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Is Spatial Memory Age-Related?
There is a commonly-held belief that it is more
difficult for the Elderly than for the Young to
learn and remember new material.
It is possible that the Elderly have a reduced
capacity to recall or retain learnt information, but
there are alternative explanations that relate to
the way in which they learn.
For example the Elderly may use fewer, or less
suitable, strategies for memorising the material, or
they may be over-confident in their own abilities
and so devote insufficient time to learning the
material.
1
Is Spatial Memory Age-Related?
In order to investigate spatial memory, a study was
carried out on two groups of people, designated as
Young (20-25) and Elderly (over 65).
The trick is to see if you can answer the questions
posed and write your conclusions in plain English?
2
Is Spatial Memory Age-Related?
In the study, 18 labelled objects were arranged
randomly on a 10 x 10 grid.
3
Is Spatial Memory Age-Related?
Thirteen Young and fourteen Elderly subjects were
allowed to examine the positions of the objects for
as long as they liked and were subsequently asked
to recall these positions by replacing the objects
on the grid.
Their study times and two measures of recall
performance were recorded.
4
Is Spatial Memory Age-Related?
The main objective is to compare the age groups.
agegroup
Age group, defined as 1 = Elderly or
2 = Young.
subject
Identification number for each subject
within the age groups.
ncorrect
Number of objects correctly replaced (out
of 18).
pccorrect
Percentage of objects correctly replaced.
cityblock
City block score – a measurement of the
errors between the target and actual
positions.
time
Study time – the time each individual spent
examining the positions of the object.
5
Is Spatial Memory Age-Related?
The city block score, attempts to account for near
misses by measuring the distances (in “city blocks”,
i.e. horizontal and vertical steps across the grid)
between the actual and replaced positions, and
totalling these over the 18 objects.
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6
Is Spatial Memory Age-Related?
The main objective is to compare the age groups.
One particular topic that might arise here is the
risk of confounding in the two group study because
any differences seen between the Young and
Elderly might be due not to their age differences
but to difference(s) in some other variable(s).
7
Is Spatial Memory Age-Related?
In this study the groups were, in fact, generally
balanced in terms of sex ratio, IQ and educational
experience, but this does not preclude the
possibility that further, unsuspected, differences
are present. Additionally, some people naturally
tend to process information verbally, while others
process information spatially or visually. Thus, a
person who processes information verbally may
score poorly in the spatial memory test although
(s)he may have a generally good memory.
8
Is Spatial Memory Age-Related?
We are going to use some basic graphs to explore
the data, particularly to compare the results of the
Elderly and Young groups. We shall first look at
boxplots.
9
Is Spatial Memory Age-Related?
Question - What can you tell about the scores
achieved by the two age groups? To what extent do
the scores for the two groups overlap? Comment on
the median scores and the variation in scores within
each group.
10
Is Spatial Memory Age-Related?
Graphs > Legacy Dialogs > Boxplot
11
Is Spatial Memory Age-Related?
Simple > Define
12
Is Spatial Memory Age-Related?
ncorrect for the variables and agegroup for the Category Axis
13
Is Spatial Memory Age-Related?
Finally
Question - What
can you tell about
the scores
achieved by the
two age groups?
To what extent do
the scores for the
two groups
overlap? Comment
on the median
scores and the
variation in scores
within each group.
14
Is Spatial Memory Age-Related?
Answer - On the whole Elderly subjects got fewer
correct than the Young, with scores for the Elderly
group overlapping the lowest quartile of scores
achieved by Young subjects. Although scores for the
Elderly were typically lower, the lowest scores
achieved in each group were the same. One person,
case number 5, in the Elderly group has been
identified as an outlier. The scores for the Young
were more spread out and most were over 10.
15
Is Spatial Memory Age-Related?
Question - What do the boxplots tell you about the
differences between the age groups in their city block
scores? Remember that the city block score measures
the errors made in positioning objects on the grid.
Look at the medians, the Inter Quartile Ranges (IQR)
and comment on the degree of overlap. Does the
diagram show any outliers?
16
Is Spatial Memory Age-Related?
cityblock for the variables and agegroup for the Category Axis
Question - What do the
boxplots tell you about
the differences
between the age groups
in their city block
scores? Look at the
medians, the Inter
Quartile Ranges (IQR)
and comment on the
degree of overlap. Does
the diagram show any
outliers?
17
Is Spatial Memory Age-Related?
Answer - The median city block score is
approximately 12 for the Young subjects and 27
for the Elderly. This means that generally the
Young subjects were more accurate in placing the
objects than the Elderly. The upper quartile for
the Young subjects is about the same as the lower
quartile for the Elderly subjects. This means that
three quarters of Young subjects have city block
scores similar to those of the lowest scoring (most
accurate) quarter of the Elderly subjects. The
IQR is similar for both groups and neither group
has any outliers.
18
Is Spatial Memory Age-Related?
Question - Now use boxplots to compare the study
times of the two groups and comment on the results.
Look at the same features as in the last two questions
and also comment on the shape of each graph.
19
Is Spatial Memory Age-Related?
time for the Variables and agegroup for the Category Axis
Question - Now use
boxplots to
compare the study
times of the two
groups and
comment on the
results. Look at the
same features as in
the last two
questions and also
comment on the
shape of each
graph.
20
Is Spatial Memory Age-Related?
Answer - Almost all of the Elderly subjects spent much
less time on the task than Young subjects. The median
study times are 42.5 seconds for Elderly subjects and
95 seconds for Young subjects. Both groups have a
slight positive skew. Two Elderly subjects are shown as
outliers as the result of taking longer than other
subjects in the same group.
21
Is Spatial Memory Age-Related?
Question - From the evidence above do you think that
city block score or number correct is better as a
measurement of memory?
22
Is Spatial Memory Age-Related?
Answer - The number correct is a crude, but easy way
of measuring spatial memory; it does not allow for
“near-misses”. Comparing, for example, the two sets of
boxplots, we see that comparing the Elderly and Young,
the former do not get many repositions absolutely
right. However, in the city block scores, although the
Young group are generally better, some of the Elderly
do just as well and some of the Young are just as poor
as the Elderly. City block score seems to be a better
method.
23
Is Spatial Memory Age-Related?
In the next few questions we will look at some
alternatives to the boxplots used above, to see
whether other diagrams can be equally successful as a
tool for showing the differences between groups.
First try using stem and leaf plots.
24
Is Spatial Memory Age-Related?
Question - What are the differences between the age
groups in the number of correctly placed objects? How
well do the diagrams allow you to make comparisons
between the groups of subjects?
25
Is Spatial Memory Age-Related?
Analyze > Descriptive Statistics > Explore
26
Is Spatial Memory Age-Related?
Select ncorrect for the Dependent List box
Select agegroup for the Factor List
27
Is Spatial Memory Age-Related?
Finally
Question - What are
the differences
between the age
groups in the number
of correctly placed
objects? How well do
the diagrams allow
you to make
comparisons between
the groups of
subjects?
number correct Stem-and-Leaf Plot for
agegroup= Elderly
Frequency Stem & Leaf
2*6
1.00 Extremes (=<5.0)
2*7
2.00
6 . 00
7*8
2.00
7 . 00
2*9
7.00
8 . 0000000
2.00
9 . 00
Stem width: 1
Each leaf:
1 case(s)
number correct Stem-and-Leaf Plot for
agegroup= Young
Frequency Stem & Leaf
5,7,9,9
.00
0.
10,11,11,12,13,14,14,14
4.00
0 . 5799
16
8.00
1 . 01123444
1.00
1. 6
Stem width: 10
Each leaf:
1 case(s)
28
Is Spatial Memory Age-Related?
Answer - This is not a particularly helpful way to draw
the data here as the diagrams for the two groups are
not displayed side by side as they were in the boxplots.
Also the ‘leaf’ for the Elderly consists of one unit
where as each ‘leaf’ for the Young subjects covers 5
units. The boxplot shown below the stem and leaf
diagram (and constructed earlier) is much clearer .
29
Is Spatial Memory Age-Related?
Barcharts are helpful when we have discrete variables
with not too many values.
30
Is Spatial Memory Age-Related?
Question - Describe the distribution of the number of
correctly replaced objects. What do you notice about
the horizontal axis?
31
Is Spatial Memory Age-Related?
Graphs > Legacy Dialogs > Bar
32
Is Spatial Memory Age-Related?
Simple > Define
33
Is Spatial Memory Age-Related?
Select ncorrect for the Category Axis and click on % of cases
34
Is Spatial Memory Age-Related?
Finally
Question Describe the
distribution of
the number of
correctly
replaced
objects. What
do you notice
about the
horizontal axis?
35
Is Spatial Memory Age-Related?
Answer - There were 18 objects to be correctly
replaced on the grid; the highest score was 16 and the
lowest 5. The most frequent number of objects
replaced correctly (the mode) is 8. Only 9 of the 27
subjects, i.e. one third, replaced more than half
correctly. The horizontal axis is in order but not
drawn to scale – individual values are treated as
categories, so that 14 and 16 are shown as adjacent
values.
36
Is Spatial Memory Age-Related?
A variation of this can help us to see the differences
between the Elderly and Young groups.
Question - What does this tell you about the
distribution of the number correct in the two groups?
