Unformatted text preview: Discovering Statistics Using SPSS: Chapter 9 Chapter 9: Answers
Task 1
Stalking is a very disruptive and upsetting (for the person being stalked) experience in which
someone (the stalker) constantly harasses or obsesses about another person. It can take
many forms, from sending intensely disturbing letters threatening to boil your cat if you don’t
reciprocate the stalkers undeniable love for you, to literally following you around your local
area in a desperate attempt to see which CD you buy on a Saturday (as if it would be anything
other than Fugazi!). A psychologist, who’d had enough of being stalked by people, decided to
try two different therapies on different groups of stalkers (25 stalkers in each group—this
variable is called Group). The first group of stalkers he gave what he termed cruel to be kind
therapy. This therapy was based on punishment for stalking behaviours; in short every time
the stalker followed him around, or sent him a letter, the psychologist attacked them with a
cattle prod until they stopped their stalking behaviour. It was hoped that the stalkers would
learn an aversive reaction to anything resembling stalking. The second therapy was
psychodyshamic therapy, which was a recent development on Freud’s psychodynamic therapy
that acknowledges what a sham this kind of treatment is (so, you could say it’s based on
Fraudian theory!). The stalkers were hypnotised and regressed into their childhood, the
therapist would also discuss their penis (unless it was a woman in which case they discussed
their lack of penis), the penis of their father, their dog’s penis, the penis of the cat down the
road, and anyone else’s penis that sprang to mind. At the end of therapy, the psychologist
measured the number of hours in the week that the stalker spent stalking their prey (this
variable is called stalk2). Now, the therapist believed that the success of therapy might well
depend on how bad the problem was to begin with, so before therapy the therapist measured
the number of hours that the patient spent stalking as an indicator of how much of a stalker
the person was (this variable is called stalk1). The data are in the file Stalker.sav, analyse the
effect of therapy on stalking behaviour after therapy, controlling for the amount of stalking
behaviour before therapy.
SPSS Output
Tests of BetweenSubjects Effects
Dependent Variable: Time Spent Stalking After Therapy (hours per week)
Source
Corrected Model
Intercept
THERAPY
Error
Total
Corrected Total Type III Sum
of Squares
591.680a
170528.000
591.680
8526.320
179646.000
9118.000 df
1
1
1
48
50
49 Mean Square
591.680
170528.000
591.680
177.632 F
3.331
960.009
3.331 Sig.
.074
.000
.074 a. R Squared = .065 (Adjusted R Squared = .045) This output shows the ANOVA table when the covariate is not included. It is clear from the
significance value that there is no difference in the hours spent stalking after therapy for the
two therapy groups (p is 0.074 which is greater than 0.05). You should note that the total
amount of variation to be explained (SST) was 9118, of which the experimental manipulation
accounted for 591.68 units (SSM), whilst 8526.32 were unexplained (SSR). Dr. Dr. Andy Field Page 1 8/18/2003 Discovering Statistics Using SPSS: Chapter 9 Mean Hours Spent Stalking After Therapy 70
Cruel to be Kind Therapy
Psychodyshamic 60 50 0
Unadjusted Adjusted Type of Mean This bar chart shows the mean number of hours spent stalking after therapy. The normal
means are shown as well as the same means when the data are adjusted for the effect of the
covariate. In this case the adjusted and unadjusted means are relatively similar.
Descriptive Statistics
Dependent Variable: Time Spent Stalking After Therapy (hours per
week)
Group
Cruel to be Kind Therapy
Psychodyshamic Therapy
Total Mean
54.9600
61.8400
58.4000 Std. Deviation
16.33116
9.41046
13.64117 N
25
25
50 This table shows the unadjusted means (i.e. the normal means if we ignore the effect of the
covariate). These are the same values plotted on the left hand side of the bar chart. These
results show that the time spent stalking after therapy was less after cruel to be kind therapy.
However, we know from our initial ANOVA that this difference is nonsignificant. So, what now
happens when we consider the effect of the covariate (in this case the extent of the stalker’s
problem before therapy)?
a
Levene's Test of Equality of Error Variances Dependent Variable: Time Spent Stalking After
Therapy (hours per week)
F
7.189 df1 df2
1 Sig.
.010 48 Tests the null hypothesis that the error variance of
the dependent variable is equal across groups.
a. Design: Intercept+STALK1+GROUP This table shows the results of Levene’s test, which is significant because the significance value
is 0.01 (less than 0.05). This finding tells us that the variances across groups are different and
the assumption has been broken.
