Unformatted text preview: Discovering Statistics Using SPSS: Chapter 10 Chapter 10: Answers
Task 1
People’s musical taste tends to change as they get older (my parents, for example, after years
of listening to relatively cool music when I was a kid in the 1970s, subsequently hit their mid40s and developed a worrying obsession with country and western music—or maybe it was the
stress of having me as a teenage son!). Anyway, this worries me immensely as the future
seems incredibly bleak if it is spent listening to Garth Brooks and thinking ‘oh boy, did I
underestimate Garth’s immense talent when I was in my 20s’. So, I thought I’d do some
research to find out whether my fate really was sealed, or whether it’s possible to be old and
like good music too. First, I got myself two groups of people (45 people in each group): one
group contained young people (which I arbitrarily decided was under 40 years of age), and the
other group contained more mature individuals (above 40 years of age). This is my first
independent variable, age, and it has two levels (less than or more than 40 years old). I then
split each of these groups of 45 into three smaller groups of 15 and assigned them to listen to
either Fugazi (who everyone knows are the coolest band on the planet)1, ABBA, or Barf Grooks
(who is a lesser known country and western musician not to be confused with anyone who has
a similar name and produces music that makes you want to barf). This is my second
independent variable, music, and has three levels (Fugazi, ABBA or Barf Grooks). There were
different participants in all conditions, which means that of the 45 under 40s, 15 listened to
Fugazi, 15 listened to ABBA and 15 listened to Barf Grooks; likewise of the 45 over 40s, 15
listened to Fugazi, 15 listened to ABBA and 15 listened to Barf Grooks. After listening to the
music I got each person to rate it on a scale ranging from –100 (I hate this foul music of
Satan) through 0 (I am completely indifferent) to +100 (I love this music so much I’m going to
explode). This variable is called liking. The data are in the file Fugazi.sav. Conduct a twoway independent ANOVA on them.
SPSS Output
The error bar chart of the music data shows the mean rating of the music played to each
group. It’s clear from this chart that when people listened to Fugazi the two age groups were
divided: the older ages rated it very low, but the younger people rated it very highly. A reverse
trend is found if you look at the ratings for Barf Grooks: the youngsters give it low ratings
while the wrinklyones love it. For ABBA the groups agreed: both old and young rated them
highly. 1 See http://www.dischord.com Dr. Dr. Andy Field Page 1 8/22/2003 Discovering Statistics Using SPSS: Chapter 10 100.00 Age Group 80.00
W Mean Liking Rating 60.00 40+ W 040 W W 40.00
20.00
0.00
20.00
40.00
60.00
80.00 W W 100.00
Fugazi Abba Barf Grooks Music The following output shows Levene’s test. For these data the significance value is 0.322, which
is greater than the criterion of 0.05. This means that the variances in the different
experimental groups are roughly equal (i.e. not significantly different), and that the
assumption has been met.
a
Levene's Test of Equality of Error Variances Dependent Variable: Liking Rating
F
1.189 df1 df2
5 84 Sig.
.322 Tests the null hypothesis that the error variance of the
dependent variable is equal across groups.
a. Design: Intercept+MUSIC+AGE+MUSIC * AGE The next output shows the main ANOVA summary table.
Tests of BetweenSubjects Effects
Dependent Variable: Liking Rating
Source
Corrected Model
Intercept
MUSIC
AGE
MUSIC * AGE
Error
Total
Corrected Total Type III Sum
of Squares
392654.933a
34339.600
81864.067
.711
310790.156
32553.467
459548.000
425208.400 df
5
1
2
1
2
84
90
89 Mean Square
78530.987
34339.600
40932.033
.711
155395.078
387.541 F
202.639
88.609
105.620
.002
400.977 Sig.
.000
.000
.000
.966
.000 a. R Squared = .923 (Adjusted R Squared = .919) The main effect of music is shown by the Fratio in the row labeled music, in this case the
significance is 0.000, which is lower than the usual cutoff point of 0.05. Hence, we can say
that there was a significant effect of the type of music on the ratings. To understand what this
actually means, we need to look at the mean ratings for each type of music when we ignore
whether the person giving the rating was old or young: Dr. Dr. Andy Field Page 2 8/22/2003 Discovering Statistics Using SPSS: Chapter 10 Error Bars show 95.0% Cl of Mean
Bars show Means
75.00 Liking Rating W 50.00 25.00 0.00 W
W 25.00 Fugazi Abba Barf Grooks Music What this graph shows is that the significant main effect of music is likely to reflect the fact
that ABBA were rated (overall) much more positively than the other two artists.