37
Is Spatial Memory Age-Related?
Select Barchart as before then Stacked > Define
38
Is Spatial Memory Age-Related?
Select ncorrect for the Category Axis and agegroup for the box
labelled and Define Stacks by Under Bars Represent select % of
cases
39
Is Spatial Memory Age-Related?
Finally
Question - What
does this tell
you about the
distribution of
the number
correct in the
two groups?
40
Is Spatial Memory Age-Related?
Answer - All of those with more than half right were in
the Young group. Scores for this group range from 5
to 16. The Elderly group’s scores range from 5 to 9,
with half of the group scoring 8 correct.
The stacked Barchart shows clearly that the Young are
more successful than the Elderly in replacing the
objects correctly.
41
Is Spatial Memory Age-Related?
In the same way, draw barcharts for city block score
for the two age groups.
Be careful
to check
how
different
scores and
times are
shown on
the x-axis.
42
Is Spatial Memory Age-Related?
In the same way, draw barcharts for study time stacked
for the two age groups.
Be careful
to check
how
different
scores and
times are
shown on
the x-axis.
43
Is Spatial Memory Age-Related?
Question - Are these barcharts a good way of showing
the differences between the age groups in city block
scores and study times?
44
Is Spatial Memory Age-Related?
Answer - Not really, as there are blocks for each value
that may not be evenly spaced. Also the default
graphs have rather too many bars.
The graphs show that the Elderly generally take
shorter study times than the Young but that their city
block scores are generally poorer.
45
Is Spatial Memory Age-Related?
Histograms are used to represent the frequency
distributions of continuous variables.
46
Is Spatial Memory Age-Related?
Question - Are study time or city block scores
continuous variables?
47
Is Spatial Memory Age-Related?
Answer - Time is usually regarded as a continuous
variable. The city block score, being the sum of blocks
in horizontal and vertical directions is a discrete
variable.
48
Is Spatial Memory Age-Related?
Question – How easy is it to compare the distribution of
study time between the Young and Elderly groups?
What is the main problem?
49
Is Spatial Memory Age-Related?
Analyze > Descriptive Statistics > Explore
50
Is Spatial Memory Age-Related?
Select time for the Dependent List box and age group
for the Factor Listbox Under Display, select Plots
51
Is Spatial Memory Age-Related?
Click on the Plots button De-select Stem and Leaf and
select Histogram
52
Is Spatial Memory Age-Related?
Finally - Question – How easy is it to compare the distribution of time
between the Young and Elderly groups? What is the main problem?
53
Is Spatial Memory Age-Related?
Answer - Making comparisons is not easy as you have to
keep looking backwards and forwards between two
diagrams. The biggest problem is that the diagrams use
different scales and this makes comparisons very
difficult.
54
Is Spatial Memory Age-Related?
The purpose of this experiment was to see if there is
a difference in the spatial memories of the two Age
groups. We shall first look at the summary statistics,
measures of location (mean and median) and dispersion
(standard deviation, range and inter-quartile range) of
the times taken to study the grid for each of the age
groups in order to compare them.
55
Is Spatial Memory Age-Related?
Analyze > Descriptive Statistics > Explore as before
Select time for the Dependent Listbox
Select age group for the Factor Listbox
Under Display choose Both
56
Is Spatial Memory Age-Related?
The descriptive statistics.
Descriptives
Study time
Question - Describe
the differences
between the Elderly
and Young age
groups in the
average times they
took to study the
grid.
Age group
Elderly
Young
Mean
95% Confidence
Interval for Mean
5% Trimmed Mean
Median
Variance
Std. Deviation
Minimum
Maximum
Range
Interquartile Range
Skewness
Kurtos is
Mean
95% Confidence
Interval for Mean
5% Trimmed Mean
Median
Variance
Std. Deviation
Minimum
Maximum
Range
Interquartile Range
Skewness
Kurtos is
Lower Bound
Upper Bound
Lower Bound
Upper Bound
Statis tic
50.71
37.71
Std. Error
6.019
63.72
49.40
42.50
507.143
22.520
25
100
75
25
1.235
.639
98.85
80.92
.597
1.154
8.227
116.77
98.72
95.00
879.808
29.662
55
145
90
50
.074
-.908
.616
1.191
57
Is Spatial Memory Age-Related?
The boxplot
Question Describe the
differences
between the
Elderly and
Young age
groups in the
average times
they took to
study the grid.
58
Is Spatial Memory Age-Related?
Question - Describe the differences between the
Elderly and Young age groups in the average times they
took to study the grid.
Age group
Elderly
Young
Statistic
Mean
50.71
Median
42.50
Mean
98.85
Median
95.00
59
Is Spatial Memory Age-Related?
Answer - The mean and median values of the study
times of the Young group (98.85 seconds and 95.00
seconds respectively) are much greater than those of
the Elderly group (50.71 seconds and 42.50 seconds
respectively). The mean and median values for the
Young groups are close, those for the Elderly group
quite different.
Age group
Elderly
Young
Statistic
Mean
50.71
Median
42.50
Mean
98.85
Median
95.00
60
Is Spatial Memory Age-Related?
Question - Describe the differences between the
Elderly and Young age groups in variability of the times
they took to study the grid.
Age group
Statistic
Elderly
Variance
Std.
Deviation
507.143
Young
Variance
Std.
Deviation
879.808
22.520
29.662
61
Is Spatial Memory Age-Related?
Answer - All the measures of variability are greater for
the Young group than for the Elderly. From the table
the standard deviation for the Young is 29.66 seconds,
whilst for the Elderly it is 22.52 seconds.
Age group
Elderly
Young
Variance
Std.
Deviation
Variance
Std.
Deviation
Statistic
507.143
22.520
879.808
29.662
62
Is Spatial Memory Age-Related?
The boxplots show that the
inter-quartile range and
range are both greater for
the Young group than for the
Elderly. Further, the
boxplots indicate that the
two groups are very
different in their study
times as the inter-quartile
ranges do not overlap and
the median value for the
Young group would be an
outlier for the Elderly group.
The Elderly group has two
outliers, both with unusually
high study time values; there
are no outliers in the Young
group.
63
Is Spatial Memory Age-Related?
Question - Describe the differences between the
Elderly and Young age groups in the measures of
performance for the number correct.
64
Is Spatial Memory Age-Related?
Descriptives
Descriptive
statistics.
Question - Describe
the differences
between the Elderly
and Young age
groups in the
measures of
performance for the
number correct.
No. correct
Age group
Elderly
Young
Mean
95% Confidence
Interval for Mean
5% Trimmed Mean
Median
Variance
Std. Deviation
Minimum
Maximum
Range
Interquartile Range
Skewness
Kurtos is
Mean
95% Confidence
Interval for Mean
5% Trimmed Mean
Median
Variance
Std. Deviation
Minimum
Maximum
Range
Interquartile Range
Skewness
Kurtos is
Lower Bound
Upper Bound
Lower Bound
Upper Bound
Statistic
7.50
6.83
Std. Error
.310
8.17
7.56
8.00
1.346
1.160
5
9
4
1
-.862
.203
11.15
9.26
.597
1.154
.869
13.05
11.23
11.00
9.808
3.132
5
16
11
5
-.437
-.290
65
.616
1.191
Is Spatial Memory Age-Related?
Boxplot
Question Describe the
differences
between the
Elderly and
Young age
groups in the
measures of
performance
for the number
correct.
66
Is Spatial Memory Age-Related?
Answer - Within each age group the mean and median scores are
very close. The mean and median values for the Young group, at
11.15 and 11.00 respectively, are larger than for the Elderly group at
7.50 (mean) and 8.00 (median). The measures of dispersion are all
larger for the Young than for the Elderly group. There is very little
variability in the Elderly group with a standard deviation of 1.16,
range of 4 and IQR of 1. Also the median and upper quartile are
the same at 8.
Age group
Elderly
Young
Statistic
Mean
7.50
Median
8.00
Variance
1.346
Std. Deviation
1.160
Mean
11.15
Median
11.00
Variance
9.808
Std. Deviation
3.132
67
Is Spatial Memory Age-Related?
Question - Describe the differences between the
Elderly and Young age groups in the measures of
performance for the city block score.
68
Is Spatial Memory Age-Related?
Descriptives
Descriptive
statistics
Question Describe the
differences
between the
Elderly and Young
age groups in the
measures of
performance for
the city block
score.
City block s core
Age group
Elderly
Young
Mean
95% Confidence
Interval for Mean
5% Trimmed Mean
Median
Variance
Std. Deviation
Minimum
Maximum
Range
Interquartile Range
Skewness
Kurtos is
Mean
95% Confidence
Interval for Mean
5% Trimmed Mean
Median
Variance
Std. Deviation
Minimum
Maximum
Range
Interquartile Range
Skewness
Kurtos is
Lower Bound
Upper Bound
Lower Bound
Upper Bound
Statistic
27.71
22.13
Std. Error
2.584
33.30
27.68
27.50
93.451
9.667
13
43
30
15
.070
-1.102
14.46
8.47
.597
1.154
2.752
20.46
13.85
12.00
98.436
9.921
4
36
32
15
1.008
.307
.616
1.191
69
Is Spatial Memory Age-Related?
