(Constant) -1.470 .204
PARENT_INV .022 .038 .446 .446 .446 1.000 1.000
2
(Constant) -1.207 .372
PARENT_INV .003 .023 .446 .181 .154 .613 1.632
ATTENTION .049 .103 .523 .351 .314 .613 1.632
In the mediation model, β
for Path c = .446, the
correlation between GPA
(DV) and parental
involvement (IV). Because
this is a simple regression
the correlation is the same
as the β value in Model 1
of the sequential regression
below.
© Charles T. Diebold, Ph.D., 7/16/13, 10/11/13. All Rights
Reserved. Page 15 of 25

45. Regression 2. From the first regression’s correlation matrix we
knew that parental involvement (IV) was
statistically significantly correlated with attention span
(mediator). What we need from the simple regression in
which parental involvement predicts attention span are the B,
SEB, and β coefficients, which correspond to Path
a in the mediation model.
Coefficientsa
Model Unstandardized Coefficients Standardized
Coefficients
t Sig.
B Std. Error Beta
1
(Constant) -2.834 1.958 -1.447 .149
PARENT_INV .221 .019 .622 11.626 .000
a. Dependent Variable: ATTENTION
Mediation model coefficients and Sobel test. Figure 3 displays
the mediation model with coefficients from the
preceding example outputs. The values are needed to test the
statistical significance of the indirect effect and to
calculate the proportion of direct and indirect effects.
Figure 3. Mediation model path diagram with obtained
coefficients. Outer notations are unstandardized B coefficients

46. and their
standard errors (SEB) from the regression outputs, and inner
notations are the standardized beta (β) coefficients. The values
within
brackets are the baseline coefficients for the simple relationship
between IV and DV. It is these baseline B and β values that are
expected to decrease if there is a mediating effect.
From Figure 3 it is evident that Path c’ B coefficient of .013
and β of .197 are reduced, as would be expected
for mediation, from the baseline Path c coefficients of B and β,
.030 and .446, respectively. The Sobel test tells
us whether the reduction was significant by inputting the B and
SEB values for Paths a and b into the equation
or the online calculator. The Sobel z is evaluated against a two-
tailed critical z value, which for alpha = .05 is ±
1.96.
The results from the online calculator, available at
http://www.quantpsy.org/sobel/sobel.htm , are shown in
Figure 4. Inputted are the B and SEB values for Path a and Path
b. Pay attention to input values into the correct
box. Clicking the “Calculate” button provides the test statistic
and p values. Here, Sobel z = 4.92, p < .001.
Attention
span
Parental
involvement

47. Overall
GPA
.221 (.019) .076 (.014)
.197 [.446]
.622 .401
.013 (.005)
[.030 (.004)]
http://www.quantpsy.org/sobel/sobel.htm�
© Charles T. Diebold, Ph.D., 7/16/13, 10/11/13. All Rights
Reserved. Page 16 of 25
(FYI: 8.7e-7 is scientific notation, meaning move the decimal
place 7 places to the left, which results in p =
.00000087, but per APA, report as p < .001).
Figure 4. Sobel test of the mediating effect. Input values are the
B and SEB values for Paths a and b. The mediating effect was
statistically significant, Sobel z = 4.92, p < .001. (Formulae and
comparative differences of the Aroian and Goodman tests are on
the
website).
Direct and indirect effects. The mediating effect was
significant, but because the IV (Path c’) was still
significant in Block 2 of the sequential regression, the effect of
the IV on the DV was only partially mediated.

48. Calculation of the direct and indirect proportions are the ratios
of β coefficients for Path c’ to Path c (direct
effect) and for Paths ab to Path c (indirect effect). As calculated
below, 44% of the IV effect on the DV was
direct, while 56% was transmitted by the mediator.
Direct effect = βc’ ÷ βc = .197 ÷ .446 = .4417
Indirect effect = βa(βb) ÷ βc = .622(.401) ÷ .446 = .5592
© Charles T. Diebold, Ph.D., 7/16/13, 10/11/13. All Rights
Reserved. Page 17 of 25
Example Moderation Analysis
Descriptive statistics. For the annotated example output, the DV
is overall grade point average (GPA) of 9th
grade students. The IV is IQ and the moderator is attention span
(ATTENTION). The research question is: To
what extent is the effect of IQ on overall GPA a function of
attention span? That is, the supposition is that the
relationship between IQ and overall GPA is not the same at all
levels of attention span, that attention span and
IQ have an interaction effect on overall GPA.
The minimum, maximum, mean, and standard deviation (from
DESCRIPTIVES procedure) for each variable is
shown below. Reporting on the operationalization of each
variable and the observed values in the sample give
the reader insight into the variable being analyzed. For
example: “Attention was measured for 9th grade students

