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Unformatted text preview: Discovering Statistics Using SPSS: Chapter 3 Chapter 3: Answers
Task 1
Using the data from Chapter 2 plot some graphs of the mean number of friends, alcohol
consumption, income and neuroticism of students and lecturers. Which have the most friends,
drink the most, earn the most and are the most neurotic?
We’re interested in looking at the differences between lecturers and students. We took a
random sample of five lecturers and five psychology students from the University of Sussex
and then measured several variables: how many friends they had, their weekly alcohol
consumption (in units), their yearly income (in pounds) and how neurotic they were (higher
score is more neurotic). These data are in Chapter 2 and reproduced below. You should enter
them into the SPSS data editor using what you learnt in Chapter 2. You should’ve already
entered and saved these data, so retrieve the file.
Table 1: Data for differences between students and lecturers
Type of
Person No. of
Friends Alcohol
Consumption Income
(p.a.) Neuroticism Lecturer 5 10 20000 10 Lecturer 2 15 40000 17 Lecturer 0 20 35000 14 Lecturer 4 5 22000 13 Lecturer 1 30 50000 21 Student 10 25 5000 7 Student 12 20 100 13 Student 15 16 3000 9 Student 12 17 10000 14 Student 17 18 10 13 Having entered these data we can look at trends by using graphs. To draw a graph, simply
click on the word describing the graph that you want to plot. In most cases you will be
presented with a provisional dialog box asking you whether you’d
like to plot a simple chart or a clustered one (see Figure). A
What is the
simple chart is one in which you plot one graph element
difference between
per group or variable. For example we might want to plot
a simple graph and
a clustered graph?
the average number of friends for lecturers and students.
As such, we want one bar representing the average
number of friends that lecturers had and one representing
the average number that students had. We could also plot a single
line (connecting the lecturers’ average to the students’ average) or a boxplot
(one representing the lecturers’ data and one representing the students). If you
want to plot one bar for different groups (this is used when you have a betweengroup design), then you should select Summaries for groups of cases. If you have only one
group and you want to plot a graph of several dependent variables (a repeated measures
design) then select Summaries of separate variables. An example of this would be if we
ignored whether the person was a lecturer or student and just wanted to plot the average
number of friends and the average neuroticism score on the same graph. Dr. Andy Field Page 1 4/21/2003 Discovering Statistics Using SPSS: Chapter 3
A clustered chart is one in which each group or category of people has several chart elements.
These graphs can be useful if you want to plot two independent variables. For example, if we
had noted the gender of each student and lecturer we would have two independent variables
(gender and job) and one dependent variable (number of friends). Therefore, we could use a
clustered plot to display the average number of friends for lecturers and students and have
separate bars (or lines) representing males and females. In this latter case, in which both
variables were measured using a betweengroup design, the Summaries for groups of cases
option should be used. Alternatively, you can plot values of several groups along several
variables. Imagine we wanted to plot the average number of friends and the average
neuroticism score and split these scores according to whether the person was a lecturer or
student. We want to plot two bars for the lecturers (one representing the number of friends
and one representing neuroticism) and two for the students. To plot this graph we should
choose a clustered chart but ask for Summaries of separate variables.
to
When a type of graph has been selected (simple or clustered) you need to click on
move to the next dialog box. On many occasions you will see the term Category axis, and this
refers to the Xaxis (horizontal). This axis usually requires a grouping variable (in these
examples I have used type of person). Variables can be selected by clicking on them in the
variable list (lefthand side of dialog box) and moving them to the appropriate space by using
button. In the case of bar charts, you can make the bars represent many things
the
(number of cases etc.), but on the vast majority of occasions you will want them to represent
the mean value and so you should select Other summary function and then enter a variable.
enables this default to be changed.
The default function is the mean, but clicking on
and the graph will appear in the
Once the graphs options have been selected click on
output viewer. These charts can then be edited by doubleclicking on them in the viewer. This
action produces a new window (called the chart editor) in which you can change just about any
property of the graph by doubleclicking with the mouse (have a play around with some of the
functions!).
Try putting some of these principles into practice using our lecturerstudent data. Figure 1
shows how to create a bar chart and boxplot of two of the variables measured for the
lecturers. Follow these options and see whether you can recreate these graphs (remember
that you can edit them to add bar labels and change the colours). A bar chart of the means is
a useful way to see the pattern of results (i.e. which group got the highest scores). In Figure 1
the graph shows us at a glance that students, on average, have more friends than their
lecturers. Boxplots tell us a little bit more. For one thing the whiskers on the plot (the lines
that stick out of the top and bottom) give an indicator of the spread of scores. More important,
unusual cases can be identified (outliers) because they are displayed as a dot outside of the
main range of scores. In Figure, the boxplot displayed has a single outlier who is represented
by the dot above the graph. This person is a student who drank rather more than the other
students. The dark line also shows the median score, so we can tell that the median amount of
units drunk was higher for students than lecturers. Try plotting graphs of some of the other
variables. Dr. Andy Field Page 2 4/21/2003 Discovering Statistics Using SPSS: Chapter 3 Bar Chart Boxplot 14.00 40
13.20 12.00
30
10.00 Units of alcohol (per week) 6 Mean No. of Friends 8.00 6.00 4.00 2.00 2.40 0.00 20 10 0
N= Lecturer Type of Person 5 5 Lecturer Student Student Type of Person Figure 1: Plotting graphs on SPSS Task 2
Using the ChickFlick.sav data, check the distributions for the two films (ignore gender): are
they normally distributed.