Boxplot
Question Describe the
differences
between the
Elderly and
Young age
groups in the
measures of
performance
for the city
block score.
70
Is Spatial Memory Age-Related?
Answer - Again, within each age group the mean and
median scores are very close. The mean and median
values for the Elderly group at about 28 are larger
than for the Young group at 14.5 (mean) and 12
(median). The measures of dispersion are much the
same for the two age groups, with standard deviations
of about 10, ranges of 30 and 32 and IQR of 15.
Age group
Elderly
Young
Statistic
Mean
27.71
Median
27.50
Variance
93.451
Std. Deviation
9.667
Mean
14.46
Median
12.00
Variance
98.436
Std. Deviation
9.921
71
Is Spatial Memory Age-Related?
We can look a little more closely at the distributions of
the measures of performance and study time using
Frequency tables. We first consider the number of
correctly replaced objects.
72
Is Spatial Memory Age-Related?
Question - Describe the distribution of the number of
correctly replaced objects.
73
Is Spatial Memory Age-Related?
Analyze > Descriptive Statistics > Frequencies
74
Is Spatial Memory Age-Related?
Select ncorrect as the Variable
75
Is Spatial Memory Age-Related?
No. correct
Finally
Question Describe the
distribution
of the
number of
correctly
replaced
objects.
Valid
5
6
7
8
9
10
11
12
13
14
16
Total
Frequency
2
2
3
7
4
1
2
1
1
3
1
27
Percent
7.4
7.4
11.1
25.9
14.8
3.7
7.4
3.7
3.7
11.1
3.7
100.0
Valid Percent
7.4
7.4
11.1
25.9
14.8
3.7
7.4
3.7
3.7
11.1
3.7
100.0
Cumulative
Percent
7.4
14.8
25.9
51.9
66.7
70.4
77.8
81.5
85.2
96.3
100.0
76
Is Spatial Memory Age-Related?
Answer - About half (52%) of the subjects replaced 8
or fewer objects in the correct position. Only one
person replaced more than 14 correctly.
No. correct
Valid
5
6
7
8
9
10
11
12
13
14
16
Total
Frequency
2
2
3
7
4
1
2
1
1
3
1
27
Percent
7.4
7.4
11.1
25.9
14.8
3.7
7.4
3.7
3.7
11.1
3.7
100.0
Valid Percent
7.4
7.4
11.1
25.9
14.8
3.7
7.4
3.7
3.7
11.1
3.7
100.0
Cumulative
Percent
7.4
14.8
25.9
51.9
66.7
70.4
77.8
81.5
85.2
96.3
100.0
77
Is Spatial Memory Age-Related?
We now look at the frequency counts for the number of
objects correctly replaced for the different age
groups.
78
Is Spatial Memory Age-Related?
Question - What does the table tell you about the data?
What are the modes?
79
Is Spatial Memory Age-Related?
Analyze > Descriptive Statistics > Crosstabs
80
Is Spatial Memory Age-Related?
Select ncorrect as the Row variable and agegroup as the
Column variable
81
Is Spatial Memory Age-Related?
Click on Cells and under Percentages, select Column.
82
Is Spatial Memory Age-Related?
No. correct * Age group Crosstabulation
Finally
Question - What does
the table tell you about
the data? What are the
modes?
No.
correct
5
6
7
8
9
10
11
12
13
14
16
Total
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Age group
Elderly
Young
1
1
7.1%
7.7%
2
0
14.3%
.0%
2
1
14.3%
7.7%
7
0
50.0%
.0%
2
2
14.3%
15.4%
0
1
.0%
7.7%
0
2
.0%
15.4%
0
1
.0%
7.7%
0
1
.0%
7.7%
0
3
.0%
23.1%
0
1
.0%
7.7%
14
13
100.0%
100.0%
Total
2
7.4%
2
7.4%
3
11.1%
7
25.9%
4
14.8%
1
3.7%
2
7.4%
1
3.7%
1
3.7%
3
11.1%
1
3.7%
27
100.0%
83
Is Spatial Memory Age-Related?
Answer - On the whole the Elderly got fewer correct
than the Young. All of the scores for the Elderly were
under 10, with the mode at 8. The scores for the
Young were more spread out and most were over 10
correct; the mode is 14.
84
Is Spatial Memory Age-Related?
In the same way, cross-tabulate both city block score
and study time by age group.
85
Is Spatial
Memory AgeRelated?
City block score * Age group Crosstabulation
City
block
score
4
5
6
7
11
12
13
14
15
16
Question - Describe
the differences in city
block scores between
the age groups.
17
20
21
22
23
26
29
32
34
35
36
42
43
Total
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Age group
Elderly
Young
0
1
.0%
7.7%
0
1
.0%
7.7%
0
2
.0%
15.4%
0
1
.0%
7.7%
0
1
.0%
7.7%
0
1
.0%
7.7%
1
0
7.1%
.0%
0
1
.0%
7.7%
1
0
7.1%
.0%
0
1
.0%
7.7%
1
0
7.1%
.0%
0
1
.0%
7.7%
1
0
7.1%
.0%
1
1
7.1%
7.7%
1
0
7.1%
.0%
1
0
7.1%
.0%
1
1
7.1%
7.7%
1
0
7.1%
.0%
1
0
7.1%
.0%
1
0
7.1%
.0%
1
1
7.1%
7.7%
1
0
7.1%
.0%
1
0
7.1%
.0%
14
13
100.0%
100.0%
Total
1
3.7%
1
3.7%
2
7.4%
1
3.7%
1
3.7%
1
3.7%
1
3.7%
1
3.7%
1
3.7%
1
3.7%
1
3.7%
1
3.7%
1
3.7%
2
7.4%
1
3.7%
1
3.7%
2
7.4%
1
3.7%
1
3.7%
1
3.7%
2
7.4%
1
3.7%
1
3.7%
27
100.0%
86
City block score * Age group Crosstabulation
Is Spatial
Memory AgeRelated?
City
block
score
4
5
6
7
11
12
13
Answer - The city block
scores are spread out for
both age groups, with
generally just one person
in each category. Scores
for the Young are
generally lower than
those for the Elderly.
14
15
16
17
20
21
22
23
26
29
32
34
35
36
42
43
Total
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Age group
Elderly
Young
0
1
.0%
7.7%
0
1
.0%
7.7%
0
2
.0%
15.4%
0
1
.0%
7.7%
0
1
.0%
7.7%
0
1
.0%
7.7%
1
0
7.1%
.0%
0
1
.0%
7.7%
1
0
7.1%
.0%
0
1
.0%
7.7%
1
0
7.1%
.0%
0
1
.0%
7.7%
1
0
7.1%
.0%
1
1
7.1%
7.7%
1
0
7.1%
.0%
1
0
7.1%
.0%
1
1
7.1%
7.7%
1
0
7.1%
.0%
1
0
7.1%
.0%
1
0
7.1%
.0%
1
1
7.1%
7.7%
1
0
7.1%
.0%
1
0
7.1%
.0%
14
13
100.0%
100.0%
Total
1
3.7%
1
3.7%
2
7.4%
1
3.7%
1
3.7%
1
3.7%
1
3.7%
1
3.7%
1
3.7%
1
3.7%
1
3.7%
1
3.7%
1
3.7%
2
7.4%
1
3.7%
1
3.7%
2
7.4%
1
3.7%
1
3.7%
1
3.7%
2
7.4%
1
3.7%
1
3.7%
27
100.0%
87
Is Spatial
Memory AgeRelated?
Study time * Age group Crosstabulation
Study
time
25
30
35
40
45
55
70
Question - Describe the
differences in study
times between the age
groups.
75
85
90
95
100
105
125
130
140
145
Total
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Age group
Elderly
Young
1
0
7.1%
.0%
1
0
7.1%
.0%
2
0
14.3%
.0%
3
0
21.4%
.0%
2
0
14.3%
.0%
2
2
14.3%
15.4%
0
1
.0%
7.7%
1
0
7.1%
.0%
0
1
.0%
7.7%
1
2
7.1%
15.4%
0
1
.0%
7.7%
1
1
7.1%
7.7%
0
1
.0%
7.7%
0
1
.0%
7.7%
0
1
.0%
7.7%
0
1
.0%
7.7%
0
1
.0%
7.7%
14
13
100.0%
100.0%
Total
1
3.7%
1
3.7%
2
7.4%
3
11.1%
2
7.4%
4
14.8%
1
3.7%
1
3.7%
1
3.7%
3
11.1%
1
3.7%
2
7.4%
1
3.7%
1
3.7%
1
3.7%
1
3.7%
1
3.7%
27
100.0%
88
Is Spatial
Memory AgeRelated?
Study time * Age group Crosstabulation
Study
time
25
30
35
40
45
Answer - study times
for the Elderly are
generally much lower
than for the Young,
with most of the
former taking 55
seconds or less
whilst all of the
latter took 55
seconds or more.