49. in minutes on three separate occasions for three separate tasks.
Attention span was the average of these and
ranged from 13.04 to 40.54 minutes with a mean of 19.76 (SD =
4.46).”
Descriptive Statistics
N Minimum Maximum Mean Std. Deviation
GPA 216 .25 4.00 2.4386 .84507
ATTENTION 216 13.04 40.54 19.7605 4.45536
IQ 216 45.00 199.00 102.3565 29.58170
Valid N (listwise) 216
The interaction between attention span and IQ is created by
multiplying the two values for each participant.
This will create multicollinearity between the attention span
variable, the IQ variable, and the interaction
variable, which can invalidate the regression because
multicollinearity increases the standard error that can
erroneously lead to conclusions of nonsignificance. To avoid
this, attention span and IQ need to be centered and
the interaction created as the cross-product of the new centered
versions of these two variables.
Centering is accomplished by subtracting the mean. For
example, the mean for attention span is 19.7605, so to
center it you subtract 19.7605 from each participant’s score.
Similarly, IQ is centered by subtracting 102.3565
from each score. Centering shifts central tendencies such as
mean and median, but does not change
distributional characteristics such as standard deviation,
skewness, or kurtosis, which is evident below.

50. Statistics
IQ IQ_centered ATTENTION ATT_centered
N
Valid 216 216 216 216
Missing 0 0 0 0
Mean 102.3565 .0000 19.7605 .0000
Std. Error of Mean 2.01278 2.01278 .30315 .30315
Median 99.0000 -3.3565 18.8679 -.8926
Std. Deviation 29.58170 29.58170 4.45536 4.45536
Skewness 1.119 1.119 1.405 1.405
Std. Error of Skewness .166 .166 .166 .166
Kurtosis 1.516 1.516 3.424 3.424
Std. Error of Kurtosis .330 .330 .330 .330
Minimum 45.00 -57.36 13.04 -6.72
Maximum 199.00 96.64 40.54 20.78
© Charles T. Diebold, Ph.D., 7/16/13, 10/11/13. All Rights
Reserved. Page 18 of 25
From the regression’s correlation matrix, it is seen that overall
GPA is statistically significantly related to IQ,

51. r(214) = .217, p = .001; and also statistically significantly
related to attention span, r(214) = .523, p < .001.
However, IQ and attention span are not statistically
significantly correlated, r(214) = .004, p = .475. The fact
that it is often the case that IV and moderator are not correlated
exemplifies why you would not propose both a
moderation analysis and a mediation analysis (which requires
statistically significant correlation between IV
and mediator).
Correlations
GPA IQ_centered ATT_centered IQxATT_centered
Pearson Correlation
GPA 1.000 .217 .523 -.153
IQ_centered .217 1.000 .004 -.210
ATT_centered .523 .004 1.000 .009
IQxATT_centered -.153 -.210 .009 1.000
Sig. (1-tailed)
GPA . .001 .000 .012
IQ_centered .001 . .475 .001
ATT_centered .000 .475 . .449
IQxATT_centered .012 .001 .449 .
N

52. GPA 216 216 216 216
IQ_centered 216 216 216 216
ATT_centered 216 216 216 216
IQxATT_centered 216 216 216 216
The combined effect of attention span, IQ, and their interaction
accounted for one-third of the variance in
overall GPA, F(3, 212) = 35.32, p < .001, R2 = .333. You
should be able to locate these values in the output
below.
Model Summary
Model R R Square Adjusted R
Square
Std. Error of
the Estimate
Change Statistics
R Square
Change
F Change df1 df2 Sig. F Change
1 .577a .333 .324 .69490 .333 35.322 3 212 .000