Tests of BetweenSubjects Effects
Dependent Variable: Time Spent Stalking After Therapy (hours per week)
Source
Corrected Model
Intercept
HOURS SPENT STALKING BEFORE THERAPY
THERAPY
Error
Total
Corrected Total Type III Sum
of Squares
5006.278a
8.646E02
4414.598
480.265
4111.722
179646.000
9118.000 df
2
1
1
1
47
50
49 Mean Square
2503.139
8.646E02
4414.598
480.265
87.483 F
28.613
.001
50.462
5.490 Sig.
.000
.975
.000
.023 a. R Squared = .549 (Adjusted R Squared = .530) This table shows the ANCOVA. Looking first at the significance values, it is clear that the
covariate significantly predicts the dependent variable, so the hours spent stalking after
therapy depends on the extent of the initial problem (i.e. the hours spent stalking before Dr. Dr. Andy Field Page 2 8/18/2003 Discovering Statistics Using SPSS: Chapter 9
therapy). More interesting is that when the effect of initial stalking behaviour is removed, the
effect of therapy becomes significant (p has gone down from 0.074 to 0.023, which is less than
0.05).
Group
Dependent Variable: Time Spent Stalking After Therapy (hours per week)
Group
Cruel to be Kind Therapy
Psychodyshamic Therapy 95% Confidence Interval
Lower Bound Upper Bound
51.534
59.063
57.737
65.266 Mean
Std. Error
55.299a
1.871
61.501a
1.871 a. Evaluated at covariates appeared in the model: Time Spent Stalking Before
Therapy (hours per week) = 65.2200. To interpret the results of the main effect of therapy we need to look at adjusted means. These
adjusted means are shown above. There are only two groups being compared in this example
so we can conclude that the therapies had a significantly different effect on stalking behaviour;
specifically stalking behaviour was lower after the therapy involving the cattle prod compared
to psychodyshamic therapy. Stalking After Therapy (hours per week) Linear Regression
W 80.00 W W W W W
W 60.00
W
W
W W WW
W WW W
W
W
W
W W
W W W
W W
W W
W W W
W
W W W W
W W W 40.00 W W 20.00 W
W 50.00 60.00 70.00 80.00 90.00 Stalking Before Therapy (hours per week)
We need to interpret the covariate. The graph above shows the time spent stalking after
therapy (dependent variable) and the initial level of stalking (covariate). This graph shows that
there is a positive relationship between the two variables, that is, high scores on one variable
correspond with high scores on the other, whereas low scores on one variable correspond with
low scores on the other.
Calculating the Effect Size
Omegasquared can be calculated for the effect of therapy using the mean squares for the
experimental effect (480.27), the mean squares for the error term (87.48), and the sample
size per group (25): Dr. Dr. Andy Field Page 3 8/18/2003 Discovering Statistics Using SPSS: Chapter 9
2
480.
87 48
ωTherapy = 480.27 +(27 −−1).×87.48 )
(25 392.78
480.27 + 2099.59
= 0.15
= ωTherapy = 0.15 = 0.39 This represents a medium to large effect. Therefore, the effect of a cattle prod compared to
psychodyshamic therapy is a substantive finding.
For the effect of the covariate, the error mean squares is the same, but the effect is much
bigger (MSM is 4414.60 rounded to 2 decimal places). If we place this value in the equation,
we get the following:
2
87 48
.
ωCo var iate = 44144414(60 −−1).×87.48 )
.60 + (25 4327.12
4414.60 + 2099.59
= 0.66
= ωCo var iate = 0.66 = 0.82 This represents a very large effect (it is well above the threshold of 0.5, and is close to 1).
Therefore, the relationship between initial stalking behaviour and the stalking behaviour after
therapy is very strong indeed.
Interpreting and Writing the Result
The correct way to report the main finding would be:
Levene’s test was significant (F(1, 48) = 7.19, p < .05) indicating that the assumption
of homogeneity of variance had been broken. The main effect of therapy was significant
(F(1, 47) = 5.49, p < .05, r = .39) indicating that the time spent stalking was lower
after using a cattle prod (M = 55.30, SE = 1.87) compared to after psychodyshamic
therapy (M = 61.50, SE = 1.87).