55
70
75
85
90
95
100
105
125
130
140
145
Total
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Count
% within Age group
Age group
Elderly
Young
1
0
7.1%
.0%
1
0
7.1%
.0%
2
0
14.3%
.0%
3
0
21.4%
.0%
2
0
14.3%
.0%
2
2
14.3%
15.4%
0
1
.0%
7.7%
1
0
7.1%
.0%
0
1
.0%
7.7%
1
2
7.1%
15.4%
0
1
.0%
7.7%
1
1
7.1%
7.7%
0
1
.0%
7.7%
0
1
.0%
7.7%
0
1
.0%
7.7%
0
1
.0%
7.7%
0
1
.0%
7.7%
14
13
100.0%
100.0%
Total
1
3.7%
1
3.7%
2
7.4%
3
11.1%
2
7.4%
4
14.8%
1
3.7%
1
3.7%
1
3.7%
3
11.1%
1
3.7%
2
7.4%
1
3.7%
1
3.7%
1
3.7%
1
3.7%
1
3.7%
27
100.0%
89
Is Spatial Memory Age-Related?
Here we are going to test the (null) hypothesis that
there is no difference in the performances of the
two groups - Elderly and Young. We have two
measures – the number of objects correctly replaced
and the city block score that measures the distance
between the actual and replaced positions and totals
this over the 18 objects. These distances are
measured as “city blocks” i.e. horizontal and vertical
steps across the grid. Each of these measurements
is a discrete variable, so we need to be careful in
deciding which tests are appropriate.
90
Is Spatial Memory Age-Related?
Question – Recall the boxplot, how did the two groups
perform? Looking at the distribution of scores in
each group, does the diagram support the
assumptions underlying the t-test?
91
Is Spatial Memory Age-Related?
Answer - The boxplots show that the median scores
are about 27 for the Elderly group and 12 for the
Young group, which are quite different.
The t-test assumes that the scores are normally
distributed within each population.
This means that for each age group, we want to see
that the distribution of scores is reasonably
symmetric, with no outliers. The distribution of
scores for Young subjects has a positive skew but
otherwise there are no problems. The test also
assumes that the population variances are equal and
this seems reasonable as both groups have similar
ranges and IQRs.
92
Is Spatial Memory Age-Related?
Now we want to compare the city block scores for
the two groups, Elderly and Young.
93
Is Spatial Memory Age-Related?
Analyze > Compare Means > Independent-Samples T Test
94
Is Spatial Memory Age-Related?
Select cityblock as the Test variable and agegroup as
the Grouping variable
95
Is Spatial Memory Age-Related?
Click on Define Groups, then type 1 into the box
labelled Group 1 and 2 into the box labelled Group 2.
96
Is Spatial Memory Age-Related?
Finally
Independent Samples Test
Levene's Test for
Equality of Variances
F
City block s core
Equal variances
as sumed
Equal variances
not ass umed
.029
Sig.
.865
t-test for Equality of Means
t
df
Sig. (2-tailed)
Mean
Difference
Std. Error
Difference
95% Confidence
Interval of the
Difference
Lower
Upper
3.515
25
.002
13.253
3.771
5.487
21.019
3.511
24.737
.002
13.253
3.775
5.475
21.031
Question - Can we assume that the population variances
are equal?
97
Is Spatial Memory Age-Related?
Independent Samples Test
Levene's Test for
Equality of Variances
F
City block s core
Equal variances
as sumed
Equal variances
not ass umed
.029
Sig.
.865
t-test for Equality of Means
t
df
Sig. (2-tailed)
Mean
Difference
Std. Error
Difference
95% Confidence
Interval of the
Difference
Lower
Upper
3.515
25
.002
13.253
3.771
5.487
21.019
3.511
24.737
.002
13.253
3.775
5.475
21.031
Looking at the first two columns of the table, you
can see the results of Levene’s test, which tests
whether the population variances of the city block
scores are the same for both Elderly and Young
subjects. If there is no evidence of a difference
between these variances then we can use a test that
assumes that they are equal to compare the
population means.
More formally.
98
Is Spatial Memory Age-Related?
Independent Samples Test
Levene's Test for
Equality of Variances
F
City block s core
Equal variances
as sumed
Equal variances
not ass umed
.029
Sig.
.865
t-test for Equality of Means
t
df
Sig. (2-tailed)
Mean
Difference
Std. Error
Difference
95% Confidence
Interval of the
Difference
Lower
Upper
3.515
25
.002
13.253
3.771
5.487
21.019
3.511
24.737
.002
13.253
3.775
5.475
21.031
Answer –
Null hypothesis (H0): the variances are the same or
 E2   Y2 versus
Alternative hypothesis (H1): the variances are
different or  E2   Y2
Test statistic, F = 0.029, with p-value = 0.865.
Therefore there is no evidence to reject the null
hypothesis, H0. We can assume that the variances
are equal and hence they can be pooled in the t-test
on the means.
99
Is Spatial Memory Age-Related?
Now we can return to our test on the means. As it is
reasonable to assume that the population variances
are equal, we can use the test results based on this
assumption and shown on the first line of the same
table in SPSS.
Independent Samples Test
Levene's Test for
Equality of Variances
F
City block s core
Equal variances
as sumed
Equal variances
not ass umed
.029
Sig.
.865
t-test for Equality of Means
t
df
Sig. (2-tailed)
Mean
Difference
Std. Error
Difference
95% Confidence
Interval of the
Difference
Lower
Upper
3.515
25
.002
13.253
3.771
5.487
21.019
3.511
24.737
.002
13.253
3.775
5.475
21.031
Question - What do you conclude from this output?
100
Is Spatial Memory Age-Related?
Answer –
Null hypothesis (H0): the means are the same or  E  Y
versus
Alternative hypothesis (H1): the means are different
or  E  Y
The test statistic is t-Value = 3.515, d.f. = 25 with a
p-value = 0.002. As this is much smaller than 0.05
there is evidence to reject H0 and so we conclude
that there is a significant difference in the mean city
block scores for the Elderly and Young groups.
Note that in this case the t values and confidence
intervals are little affected by assumptions about the
variance.
101
Is Spatial Memory Age-Related?
Now use the same methods to compare study time
(time) between the Elderly and Young groups. Draw a
boxplot as before and then use the Compare Means
option to check whether the variances can be
assumed equal and perform a t-test. Use the t-test
to determine whether Elderly subjects underestimate
the time required to study the grid: to make the test
one-sided, you will need to divide the p-value by 2.
102
Is Spatial Memory Age-Related?
boxplot
103
Is Spatial Memory Age-Related?
t test
Independent Samples Test
Levene's Test for
Equality of Variances
F
Study time
Equal variances
as sumed
Equal variances
not ass umed
1.049
Sig.
.316
t-test for Equality of Means
t
df
Sig. (2-tailed)
Mean
Difference
Std. Error
Difference
95% Confidence
Interval of the
Difference
Lower
Upper
-4.771
25
.000
-48.132
10.088
-68.909
-27.355
-4.722
22.368
.000
-48.132
10.193
-69.251
-27.013
Question - What is the result of Levene’s test?
104
Is Spatial Memory Age-Related?
Answer –
Null hypothesis (H0): the variances are the same or
 E2   Y2 versus
Alternative hypothesis (H1): the variances are
different or  E2   Y2
Test statistic, F = 1.049 with p-value 0.316.
Therefore there is no evidence to reject the null
hypothesis, H0. We can assume that the variances
are equal and hence they can be pooled in the t-test
on the means, for which the hypotheses in the next
question.
105
Is Spatial Memory Age-Related?
Question - Now write down the null and alternative
hypotheses for the t-test and then look at the
results. What do you conclude?
Independent Samples Test
Levene's Test for
Equality of Variances
F
Study time
Equal variances
as sumed
Equal variances
not ass umed
1.049
Sig.
.316
t-test for Equality of Means
t
df
Sig. (2-tailed)
Mean
Difference
Std. Error
Difference
95% Confidence
Interval of the
Difference
Lower
Upper
-4.771
25
.000
-48.132
10.088
-68.909
-27.355
-4.722
22.368
.000
-48.132
10.193
-69.251
-27.013
106
Is Spatial Memory Age-Related?
Answer –
Null hypothesis (H0): the means are the same or  E  Y
versus
Alternative hypothesis (H1): the mean time is lower
for the Elderly or  E  Y
The test statistic is t-Value = -4.771, d.f. = 25. The
p-value, shown to 3 decimal places, is 0.000, which we
report as p < 0.001: dividing by 2 to obtain the p-value
for a one-sided test gives us p < 0.0005. Hence there
is very strong evidence to reject H0 and we conclude
that the means of the study times of the two groups
are significantly different. Elderly subjects do seem
to have underestimated the time required to study
the grid.
107
Is Spatial Memory Age-Related?
Although we have assumed that city block scores can
be approximated by a Normal distribution, they are in
fact discrete, being the sums of counts of horizontal
and vertical blocks. We might also want to compare
the Elderly and Young groups on the other measure of
spatial memory – the number of correct replacements.
We therefore need a test that does not rely on the
underlying distribution being Normal. The
non-parametric test that is “equivalent” to the two
sample t-test above is that due to Mann and Whitney.
We shall first use this test on the city block scores.
108
Is Spatial Memory Age-Related?
Analyze > Nonparametric Tests > Legacy Dialogs >
2 Independent Samples
109
Is Spatial Memory Age-Related?
Select cityblock for the Test Variable List and
agegroup for the Grouping Variable
110
Is Spatial Memory Age-Related?
Click on Define Groups and type 1 and 2 into the
boxes.