The main effect of age is shown by the Fratio in the row labeled age; the probability
associated with this Fratio is 0.966, which is so close to 1 that it means that it is a virtual
certainty that this F could occur by chance alone. Again, to interpret the effect we need to look
at the mean ratings for the two age groups ignoring the type of music to which they listened. 50.00 Error Bars show 95.0% Cl of Mean
Bars show Means Liking Rating 40.00 30.00 W W 40+ 20.00 040 10.00 0.00 10.00 Age Group This graph shows that when you ignore the type of music that was being rated, older people,
on average, gave almost identical ratings to younger people (i.e. the mean ratings in the two
groups are virtually the same).
The interaction effect is shown by the Fratio in the row labeled Music * Age; The associated
significance value is small (0.000) and is less than the criterion of 0.05. Therefore, we can say
that there is a significant interaction between age and the type of music rated. To interpret
this effect we need to look at the mean ratings in all conditions and these means were Dr. Dr. Andy Field Page 3 8/22/2003 Discovering Statistics Using SPSS: Chapter 10
originally plotted at the beginning of this output. The fact there is a significant interaction tells
us that for certain types of music the different age groups gave different ratings. In this case,
although they agree on ABBA, there are large disagreements in ratings of Fugazi and Barf
Grooks.
Given that we found a main effect of music, and of the interaction between music and age, we
can look at some of the post hoc tests to establish where the difference lies. The next output
shows the result of GamesHowell post hoc tests. First, ratings of Fugazi are compared to
ABBA, which reveals a significant difference (the value in the column labeled Sig. is less than
0.05), and then Barf Grooks, which reveals no difference (the significance value is greater than
0.05). In the next part of the table, ratings to ABBA are compared first to Fugazi (which just
repeats the finding in the previous part of the table) and then to Barf Grooks, which reveals a
significant difference (the significance value is below 0.05). The final part of the table
compares Barf Grooks to Fugazi and ABBA but these results repeat findings from the previous
sections of the table.
Multiple Comparisons
Dependent Variable: Liking Rating GamesHowell (I) Music
Fugazi
Abba
Barf Grooks (J) Music
Abba
Barf Grooks
Fugazi
Barf Grooks
Fugazi
Abba Mean
Difference
(IJ)