53. a. Predictors: (Constant), IQxATT_centered, ATT_centered,
IQ_centered
ANOVAa
Model Sum of Squares df Mean Square F Sig.
1
Regression 51.169 3 17.056 35.322 .000b
Residual 102.371 212 .483
Total 153.540 215
a. Dependent Variable: GPA
b. Predictors: (Constant), IQxATT_centered, ATT_centered,
IQ_centered
© Charles T. Diebold, Ph.D., 7/16/13, 10/11/13. All Rights
Reserved. Page 19 of 25
Centered IQ statistically significantly uniquely accounted for
3.5% of the variance in overall GPA, t(212) =
3.32, p = .001, sr2 = .0346. (As reminder, sr stands for
semipartial correlation, the more common term used in
the literature for what SPSS labels part correlation).
Centered attention span uniquely accounted for 27.4% of
variance in overall GPA, t(212) = 9.33, p < .001, sr2 =

54. .2735. The interaction, which represents the moderated effect,
was also statistically significant, t(212) = -2.05, p
= .042, sr2 = .0132, uniquely accounting for 1.3% of the
variance in overall GPA.
Semipartial-squared values of .01, .06, and .14 represent small,
medium, and large effect sizes, respectively. So,
the interaction had a small effect, which is typical for
interactions (Frazier, Tiz, & Barron, 2004), centered IQ
had a small-to-medium effect, and attention span had a very
large effect.
Coefficientsa
Model Unstandardized Coefficients Standardized
Coefficients
t Sig.
B Std. Error Beta
1
(Constant) 2.439 .047 51.586 .000
IQ_centered .005 .002 .191 3.323 .001
ATT_centered .099 .011 .523 9.333 .000
IQxATT_centered -.001 .000 -.118 -2.049 .042
Coefficientsa
Model 95.0% Confidence Interval for B Correlations

55. Lower Bound Upper Bound Zero-order Partial Part
1
(Constant) 2.346 2.532
IQ_centered .002 .009 .217 .222 .186
ATT_centered .078 .120 .523 .540 .523
IQxATT_centered -.002 .000 -.153 -.139 -.115
Coefficientsa
Model Collinearity Statistics
Tolerance VIF
1
(Constant)
IQ_centered .956 1.046
ATT_centered 1.000 1.000
IQxATT_centered .956 1.046
a. Dependent Variable: GPA
The VIF values are 1.0, but a regression with the original
uncentered variables and their interaction had VIF

56. values of 21.7 for attention span, 32.4 for IQ, and 53.2 for the
interaction, which would have raised serious
questions about the validity of those results.
© Charles T. Diebold, Ph.D., 7/16/13, 10/11/13. All Rights
Reserved. Page 20 of 25
From the unstandardized B coefficients (see previous page) the
regression equation is:
Overall GPA’ = 2.439 + .005(IQ) + .099(attention span) -
.001(IQ X attention span)
Rearranging terms, this can be rewritten as:
Overall GPA’ = 2.439 + .099(attention span) + (.005 -
.001(attention span))(IQ)
At 1 standard deviation above the mean of attention span, which
is 4.455, the equation is:
Overall GPA’ = 2.439 + .099(4.455) + (.005 -.001(4.455)(IQ) =
2.880 + .0005(IQ)
At mean of attention span, which is 0:
Overall GPA’ = 2.439 + .005(IQ)
At 1 standard deviation below the mean of attention span, which
is -4.455, the equation is:
Overall GPA’ = 2.439 + .099(-4.455) + (.005 -.001(-4.455)(IQ)