111
Is Spatial Memory Age-Related?
Finally
Te st Statisticsb
Cit y block
sc ore
Mann-W hit ney U
29.500
W ilcox on W
120.500
Z
-2. 986
As ymp. Sig. (2-tailed)
.003
a
Ex act Sig. [2*(1-tailed
.002
Sig.)]
a. Not correct ed for ties.
b. Grouping Variable: Age group
112
Is Spatial Memory Age-Related?
Question - What is being tested here and what are
your conclusions?
Te st Statisticsb
Cit y block
sc ore
Mann-W hit ney U
29.500
W ilcox on W
120.500
Z
-2. 986
As ymp. Sig. (2-tailed)
.003
a
Ex act Sig. [2*(1-tailed
.002
Sig.)]
a. Not correct ed for ties.
b. Grouping Variable: Age group
113
Is Spatial Memory Age-Related?
Answer - This test is on the medians (denoted by the
Greek letter  or eta), rather than the means.
Null hypothesis (H0): The median city block scores of
the two populations are the same versus
Alternative hypothesis (H1): The medians of the two
populations are different.
The test statistic U = 29.5, and the test is significant
with p = 0.003. As this is less than 0.05 we have
evidence to reject H0 and conclude that there is a
difference in the median city block scores Young and
Elderly age groups.
114
Is Spatial Memory Age-Related?
Now look at the number of correct replacements and
see if these differ between the two groups.
Test Statisticsb
Mann-Whitney U
Wilcoxon W
Z
As ymp. Sig. (2-tailed)
Exact Sig. [2*(1-tailed
Sig.)]
No. correct
25.500
130.500
-3.216
.001
a
.001
a. Not corrected for ties .
b. Grouping Variable: Age group
115
Is Spatial Memory Age-Related?
Question - Is there a difference between the median
number of correct replacements between the two
groups? Explain.
Test Statisticsb
Mann-Whitney U
Wilcoxon W
Z
As ymp. Sig. (2-tailed)
Exact Sig. [2*(1-tailed
Sig.)]
No. correct
25.500
130.500
-3.216
.001
a
.001
a. Not corrected for ties .
b. Grouping Variable: Age group
116
Is Spatial Memory Age-Related?
Answer –
Null hypothesis (H0): The medians of the two populations
are the same versus
Alternative hypothesis (H1): The medians of the two
populations are different.
Here U = 25.5 with p = 0.001. Again we reject the null
hypothesis and conclude that there is a difference in the
median number of correct replacements between the
two groups.
117
Is Spatial Memory Age-Related?
Question - Which of the measurements of memory
recall (number correct or city block score) do you
think is better? Explain.
Independent Samples Test
Levene's Test for
Equality of Variances
F
No. correct
Equal variances
as sumed
Equal variances
not ass umed
Sig.
9.225
t-test for Equality of Means
t
.006
df
Sig. (2-tailed)
Mean
Difference
Std. Error
Difference
95% Confidence
Interval of the
Difference
Lower
Upper
-4.079
25
.000
-3.654
.896
-5.499
-1.809
-3.962
15.028
.001
-3.654
.922
-5.619
-1.688
Independent Samples Test
Levene's Test for
Equality of Variances
F
City block s core
Equal variances
as sumed
Equal variances
not ass umed
.029
Sig.
.865
t-test for Equality of Means
t
df
Sig. (2-tailed)
Mean
Difference
Std. Error
Difference
95% Confidence
Interval of the
Difference
Lower
Upper
3.515
25
.002
13.253
3.771
5.487
21.019
3.511
24.737
.002
13.253
3.775
5.475
21.031
118
Is Spatial Memory Age-Related?
Answer - Note that for the number correct, the
variances cannot be assumed to be equal. For
example, the F-Test gives a Test Statistic of 9.225
and corresponding p-value of 0.006.The second line
of results for the t-test (which do not assume equal
variances) gives t-Value = -3.962, d.f. = 15.028 and
p-value = 0.001. We would conclude that the means
are significantly different. In both cases, using
parametric or non-parametric tests we see that
there are significant differences in the measures of
accuracy between the age groups. city block score
seems better as it accounts for “near misses”.
However the number correct is easier to find.
119
Is Spatial Memory Age-Related?
We shall first see if the two measurements of
accuracy – the number correctly positioned and the
error in position are correlated. First look at the
scatterplot.
120
Is Spatial Memory Age-Related?
Graphs > Legacy Dialogs > Scatter/Dot
121
Is Spatial Memory Age-Related?
Simple > Define
122
Is Spatial Memory Age-Related?
Select ncorrect for the x-axis and cityblock for the
y-axis.
123
Is Spatial Memory Age-Related?
Finally
This seems reasonably linear, so the next step is
to find the correlation coefficient.
124
Is Spatial Memory Age-Related?
More flamboyant plots are possible within SAS.
Galleries of available graphics and source code have
been provided.
•Graphics gallery for the SGPLOT procedure: create
one plot
•Graphics gallery for the SGPANEL procedure: create
a panel of plots, each of the same plot type
•Graphics gallery for the SGRENDER procedure: use
with the GTL to layout multiple plots of different
types, or to produce nonstandard plots
•Graphics gallery for the SGSCATTER procedure:
create a panel of scatter plots
125
Is Spatial Memory Age-Related?
This example follows suggestions from
How to create a scatter plot with marginal
histograms in SAS
The syntax should be saved in an ascii file, ideally
with the extension “.sas”.
126
proc template;
define statgraph scatterhist;
dynamic XVAR YVAR XTYPE YTYPE TITLE;
begingraph / designwidth=600px designheight=400px borderattrs=(thickness=3px);
entrytitle TITLE;
layout lattice / rows=2 columns=2 rowweights=(.2 .8) columnweights=(.8 .2)
rowdatarange=union columndatarange=union rowgutter=0 columngutter=0;
/* histogram or barchart at X2 axis position */
layout overlay / walldisplay=(fill) wallcolor=GraphBackground:color
xaxisopts=(display=none)
yaxisopts=(display=none offsetmin=0);
if (upcase(XTYPE) = "DISCRETE")
barchart x=XVAR / barwidth=1 stat=pct;
else
histogram XVAR / binaxis=false;
endif;
endlayout;
/* NOBS count cell */
layout overlay;
entry " "; *'NOBS = ' eval(n(XVAR));
endlayout;
/* scatter plot with conditional axis types */
layout overlay / xaxisopts=(type=XTYPE) yaxisopts=(type=YTYPE);
scatterplot y=YVAR x=XVAR / datatransparency=0 markerattrs=(symbol=circlefilled size=11px);
endlayout;
/* histogram or barchart at Y2 axis position */
layout overlay / walldisplay=(fill) wallcolor=GraphBackground:color
xaxisopts=(display=none offsetmin=0) yaxisopts=(display=none);
if (upcase(YTYPE) = "DISCRETE") barchart x=YVAR / barwidth=1 orient=horizontal stat=pct;
else histogram YVAR / orient=horizontal binaxis=false;
endif;
endlayout;
endlayout;
endgraph;
end;
run;
ods graphics;
PROC IMPORT OUT= WORK.A
DATAFILE= "\\Client\F$\spss\case study\7.sav"
DBMS=SPSS REPLACE;
RUN;
proc sgrender data=Work.A template=scatterhist;
dynamic YVAR="cityblock" XVAR="ncorrect"
TITLE="Relationship";
run;
The template,
treat as a black
box.
Import your SPSS
“.sav” file.
Produce the plot
you require.
127
Is Spatial Memory Age-Related?
Within SAS use its menu’s
File > Open Programme assess SAS source
Run > Submit
After loading the template the “log” reports
128
Is Spatial Memory Age-Related?
NOTE: PROCEDURE TEMPLATE used (Total process time):
real time
0.57 seconds
cpu time
0.43 seconds
37
38
39
40
41
ods graphics;
PROC IMPORT OUT= WORK.A
DATAFILE= "\\Client\F$\spss\case study\7.sav"
DBMS=SPSS REPLACE;
RUN;
NOTE: The import data set has 27 observations and 6 variables.
NOTE: WORK.A data set was successfully created.
NOTE: PROCEDURE IMPORT used (Total process time):
real time
0.70 seconds
cpu time
0.06 seconds
42
43
44
45
proc sgrender data=Work.A template=scatterhist;
dynamic YVAR="cityblock" XVAR="ncorrect"
TITLE="Relationship";
run;
NOTE: There were 27 observations read from the data set WORK.A.
NOTE: PROCEDURE SGRENDER used (Total process time):
real time
0.89 seconds
cpu time
0.21 seconds
thin SAS use its menu’s
File > Open Programme assess SAS source
Run > Submit
129
Is Spatial Memory Age-Related?
On the graph, right click mouse, then “Save picture as”
130
Is Spatial Memory Age-Related?
Returning
to the
thread of
the
analysis
This seems reasonably linear, so the next step is
to find the correlation coefficient.
131
Is Spatial Memory Age-Related?
Analyze > Correlate > Bivariate
132
Is Spatial Memory Age-Related?
Select ncorrect and cityblock
133
Is Spatial Memory Age-Related?