The covariate was also significant (F(1, 47) = 50.46, p < .001, r = .82) indicating that
level of stalking before therapy had a significant effect on level of stalking after therapy
(there was a positive relationship between these two variables)All significant values are
reported at p < .05.There was a significant effect of teaching style on exam marks, F(2,
27) = 21.01, ω = .82. Planned contrasts revealed that reward produced significantly
better exam grades than punishment and indifference, t(27) = –5.98, r = .75, and that
punishment produced significantly worse exam marks than indifference, t(27) = –2.51,
r = .43. Task 2
A marketing manager for a certain wellknown drinks manufacturer was interested in the
therapeutic benefit of certain soft drinks for curing hangovers. He took 15 people out on the
town one night and got them drunk. The next morning as they awoke, dehydrated and feeling
as though they’d licked a camel’s sandy feet clean with their tongue, he gave 5 of them water
to drink, 5 of them Lucozade (in case this isn’t sold outside of the UK it’s a very nice glucosebased drink), and the remaining five a leading brand of cola (this variable is called drink). He
then measured how well they felt (on a scale from 0 = I feel like death to 10 = I feel really full
of beans and healthy) two hours later (this variable is called well). He wanted to know which
drink produced the greatest level of wellness. However, he realised it was important to control
for how drunk the person got the night before, and so he’s measured this on a scale of 0 = as
sober as a nun to 10 = flapping about like a haddock out of water on the floor in a puddle of
their own vomit. The data are in the file HangoverCure.sav.
SPSS Output Dr. Dr. Andy Field Page 4 8/18/2003 Discovering Statistics Using SPSS: Chapter 9 Tests of BetweenSubjects Effects
Dependent Variable: How Well Does The Person Feel?
Source
Corrected Model
Intercept
DRINK
Error
Total
Corrected Total Type III Sum
of Squares
2.133a
459.267
2.133
15.600
477.000
17.733 df Mean Square
1.067
459.267
1.067
1.300 2
1
2
12
15
14 F
.821
353.282
.821 Sig.
.463
.000
.463 a. R Squared = .120 (Adjusted R Squared = .026) This table shows the ANOVA table for these data when the covariate is not included. It is clear
from the significance value that there are no differences in how well people feel when they
have different drinks.
a
Levene's Test of Equality of Error Variances Dependent Variable: How Well Does The Person Feel?
F
.220 df1 df2
2 12 Sig.
.806 Tests the null hypothesis that the error variance of
the dependent variable is equal across groups.
a. Design: Intercept+DRUNK+DRINK Tests of BetweenSubjects Effects
Dependent Variable: How Well Does The Person Feel?
Source
Corrected Model
Intercept
DRUNK
DRINK
Error
Total
Corrected Total Type III Sum
of Squares
13.320a
14.264
11.187
3.464
4.413
477.000
17.733 df
3
1
1
2
11
15
14 Mean Square
4.440
14.264
11.187
1.732
.401 F
11.068
35.556
27.886
4.318 Sig.
.001
.000
.000
.041 a. R Squared = .751 (Adjusted R Squared = .683) These tables show the results of Levene’s test and the ANOVA table when drunkenness the
previous night is included in the model as a covariate. Levene’s test is nonsignificant,
indicating that the group variances are roughly equal (hence the assumption of homogeneity of
variance has been met). It is clear that the covariate significantly predicts the dependent
variable, so the drunkenness of the person influenced how well they felt the next day. What’s
more interesting is that when the effect of drunkenness is removed, the effect of drink
becomes significant (p is 0.041 which is less than 0.05).
Parameter Estimates
Dependent Variable: How Well Does The Person Feel?
Parameter
Intercept
DRUNK
[DRINK=1.00]
[DRINK=2.00]
[DRINK=3.00] B
Std. Error
7.116
.377
.548
.104
.142
.420
.987
.442
0a
. t
18.861
5.281
.338
2.233
. Sig.
.000
.000
.741
.047
. 95% Confidence Interval
Lower Bound Upper Bound
6.286
7.947
.777
.320
1.065
.781
.014
1.960
.
. a. This parameter is set to zero because it is redundant. The next table shows the parameter estimates selected in the options dialog box. These
estimates are calculated using a regression analysis with drink split into two dummy coding
variables. SPSS codes the two dummy variables such that the last category (the category
coded with the highest value in the data editor—in this case the cola group) is the reference
category. This reference category (labelled dose=3 in the output) is coded with a zero for both
dummy variables. Dose=2, therefore, represents the difference between the group coded as 2
(Lucozade) and the reference category (cola), and dose=1 represents the difference between Dr. Dr. Andy Field Page 5 8/18/2003 Discovering Statistics Using SPSS: Chapter 9
the group coded as 1 (water) and the reference category (cola). The β values literally
represent the differences between the means of these groups and so the significances of the ttests tell us whether the group means differ significantly. Therefore, from these estimates we
could conclude that the cola and water groups have similar means whereas the cola and
Lucozade groups have significantly different means.