57. = 1.998 + .009(IQ)
From the above three equations, Table 1, and the lines in Figure
5, notice that the slope for IQ increases as
attention span decreases. That is, when attention span is 1
standard deviation above its mean value, GPA is
predicted to increase much less (B = .0005) for each 1 point
increase in IQ than when attention span is 1
standard deviation below its mean value for which GPA is
predicted to increase .009 points for each 1 point
increase in IQ.
So, the relationship between IQ and overall GPA is not
constant, but depends on one’s attention span—this is
the moderation effect. Those with high IQ and high attention
span are not much different in predicted GPA (M
= 2.89) than those with low IQ and high attention span (M =
2.86)—so, high attention span overcomes
differences in IQ with respect to GPA. However, those with
high IQ and low attention span (M = 2.26) have
much higher predicted GPA than those with low IQ and low
attention span (M = 1.73)—in this case, IQ makes a
difference.
If there is a moderated effect, you should discuss, for example,
why it would make sense that attention span
moderates the effect of IQ on overall GPA. In real research this
would not just be speculation, but it would
follow the theoretical or empirical foundations that lead you to
justify proposing a moderation analysis in the
first place.
Table 1
Predicted GPA for IQ Values of 1 SD Below, Mean, and 1 SD
Above as Moderated by

58. Attention Span Values of 1 SD Below, Mean, and 1 SD Above
Predicted GPA for Values of IQ
Attention span
value
Constant
IQ slope
-1 SD
(-29.582)
Mean
(0)
+1 SD
(29.582)
-1 SD (-4.455) 1.998 .0090 1.732 1.998 2.264
Mean (0) 2.439 .0050 2.291 2.439 2.587
+1 SD (4.455) 2.880 .0005 2.865 2.880 2.895
Note. Constant and slope of IQ are from the regression
equations for the specified attention span values.
Predicted GPA is the IQ slope value times the specified IQ
value (i.e., -29.582, 0, or 29.582) plus the constant.

59. © Charles T. Diebold, Ph.D., 7/16/13, 10/11/13. All Rights
Reserved. Page 21 of 25
Figure 5. Differing slopes of the relationship between IQ and
GPA as a function of attention span.
© Charles T. Diebold, Ph.D., 7/16/13, 10/11/13. All Rights
Reserved. Page 22 of 25
Results Write Up Guide
Begin the write up by describing the context of the research and
the variables. If known, state how each variable
was operationalized, for example: “Overall GPA was measured
on the traditional 4-point scale from 0 (F) to 4
(A)”, or “Satisfaction was measured on a 5-point likert-type
scale from 1 (not at all satisfied) to 5 (extremely
satisfied).” Please pay attention to APA style for reporting scale
anchors (see p. 91 and p. 105 in the 6th edition
of the APA Manual).
Report descriptive statistics such as minimum, maximum, mean,
and standard deviation for each metric
variable. For nominal variables, report percentage for each level
of the variable, for example: “Of the total
sample (N = 150) there were 40 (26.7%) males and 110 (73.3%)
females.” Keep in mind that a sentence that
includes information in parentheticals must still be a sentence
(and make sense) if the parentheticals are
removed. For example: “Of the total sample there were 40 males

60. and 110 females.”
State the purpose of the analysis or provide the guiding research
question(s). If you use research questions, do
not craft them such that they can be answered with a yes or no.
Instead, craft them so that they will have a
quantitative answer. For example: “What is the strength and
direction of relationship between X and Y?” or
“What is the difference in group means on X between males and
females?”
Present null and alternative hypothesis sets applicable to the
analysis. For the mediation analysis, following
Baron and Kenny (1986), there would be three hypothesis sets:
(a) DV on IV, (b) mediator on IV, and (c) DV
on mediator while controlling for IV. For the moderation
analysis there would be four sets of hypotheses, one
each for IV, moderator, and interaction, and one combined
effect. Where appropriate, be careful to note within a
hypotheses while “controlling for” or “holding constant” the
effects of the other predictors.
State assumptions or other considerations for the analysis, and
report the actual statistical result for relevant
tests. For this course, the only regression consideration that
needs to be presented and discussed is for
multicollinearity. Even if violated, you must still report and
interpret the remaining results.
Report and interpret the overall regression results. Report and
interpret the results of each predictor. Be sure to
include the actual statistical results in text—examples were
provided within the annotated output section of this
tutorial. Don’t forget to interpret the results (e.g., as IQ
increased, overall GPA was predicted to increase; based
on semipartial correlations, variable x was the most important