The result is
Correlations
No. correct
City block s core
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
City block
No. correct
score
1
-.735**
.000
27
27
-.735**
1
.000
27
27
**. Correlation is s ignificant at the 0.01 level (2-tailed).
134
Is Spatial Memory Age-Related?
Question - What do you conclude about the two
measurements of accuracy?
Correlations
No. correct
City block s core
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
City block
No. correct
score
1
-.735**
.000
27
27
-.735**
1
.000
27
27
**. Correlation is s ignificant at the 0.01 level (2-tailed).
135
Is Spatial Memory Age-Related?
Answer - They are negatively related i.e. an increase
in city block score is generally associated with a
decrease in number correct and vice versa. The
correlation coefficient is quite high.
Correlations
No. correct
City block s core
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
City block
No. correct
score
1
-.735**
.000
27
27
-.735**
1
.000
27
27
**. Correlation is s ignificant at the 0.01 level (2-tailed).
136
Is Spatial Memory Age-Related?
Study time may also be included by adding it to the
list of variables to be correlated.
137
Is Spatial Memory Age-Related?
The plots are
138
Is Spatial Memory Age-Related?
The plots are
139
Is Spatial Memory Age-Related?
With correlation
Correlations
No. correct
City block s core
Study time
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
City block
No. correct
score
Study time
1
-.735**
.780**
.000
.000
27
27
27
-.735**
1
-.732**
.000
.000
27
27
27
.780**
-.732**
1
.000
.000
27
27
27
**. Correlation is s ignificant at the 0.01 level (2-tailed).
140
Is Spatial Memory Age-Related?
Question - Report the correlation coefficients and
what you can conclude about the variables.
Correlations
No. correct
City block s core
Study time
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
City block
No. correct
score
Study time
1
-.735**
.780**
.000
.000
27
27
27
-.735**
1
-.732**
.000
.000
27
27
27
.780**
-.732**
1
.000
.000
27
27
27
**. Correlation is s ignificant at the 0.01 level (2-tailed).
141
Is Spatial Memory Age-Related?
Answer - City block score and time: r = -0.732. They
are negatively related i.e. an increase in study time is
generally associated with a decrease in city block
score. The correlation coefficient is quite high.
Number correct and time: r = 0.780. They are
positively related i.e. an increase in study time is
generally associated with a increase in the number
correctly replaced. The correlation coefficient is
quite high.
142
Is Spatial Memory Age-Related?
Question - What do the p-values tell you and what
assumption is made here?
Correlations
No. correct
City block s core
Study time
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
City block
No. correct
score
Study time
1
-.735**
.780**
.000
.000
27
27
27
-.735**
1
-.732**
.000
.000
27
27
27
.780**
-.732**
1
.000
.000
27
27
27
**. Correlation is s ignificant at the 0.01 level (2-tailed).
143
Is Spatial Memory Age-Related?
Answer - Here we are testing hypotheses on the
correlation coefficient for the populations,
designated by the Greek letter  (rho).
Null hypothesis (H0): there is no correlation or   0
Alternative hypothesis (H1): there is some correlation
or   0
City block and number correct. The p-value is given as
0.000. This is how SPSS records the probability, it
does not mean that it is exactly 0.000 but we can say
that p < 0.001, so there is strong evidence to reject
H0 and we conclude that the correlation is
significantly different from zero.
144
Is Spatial Memory Age-Related?
City block and study time. Again, p < 0.001, so there
is strong evidence to reject H0 and we conclude that
the correlation is significantly different from zero.
Number correct and study time. Again, p < 0.001, so
there is strong evidence to reject H0 and we
conclude that the correlation is significantly
different from zero.
The assumption is that, for each pair, the variables
are jointly normally distributed.
145
Is Spatial Memory Age-Related?
So far we have looked at all the data together but
there might be differences between the Young and
Elderly groups.
The correlations between scores can be found
separately for Young and Elderly subjects using the
Split File procedure.
146
Is Spatial Memory Age-Related?
Data > Split File
147
Is Spatial Memory Age-Related?
Select Organise output by groups and agegroup
148
Is Spatial Memory Age-Related?
Until this procedure is reversed, every analysis or
plot requested will be run separately for each age
group. First repeat the instructions for finding the
correlations between ncorrect, cityblock and time.
Question - Report the correlation coefficients for
each pair of variables in each agegroup. What you can
conclude in each case?
149
Is Spatial Memory Age-Related?
It is always wise to plot the data
Graphs > Legacy Dialogs > Scatter/Dot
150
Is Spatial Memory Age-Related?
Matrix scatter
151
Is Spatial Memory Age-Related?
Select the three variables
152
Is Spatial Memory Age-Related?
The Elderly plots are
153
Is Spatial Memory Age-Related?
The Young plots are
154
Is Spatial Memory Age-Related?
Correlationsa
No. correct
Question - Report
the correlation
coefficients for each
pair of variables in
each age group. What
can you conclude in
each case?
City block s core
Study time
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
City block
score
Study time
-.693**
.368
.006
.195
14
14
14
-.693**
1
-.418
.006
.137
14
14
14
.368
-.418
1
.195
.137
14
14
14
No. correct
1
**. Correlation is s ignificant at the 0.01 level (2-tailed).
a. Age group = Elderly
Correlationsa
No. correct
City block s core
Study time
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
No. correct
1
13
-.625*
.022
13
.724**
.005
13
City block
score
-.625*
.022
13
1
Study time
.724**
.005
13
-.692**
.009
13
13
-.692**
1
.009
13
13
*. Correlation is s ignificant at the 0.05 level (2-tailed).
**. Correlation is s ignificant at the 0.01 level (2-tailed).
a. Age group = Young
155
Is Spatial Memory Age-Related?
Answer - Here we are testing hypotheses on the
correlation coefficient for the populations,
designated by the Greek letter  (rho).
Null hypothesis (H0): there is no correlation or   0
Alternative hypothesis (H1): there is some correlation
or   0 .
156
Is Spatial Memory Age-Related?
Answer - Elderly Group
Correlationsa
No. correct
City block s core
Study time
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
City block
score
Study time
-.693**
.368
.006
.195
14
14
14
-.693**
1
-.418
.006
.137
14
14
14
.368
-.418
1
.195
.137
14
14
14
No. correct
1
**. Correlation is s ignificant at the 0.01 level (2-tailed).
a. Age group = Elderly
157
Is Spatial Memory Age-Related?
City block and number correct: r = -0.693. City block
and number correct are negatively related. The
correlation coefficient is quite high. p-value = 0.006,
so there is strong evidence to reject H0 and we
conclude that the correlation is significantly
different from zero.
City block and study time: r = -0.418, city block and
study time are negatively related. The correlation
coefficient is quite low. p-value = 0.137 so there is no
evidence to reject H0 and we conclude that the
correlation is not significantly different from zero.
158
Is Spatial Memory Age-Related?
Number correct and study time: r = 0.368, number
correct and study time are positively related. The
correlation coefficient is quite low. p-value = 0.195
so there is no evidence to reject H0 and we conclude
that the correlation is not significantly different
from zero.
159
Is Spatial Memory Age-Related?
Answer – Young Group
Correlationsa
No. correct
City block s core
Study time
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
No. correct
1
13
-.625*
.022
13
.724**
.005
13
City block
score
-.625*
.022
13
1
Study time
.724**
.005
13
-.692**
.009
13
13
-.692**
1
.009
13
13
*. Correlation is s ignificant at the 0.05 level (2-tailed).
**. Correlation is s ignificant at the 0.01 level (2-tailed).
a. Age group = Young
160
Is Spatial Memory Age-Related?
City block and number correct: r = -0.625. City block
and number correct are negatively related. The
correlation coefficient is quite high. p-value = 0.022,
so there is evidence to reject H0 and we conclude that
the correlation is significantly different from zero.
City block and study time: r = -0.692, city block and
study time are negatively related. The correlation
coefficient is quite high. p-value = 0.009 so there is
strong evidence to reject H0 and we conclude that the
correlation is significantly different from zero.
161
Is Spatial Memory Age-Related?
Number correct and study time: r = 0.724, number
correct and study time are positively related. The
correlation coefficient is quite high. p-value = 0.005
so there is strong evidence to reject H0 and we
conclude that the correlation is significantly
different from zero.
162
Is Spatial Memory Age-Related?
Correlationsa
No. correct
Question - Are there
any differences
between the Elderly
and Young groups?
City block s core
Study time
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
City block
score
Study time
-.693**
.368
.006
.195
14
14
14
-.693**
1
-.418
.006
.137
14
14
14
.368
-.418
1
.195
.137
14
14
14
No. correct
1
**. Correlation is s ignificant at the 0.01 level (2-tailed).
a. Age group = Elderly
Correlationsa
No. correct
City block s core
Study time
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
No. correct
1
13
-.625*
.022
13
.724**
.005
13
City block
score
-.625*
.022
13
1
Study time
.724**
.005
13
-.692**
.009
13
13
-.692**
1
.009
13
13
*. Correlation is s ignificant at the 0.05 level (2-tailed).
**. Correlation is s ignificant at the 0.01 level (2-tailed).
a. Age group = Young
163
Is Spatial Memory Age-Related?
Answer - For both age groups , and overall, there is significant
correlation between the two measurements of accuracy – the
number of correct replacements and the city block scores i.e. in
all cases there is a significant linear relationship between these
two measurements.