Contrast Results (K Matrix) a Drink Simple Contrast
Level 2 vs. Level 1 Contrast Estimate
Hypothesized Value
Difference (Estimate  Hypothesized)
Std. Error
Sig.
95% Confidence Interval
for Difference Level 3 vs. Level 1 Dependent
Variable
How Well
Does The
Person Feel?
1.129
0 Lower Bound
Upper Bound Contrast Estimate
Hypothesized Value
Difference (Estimate  Hypothesized)
Std. Error
Sig.
95% Confidence Interval
for Difference Lower Bound
Upper Bound 1.129
.405
.018
.237
2.021
.142
0
.142
.420
.741
.781
1.065 a. Reference category = 1 The next output shows the result of a contrast analysis that compares level 2 (Lucozade)
against level 1 (water) as a first comparison, and level 3 (cola) against level 1 (water) as a
second comparison. These results show that the Lucozade group felt significantly better than
the water group (contrast 1), but that the cola group did not differ significantly from the water
group (p = 0.741). These results are consistent with the regression parameter estimates (in
fact, note that contrast 2 is identical to the regression parameters for dose=1 in the previous
section).
Drink
Dependent Variable: How Well Does The Person Feel?
Drink
Water
Lucozade
Cola Mean
Std. Error
5.110a
.284
6.239a
.295
5.252a
.302 95% Confidence Interval
Lower Bound Upper Bound
4.485
5.735
5.589
6.888
4.588
5.916 a. Covariates appearing in the model are evaluated at the
following values: How Drunk was the Person the Night Before
= 4.6000. This table gives the adjusted values of the group means and it is these values that should be
used for interpretation. The adjusted means show that the significant ANCOVA reflects a
difference between the water and the Lucozade group. The cola and water groups appear to
have fairly similar adjusted means indicating that cola is no better than water at helping your
hangover. These conclusions support what we know from the contrasts and regression
parameters.
To look at the effect of the covariate we can examine a scatterplot: Dr. Dr. Andy Field Page 6 8/18/2003 Discovering Statistics Using SPSS: Chapter 9 W
How Well Does The Person Feel? 8.00 Linear Regression 7.00
W W 5.00 W W 6.00 W W W W W 4.00 W 3.00 2.00 1.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 How Drunk was the Person the Night Before This shows that the more drunk a person was the night before, the less well they felt the next
day.
Calculating the Effect Size
We can calculate omega squared (ω2) for the covariate:
MS − MS R
ω 2 = MS + (M −1)× MS )
M (n
R ω2 = 11.19 − 0.40
11.19 + (( 5 − 1 )× 0.40 ) = 0.84
= 0.92 We can also do the same for the main effect of drink: ω2 = 1.73 − 0.40
1.73 + (( 5 − 1 )× 0.40 ) = 0.40
= 0.63 We’ve got tstatistics for the comparisons between the cola and water group and the cola and
Lucozade groups. These tstatistics have N–2 degrees of freedom, where N is the total sample
size (in this case 15). Therefore we get:
− 0.338 2
− 0.338 2 + 13
= 0.09 rCola vs. Water = 2.233 2
2.233 2 + 13
= 0.53 rCola vs. Lucozade = Interpreting and Writing the Result
We could report the main finding as:
The covariate, drunkenness, was significantly related to the how ill the person felt the
next day, F(1, 11) = 27.89, p < .001, ω2 = .84. There was also significant effect of the Dr. Dr. Andy Field Page 7 8/18/2003 Discovering Statistics Using SPSS: Chapter 9
type of drink on how well the person felt after controlling for how drunk they were the
night before, F(2, 11) = 4.32, p < 0.05, ω2 = .40.
We can also report some contrasts:
Planned contrasts revealed that having Lucozade significantly improved how well you
felt compared to having cola, t(13) = 2.23, p < .05, r = .53, but having cola was no
better than having water, t(13) = –0.34, ns, r = .09. We can conclude that cola and
water have the same effects on hangovers but that Lucozade seems significantly better
at curing hangovers than cola. Dr. Dr. Andy Field Page 8 8/18/2003 ...
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This note was uploaded on 05/02/2010 for the course IE 0ap06 taught by Professor Ennart during the Spring '10 term at Technische Universiteit Eindhoven.
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