66.8667*
6.2333
66.8667*
60.6333*
6.2333
60.6333* Std. Error
5.08292
5.08292
5.08292
5.08292
5.08292
5.08292 Sig.
.000
.946
.000
.001
.946
.001 95% Confidence Interval
Lower Bound Upper Bound
101.1477
32.5857
53.3343
40.8677
32.5857
101.1477
24.9547
96.3119
40.8677
53.3343
96.3119
24.9547 Based on observed means.
*. The mean difference is significant at the .05 level. Calculating Effect Sizes
ˆ2
σα = (3 − 1)(40932.033 − 387.541) = 900.99
15 × 3 × 2
(2 − 1)(0.711 − 387.541)
ˆ2
σβ =
= −4.30
15 × 3 × 2
(3 − 1)(2 − 1)(155395.078 − 387.541)
ˆ2
σ αβ =
= 3444.61
15 × 3 × 2 We also need to estimate the total variability and this is just the sum of these other variables
plus the residual mean squares:
ˆ2
ˆ2 ˆ2 ˆ2
σ total = σ α + σ β + σ αβ + MSR
= 900.99 − 4.30 + 3444.61 + 387.54
= 4728.84 The effect size is then simply the variance estimate for the effect in which you’re interested
divided by the total variance estimate:
2
ωeffect = ˆ2
σ effect
ˆ2
σ total As such, for the main effect of music we get:
2
ωmusic = ˆ2
σ music
900.99
=
= 0.19
ˆ2
4728.84
σ total For the main effect of age we get:
2
ωage = Dr. Dr. Andy Field ˆ2
σ age
ˆ2
σ total = − 4.30
= 0.00
4728.84 Page 4 8/22/2003 Discovering Statistics Using SPSS: Chapter 10
For the interaction of music and age we get:
2
ωmusic × age = ˆ2
σ music × age
ˆ2
σ total = 3444.61
= 0.73
4728.84 Interpreting and Writing the Result
As with the other ANOVAs we’ve encountered we have to report the details of the Fratio and
the degrees of freedom from which it was calculated. For the various effects in these data the
Fratios will be based on different degrees of freedom: it was derived from dividing the mean
squares for the effect by the mean squares for the residual. For the effects of music and the
music × age interaction, the model degrees of freedom were 2 (dfM = 2), but for the effect of
age the degrees of freedom were only 1 (dfM = 1). For all effects, the degrees of freedom for
the residuals were 84 (dfR = 84). We can, therefore, report the three effects from this analysis
as follows:
The results show that the main effect of the type of music listened to significantly
affected the ratings of that music (F(2, 84) = 105.62, p < .001, r = .94). GamesHowell post hoc test revealed that ABBA were rated significantly higher than both
Fugazi and Barf Grooks (both ps < .01).
The main effect of age on the ratings of the music was nonsignificant (F(1, 84) < 1, r
= .00).
The music × age interaction was significant (F(2, 84) = 400.98, p < .001, r = .98)
indicating that different types of music were rated differently by the two age groups.
Specifically, Fugazi were rated more positively by the young group (M = 66.20, SD =
19.90) than the old (M = –75.87, SD = 14.37); ABBA were rated fairly equally in the
young (M = 64.13, SD = 16.99) and old groups (M = 59.93, SD = 19.98); Barf Grooks
was rated less positively by the young group (M = –71.47, SD = 23.17) compared to
the old (M = 74.27, SD = 22.29). These findings indicate that there is no hope for me,
the minute I hit 40 I will suddenly start to love country and western music and will
burn all of my Fugazi CDs (it will never happen … arghhhh!!!). Task 2
Change the syntax in GogglesSimpleEffects.sps to look at the effect of alcohol at different
levels of gender. The correct syntax to use is:
MANOVA
attract BY gender (0 1) alcohol(1 3)
/DESIGN = alcohol WITHIN gender(1) alcohol WITHIN gender (2)
/PRINT
CELLINFO
SIGNIF( UNIV MULT AVERF HF GG ). SPSS Output
The main part of the analysis is: Dr. Dr. Andy Field Page 5 8/22/2003 Discovering Statistics Using SPSS: Chapter 10
* * * * * * A n a l y s i s o f V a r i a n c e  design 1 * * * * * * Tests of Significance for ATTRACT using UNIQUE sums of squares
Source of Variation
SS
DF
MS
F Sig of F
WITHIN+RESIDUAL
ALCOHOL WITHIN GENDE
R(1)
ALCOHOL WITHIN GENDE
R(2) 3656.25
5208.33 43
2 85.03
2604.17 30.63 .000 102.08 2 51.04 .60 .553 (Model)
(Total) 5310.42
8966.67 4
47 1327.60
190.78 15.61 .000 RSquared =
Adjusted RSquared = .592
.554 What this shows is a significant effect of alcohol at level 1 of gender. Because we coded gender
as 0 = male, 1 = female, this means there’s a significant effect of alcohol for men. Think back
to the chapter and this reflects the fact that men choose very unattractive dates after 4 pints.
However, there is no significant effect of alcohol at level 2 of gender. This tells us that women
are not affected by the beer goggles effect: they attractiveness of their dates does not chance
as they drink more.
Calculating the Effect Size
These effects have 2 df in the model so we can’t calculate an effect size (well, technically we
can calculate omega squared (ω2) but I’m not entirely sure how useful that is. Dr. Dr. Andy Field Page 6 8/22/2003 ...
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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.
 Spring '10
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