When each of these is paired with study time, we have found
that the correlations are stronger, and statistically significant
for the Young group and overall, but not for the Elderly. For
study time and number correct there is a positive relationship;
for study time and city block it is negative for either age group.
The difference in the signs of these correlations reflect the
fact that performing well corresponds to low values for the city
block score and high values for the number correct.
164
Is Spatial Memory Age-Related?
To reverse the split file procedure
Data > Split File
165
Is Spatial Memory Age-Related?
Analyze all cases
166
Is Spatial Memory Age-Related?
Now recreate a scatter plot of city block scores and
study times. With city block scores on the y-axis and
study time on the x-axis.
Why are the specific variables assigned to a
particular axis?
To see any relationship, plot the line of best fit, a
linear regression.
167
Is Spatial Memory Age-Related?
The scatter plot is
168
Is Spatial Memory Age-Related?
Double click on the scatter diagram to open the Chart
Editor window
169
Is Spatial Memory Age-Related?
In the Chart Editor window, click on one of the points
to highlight the points in the graph.
170
Is Spatial Memory Age-Related?
Click on the Add fit line icon which shows a scatter
plot with a line of best fit.
171
Is Spatial Memory Age-Related?
Check that the ‘Linear’ option is selected.
172
Is Spatial Memory Age-Related?
Finally (note that this appears to be the only way to
produce such a graph, no syntax is available)
173
Is Spatial Memory Age-Related?
Question - What does the scatter plot tell you about
the variables? Do you think that study time is a good
predictor of city block score?
174
Is Spatial Memory Age-Related?
Answer - Overall there is a negative trend in the
scatter of points, indicating that, in general, an
increase in study time is associated with a decrease in
city block i.e. the longer the study time the smaller
the city block score. However the points are fairly
scattered so it is not a strong trend. Study time
might be a predictor of city block.
175
Is Spatial Memory Age-Related?
We now perform the regression analysis to find the
equation of the regression line.
y    x
176
Is Spatial Memory Age-Related?
Analyze > Regression > Linear
177
Is Spatial Memory Age-Related?
Select city block for the Dependent variable and
study time as the Independent variable – recall the
plot for identification of the variables
178
Is Spatial Memory Age-Related?
Question - What does the output tell you about the
constant term (intercept)?
Coeffi cientsa
Model
1
(Const ant)
St udy time
Unstandardized
Coeffic ient s
B
St d. Error
39.204
3.681
-.242
.045
St andardiz ed
Coeffic ient s
Beta
-.732
t
10.651
-5. 368
Sig.
.000
.000
a. Dependent Variable: City block sc ore
ANOVAb
Model
1
Regres sion
Residual
Total
Sum of
Squares
1916.754
1663.246
3580.000
df
1
25
26
Mean Square
1916.754
66.530
F
28.810
Sig.
.000a
a. Predic tors : (Const ant), Study t ime
b. Dependent Variable: City block sc ore
179
Is Spatial Memory Age-Related?
Answer - Null hypothesis (H0): the intercept
is zero   0
i.e. the line passes through the origin
Alternative hypothesis (H1): the intercept is
not zero   0
i.e. The constant term is 39.204;
The test statistic is t = 10.651 with 25 d.f.
(shown in the ANOVA table) and p < 0.001
(SPSS displays 0.000, which we report as
p < 0.001). Hence there is strong evidence to
reject H0 and conclude that the intercept is
not zero.
180
Is Spatial Memory Age-Related?
Question - What does the output tell you about the
regression term (gradient)?
Coeffi cientsa
Model
1
(Const ant)
St udy time
Unstandardized
Coeffic ient s
B
St d. Error
39.204
3.681
-.242
.045
St andardiz ed
Coeffic ient s
Beta
-.732
t
10.651
-5. 368
Sig.
.000
.000
a. Dependent Variable: City block sc ore
ANOVAb
Model
1
Regres sion
Residual
Total
Sum of
Squares
1916.754
1663.246
3580.000
df
1
25
26
Mean Square
1916.754
66.530
F
28.810
Sig.
.000a
a. Predic tors : (Const ant), Study t ime
b. Dependent Variable: City block sc ore
181
Is Spatial Memory Age-Related?
Answer - Null hypothesis (H0): the gradient is zero
i.e. there is no regression or   0
Alternative hypothesis (H1): the gradient is not zero,
i.e. there is regression or   0
The regression term is -0.242, the test statistic is
t = -5.368 with 25 d.f. (shown in the ANOVA table)
p < 0.001. Hence there is strong evidence to reject H0
and conclude that the gradient is not zero i.e. there is
some relationship.
182
Is Spatial Memory Age-Related?
Question - What does the R square term tell you and
how is it related to the correlation coefficient found
earlier?
Model Summary
Model
1
R
.732a
R Square
.535
Adjusted
R Square
.517
Std. Error of
the Estimate
8.157
a. Predictors: (Constant), Study time
Correlations
City block s core
Study time
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
City block
score
1
Study time
-.732**
.000
27
27
-.732**
1
.000
27
27
**. Correlation is s ignificant at the 0.01 level (2-tailed).
183
Is Spatial Memory Age-Related?
Answer - R-Sq tells you how much of the variation in
city block is due to the changes in study time, i.e. to
regression (the rest being attributed to error).
It is the ratio of the regression sum of squares (SS)
to the total sum of squares in the Analysis of Variance
table, written as a percentage:
1916.8/3580.0 = 53.5%
Alternatively, it is the square of the correlation
coefficient, written as a percentage
(-0.732)2= 53.5%.
Only about half of the variation in city block is due to
study time.
184
Is Spatial Memory Age-Related?
Question - What does the regression predict as
the city block score for a subject who took
(i) 50 seconds
(ii) 200 seconds?
The equation of the line is
city block = 39.2 – 0.242 study time
185
Is Spatial Memory Age-Related?
Answer - The equation of the line is
city block = 39.2 – 0.242 study time
So for 50 seconds
city block = 39.2 – 0.242 (50) = 27.1
We cannot say anything for 200 seconds as the time
is outside our range and we do not know if the linear
relationship still holds here.
186
Is Spatial Memory Age-Related?
We might also want to see the regression for each of
the two age groups separately and compare them.
Earlier we separated Young and Elderly subjects. Use
the Split File procedure to do this again and repeat
the regression analysis above. Compare the results for
different age groups to each other and to the
equation obtained using the whole sample.
187
Is Spatial Memory Age-Related?
Elderly
188
Is Spatial Memory Age-Related?
Young
189
Is Spatial Memory Age-Related?
Question - What are the best fit equations for
using study time to predict city block scores for
(i) the Elderly,
(ii) the Young?
How well do these predict the results?
190
Is Spatial Memory Age-Related?
Answer - For Elderly subjects, the equation of the
line of best fit is
cityblock = 36.8 – 0.179 Time
This is very similar to the equation for both groups
combined. There is strong evidence to conclude that
the intercept is not zero (t = 5.927, d.f. = 12,
p < 0.001). However, we must conclude that there is
no evidence to reject the hypothesis that the
gradient is zero (t = -1.593, d.f. = 12, p = 0.137) i.e.
there is no statistically significant evidence of a
regression. This is confirmed by R-Sq = 17.4% i.e.
Time is “explaining” very little of the variation in city
block.
191
Is Spatial Memory Age-Related?
The equation of the line of best fit for Young
subjects is
cityblock = 37.3 – 0.231 Time
This is very similar to the equation for both groups
combined. There is strong evidence to conclude that
neither the intercept (t = 4.984, d.f. = 11, p < 0.001)
nor the gradient (t = -3.178, d.f. = 11, p = 0.009) are
zero.
R-Sq = 47.9% i.e. Time “explains” almost half of the
variation in city block .
192
Is Spatial Memory Age-Related?
Correlationsa
Question - How
do these results
link with the
correlations
found earlier?
No. correct
City block s core
Study time
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
City block
score
Study time
-.693**
.368
.006
.195
14
14
14
-.693**
1
-.418
.006
.137
14
14
14
.368
-.418
1
.195
.137
14
14
14
No. correct
1
**. Correlation is s ignificant at the 0.01 level (2-tailed).
a. Age group = Elderly
Correlationsa
No. correct
City block s core
Study time
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
No. correct
1
13
-.625*
.022
13
.724**
.005
13
City block
score
-.625*
.022
13
1
Study time
.724**
.005
13
-.692**
.009
13
13
-.692**
1
.009
13
13
*. Correlation is s ignificant at the 0.05 level (2-tailed).
**. Correlation is s ignificant at the 0.01 level (2-tailed).
a. Age group = Young
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Is Spatial Memory Age-Related?
Answer - We found earlier that time and city block
scores were not significantly correlated for the
Elderly group i.e. they are not linearly related. This
has been confirmed in the regression analysis.
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Is Spatial Memory Age-Related?
We found that city block scores were linearly
dependent on study times.
We are now going to extend this by considering
whether the Age group is also an important factor and
look more closely at the SPSS output that we can
obtain to generate more information on the data and
outcomes of the regression model.
You might want to carry the analysis a bit further.
Does the city block score also depend on whether the
subject was Elderly or Young? In order to do this we
need to code the agegroup variable – say into 1 for
Elderly and 0 for Young.