The output you should get look like those reproduced below (I used the Explore function
described in Chapter 3). The skewness statistics gives rise to a zscore of –0.378/0.512 = 0.74
for Bridget Jones’ diary, and 0.04/0.512 = 0.08 for momento. These show no significant
skewness. The KS tests show no significant deviation from normality and the histogram for
Bridget jones’ diary even looks normal. The histogram for Momento is less normal, but the rest
of the evidence gives us no reason to suppose it isn’t. Dr. Andy Field Page 3 4/21/2003 Discovering Statistics Using SPSS: Chapter 3 Descriptives
Film
Bridget Jones' Diary Arousal Momento Mean
95% Confidence
Interval for Mean
5% Trimmed Mean
Median
Variance
Std. Deviation
Minimum
Maximum
Range
Interquartile Range
Skewness
Kurtosis
Mean
95% Confidence
Interval for Mean Lower Bound
Upper Bound Lower Bound
Upper Bound 5% Trimmed Mean
Median
Variance
Std. Deviation
Minimum
Maximum
Range
Interquartile Range
Skewness
Kurtosis Statistic
14.8000
12.1196
17.4804
14.9444
15.0000
32.800
5.72713
3.00
24.00
21.00
7.5000
.378
.254
25.2500
21.9133 .512
.992
1.59419 28.5867
25.2222
24.5000
50.829
7.12944
14.00
37.00
23.00
10.7500
.040
1.024 Histogram Std. Error
1.28062 .512
.992 Histogram For FILM= Bridget Jones' Diary For FILM= Momento 6 3.5
3.0 5 2.5 4 2.0
3
1.5
1.0 Frequency Frequency 2
Std. Dev = 5.73 1 Mean = 14.8
N = 20.00 0
2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 22.5 25.0 Mean = 25.3
N = 20.00 0.0
15.0 17.5 20.0 22.5 25.0 27.5 30.0 32.5 35.0 37.5 Arousal Dr. Andy Field Std. Dev = 7.13 .5 Arousal Page 4 4/21/2003 Discovering Statistics Using SPSS: Chapter 3 Tests of Normality
a Film
Bridget Jones' Diary
Momento Arousal KolmogorovSmirnov
Statistic
df
Sig.
.127
20
.200*
.097
20
.200* ShapiroWilk
Statistic
df
.972
20
.960
20 Sig.
.788
.552 *. This is a lower bound of the true significance.
a. Lilliefors Significance Correction Task 3
Using the SPSSExam.sav data, remember that numeracy scores appear positively skewed.
Transform these data using one of the transformations described in this chapter: do the data
become normal?
These are the original histograms and those of the transformed scores:
Histogram Histogram 40 30 30
20 20 10 Frequency Frequency 10
Std. Dev = 2.71
Mean = 4.9
N = 100.00 0
2.0 4.0 6.0 8.0 10.0 12.0 Std. Dev = .26
Mean = .62 14.0 0.00 Numeracy .13 .25 .38 .50 .63 .75 .88 1.00 1.13 Log Transformed Numeracy Scores Histogram Histogram 40 40 30 30 20 20 10 Frequency 10 Frequency N = 100.00 0 Std. Dev = .61
Mean = 2.12
N = 100.00 0
1.00 1.50 2.00 2.50 3.00 3.50 Std. Dev = .21
Mean = .29
N = 100.00 0
.13 Square Root transformed Numeracy Scores .25 .38 .50 .63 .75 .88 1.00 Reciprocal of Numeracy Scores None of these histograms appear to be normal. Below is the table of results from the KS test,
all of which are significant. The only conclusion is that although the square root transformation
does the best job of normalizing the data, none of these transformations actually works! Dr. Andy Field Page 5 4/21/2003 Discovering Statistics Using SPSS: Chapter 3 Tests of Normality
a Numeracy
Log Transformed Numeracy Scores
Square Root transformed Numeracy Scores
Reciprocal of Numeracy Scores KolmogorovSmirnov
Statistic
df
Sig.
.153
100
.000
.120
100
.001
.108
100
.006
.223
100
.000 Statistic
.924
.959
.970
.763 ShapiroWilk
df
100
100
100
100 Sig.
.000
.003
.020
.000 a. Lilliefors Significance Correction Dr. Andy Field Page 6 4/21/2003 ...
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