61. predictor of y; 56% of the effect of parental
involvement on GPA was indirect through the mediating
variable of attention span; etc.). Draw conclusions
about rejecting or failing to reject each null. If needed,
summarize the results (without statistics) in a concluding
sentence or paragraph. If there is a mediated or moderated
effect, you should briefly discuss why it would make
sense that the relationship between the IV and DV was affected
by the mediator or moderator.
Provide APA style tables appropriate to the analysis. Do not use
SPSS output, it is not in APA style. Example
APA tables are shown in the next section using the results from
the example output in this tutorial. Although
one would typically not duplicate information in text and tables,
it is important to demonstrate competence in
both ways of reporting the results; so, you cannot just provide
tables, you must also report the relevant statistical
results within the textual write up.
© Charles T. Diebold, Ph.D., 7/16/13, 10/11/13. All Rights
Reserved. Page 23 of 25
Example APA Tables
Table 2
Means, Standard Deviations, and Intercorrelations for Overall
GPA, Parental
Involvement, and Attention Span (N = 216)
Variable M SD DV IV Med.

62. DV: Overall GPA 2.44 0.85 .45 .52
IV: Parental involvement 102.35 12.56 < .001 .62
Med.: Attention span 19.76 4.46 < .001 < .001
Note. Med. = mediator. Upper diagonal contains correlation
coefficients. Lower diagonal
contains one-tailed p values.
Table 3
Regression Summaries for Mediating Effect of Attention Span
on the Relationship between
Parental Involvement and Overall GPA (N = 216)
Model B SEB 95% CI β sr
2 t p
Mediator on IV
Mediator (Path a) .221 .019 [.183, .258] .622 .387 11.6 < .001
DV on
IV and Mediatora
IV (Path c) .030 .004 [.022, .038] .446 .199 7.3 < .001
IV (Path c’) .013 .005 [.003, .023] .197 .024 2.7 .008
Mediator (Path b) .076 .014 [.049, .103] .401 .099 5.5 < .001
Note. DV = overall GPA. IV = parental involvement. Mediator

63. = attention span. sr2 = squared semipartial.
a F(2, 13) = 45.1, p < .001, R2 = .297.
© Charles T. Diebold, Ph.D., 7/16/13, 10/11/13. All Rights
Reserved. Page 24 of 25
Table 4
Means, Standard Deviations, and Intercorrelations for Overall
GPA, IQ,
and Attention Span (N = 216)
Variable M SD DV IV Mod.
DV: Overall GPA 2.44 0.85 .22 .52
IV: IQ 102.36 29.58 .001 < .01
Mod.: Attention span 19.76 4.46 < .001 .475
Note. Mod. = moderator. Upper diagonal contains correlation
coefficients. Lower diagonal
contains one-tailed p values.
Table 5
Regression Summary for Moderating Effect of Centered
Attention Span on the Relationship
between Centered IQ and Overall GPA (N = 216)

64. Model B SEB 95% CI β sr
2 t p
IQ .005 .002 [.002, .009] .191 .035 3.3 .001
Attention span (AS) .099 .011 [.078, .120] .523 .274 9.3 < .001
IQxAS -.001 < .000 [-.002, -.000] -.118 .013 -2.1 .042
Note. sr2 = squared semipartial. F(3, 212) = 35.3, p < .001, R2
= .333.
© Charles T. Diebold, Ph.D., 7/16/13, 10/11/13. All Rights
Reserved. Page 25 of 25
References and Recommended Reading
Baron, R.M., & Kenny, D.A. (1986). The moderator-mediator
variable distinction in social psychological
research: Conceptual, strategic, and statistical considerations.
Journal of Personality and Social
Psychology, 51(6), 1173-1182.
Hayes, A. F. (2013). Introduction to mediation, moderation, and
conditional process analysis: A regression-
based approach. New York, NY: The Guilford Press.
Frazier, P.A., Tix, A.P., & Barron, K.E. (2004). Testing

65. moderator and mediator effects in counseling
psychology research. Journal of Counseling Psychology, 51(1),
115-134.
MacKinnon, D.P. (2008). Introduction to statistical mediation
analysis. New York, NY: Taylor & Francis
Group, LLC.
MacKinnon, D.P., Lockwood, C.M., Hoffman, J.M., West, S.G.,
& Sheets, V. (2002). A comparison of methods
to test mediation and other intervening variable effects.
Psychological Methods, 7(1), 83-104.