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Is Spatial Memory Age-Related?
Transform > Recode Into Different Variables
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Is Spatial Memory Age-Related?
Select age group as the numeric variable type Elderly
into the box labelled Output Variable Name and click
on Change
Click on Old and New Values
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Is Spatial Memory Age-Related?
On the left, under Old Values, type 2 into the box
labelled Value
On the right, under New Values, type0 into the box
labelled Value
Click on Add – this creates the first rule
On the left,
select All other
values,
on the right
select Copy old
values and click
on Add
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Is Spatial Memory Age-Related?
SPSS now creates a new variable, with the name
Elderly, which takes value 1 for an Elderly subject and
0 otherwise.
Now repeat the regression analysis with city block as
the dependent variable and both study time and
Elderly as predictor variables.
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Is Spatial Memory Age-Related?
Question - How does this affect the regression
analysis? Is age group significant?
Model Summary
Model
1
R
.738a
R Square
.545
Adjusted
R Square
.507
Std. Error of
the Estimate
8.241
a. Predictors: (Constant), elderly, Study time
Coeffi cientsa
Model
1
(Const ant)
St udy time
elderly
Unstandardized
Coeffic ient s
B
St d. Error
35.355
6.627
-.211
.063
3.079
4.387
St andardiz ed
Coeffic ient s
Beta
-.639
.134
t
5.335
-3. 359
.702
Sig.
.000
.003
.490
a. Dependent Variable: City block sc ore
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Is Spatial Memory Age-Related?
Answer - R-Sq has hardly changed. It was 53.5% with
just study time as a predictor and is now 54.5%,
indicating that the inclusion of age group has helped
only marginally in explaining the variation in city block
score. The age group variable Elderly is not significant
(t = 0.702, d.f. = 24, p =0.490).
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Is Spatial Memory Age-Related?
Hence we now return to the simple linear regression
model as found earlier.
Every time a regression analysis is performed, the
SPSS output includes an analysis of variance
(ANOVA) table. This is a useful tool in multiple
regression (i.e. where there is more than one
independent variable) and other areas in statistics.
For the original regression of city block score on
study time recall the ANOVA table.
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Is Spatial Memory Age-Related?
Question - Explain what the Degrees of Freedom
(d.f.), Sum of Squares (SS) and Mean Square (MS)
represent and how they are related.
ANOVAb
Model
1
Regres sion
Residual
Total
Sum of
Squares
1916.754
1663.246
3580.000
df
1
25
26
Mean Square
1916.754
66.530
F
28.810
Sig.
.000a
a. Predic tors : (Const ant), Study t ime
b. Dependent Variable: City block sc ore
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Is Spatial Memory Age-Related?
Answer - d.f. or degrees of freedom represents the
amount of independent information in each sum. Thus
we have 1 for “Model” as there is 1 independent
variable, 26 -1 = 25 for “Total”, and the
“Regression” d.f. + “Residual Error” d.f. = “Total” d.f.
Each Sum of Squares (SS) represents a portion of the
variability in block – due to the “Regression”, i.e. in this
case, due to study time or that due to the “Residual
Error”, i.e. the variability around the regression line
“Regression” SS + “Residual Error” SS = “Total” SS
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Is Spatial Memory Age-Related?
The Mean Squares are found by dividing each SS by
its corresponding d.f. The Mean Square due to the
“Residual Error” (MSE) is an unbiased estimate of the
variance of the error terms.
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Is Spatial Memory Age-Related?
Question - State the hypotheses being tested in the
ANOVA, how the test statistic is calculated and what
your decision would be.
ANOVAb
Model
1
Regres sion
Residual
Total
Sum of
Squares
1916.754
1663.246
3580.000
df
1
25
26
Mean Square
1916.754
66.530
F
28.810
Sig.
.000a
a. Predic tors : (Const ant), Study t ime
b. Dependent Variable: City block sc ore
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Is Spatial Memory Age-Related?
Answer - Null hypothesis (H0): the gradient is zero
i.e. there is no regression or   0
Alternative hypothesis (H1): the gradient is not zero,
i.e. there is regression or   0
The test statistic,
" Regression " Mean Square 1916.8
F

 28.81
MSE
66.5
Under H0 the Mean Squares should be equal, i.e. F
should be 1.
Here F = 28.81 with d.f. = 1, 25 and p < 0.001. Hence
we reject H0 at the 5% significance level and conclude
that city block score is linearly dependent on study
time.
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Is Spatial Memory Age-Related?
Here we verify (or not!) some of the assumptions
made in the regression model, using the residuals,
which are estimates of the unknown error terms.
Question - What are the assumptions made about
the error terms?
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Is Spatial Memory Age-Related?
Answer - The errors have zero mean, constant
2
variance and are Normally distributed i.e.  i ~   ,  
and they are uncorrelated.
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Is Spatial Memory Age-Related?
The residuals can be calculated and plotted against
study time, the independent variable and the
predicted values of city block score.
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Is Spatial Memory Age-Related?
Returning to the
previous regression
Click on the Save
button
under Predicted
Values select
Unstandardised,
under Residuals
select Standardised
and
under Distances,
select Cook’s
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Is Spatial Memory Age-Related?
Click on the Plots button and select Histogram and
Normal Probability plot
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Is Spatial Memory Age-Related?
SPSS repeats the regression analysis, producing the
same output as before. In addition it generates plots
which we will look at later and creates three new
columns in the Data Viewer Window, storing the
predicted values, labelled PRE_1, standardised
residuals, ZRE_1 and Cook’s distances, COO_1.
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Is Spatial Memory Age-Related?
Question - How are the predicted values and residuals
calculated? What does this information tell you about
your model?
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Is Spatial Memory Age-Related?
Answer - The Predicted Values (PRE_1) are calculated
from the regression equation so, for example, at
observation 1, for a study time of 75 seconds, the
model predicts that the city block score would be
39.2 – 0.242 x 75 = 21.0646.
The residuals are the difference between the actual
and predicted values. Thus for observation 1 the
residual is 17 – 21.0646 = -4.0646.
The residuals are an indication of the fit of the model
to the original data, so that large positive or negative
residuals indicate a poor fit. Here the residuals vary
between 0.9819 (observation 17) and 16.0982
(observation 10). Note that, from the regression
output, observation 10 is flagged as having a large
residual.
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Is Spatial Memory Age-Related?
Question - How are the standardized residuals
calculated, why are they “better” than the ordinary
residuals and what further information do they give
about the model?
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Is Spatial Memory Age-Related?
Answer - A standardized residual is calculated by
dividing the residual by its standard error. The
standardized residuals follow a t distribution, which
can be approximated by the Normal for large enough
sample sizes. Standardized residuals greater than 2.5
or less than –2.5 are rare and indicate unusually large
residuals. There are none in that category here. The
standardised residual for observation 10 is 1.9734,
higher than any other but still with an absolute value
less than 2.
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Is Spatial Memory Age-Related?
Question - What do the Cook’s distances tell us?
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Is Spatial Memory Age-Related?
Answer - These distances (COO_1) can be used to
identify influential data points. A rule of thumb is
that an observation may have an adverse effect on
the analysis if D > 4/n. Here n = 26, so we would look
for D values greater than 4/26 = 0.154 (to 3 d.p.).
There are no values of D as large as this here. We
would therefore conclude that there are no influential
data points.
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Is Spatial Memory Age-Related?
Next we test the assumptions of the model (normality
etc.) by looking at various plots of the residuals.
Produce a simple scatter graph with the standardised
residuals, ZRE_1 for the y-axis and the predicted
values, PRE_1 for the x-axis.
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Is Spatial Memory Age-Related?
Giving
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Is Spatial Memory Age-Related?
Question - What does this graph tell us?
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Is Spatial Memory Age-Related?
Answer - The residuals are randomly scattered about
the line through 0, indicating that the mean of the
residuals is 0. The variation in the residuals seems to
be increasing with increasing fitted values, casting
doubt on the assumption of constant variance.
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Is Spatial Memory Age-Related?
Now
consider
the graphs that
followed
on
from the usual
regression
output.
These can be
used to check
the assumption
of
Normality.
First look at
the histogram.
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Is Spatial Memory Age-Related?
Question - What does the histogram show?
225
Is Spatial Memory Age-Related?
Answer - The histogram shows a distribution that
looks approximately Normal.
226
Is Spatial Memory Age-Related?
Next look at the P-P (Normal probability) plot.
227
Is Spatial Memory Age-Related?
Question - What does the Normal probability plot
suggest?
228
Is Spatial Memory Age-Related?
Answer - The Normal probability plot also suggests a
Normal distribution.
229
Is Spatial Memory Age-Related?
You can also use the regression procedure to find
confidence intervals for the mean city block score and
prediction intervals for an individual value of city block
score at a specified study time. We will predict the
city block score for study times of 60 seconds and
160 seconds.
Go to the Data Viewer Window and type 60 in line 28
of the column headed time and 160 in the same column
on the line below. This introduces two new lines of
data: these will not affect the regression coefficients
but will be included in making predictions.
To simplify the Data Viewer Window, highlight the
column headings for the residuals, predicted values and
Cook’s distances from previous analyses press the
delete key to empty these columns.
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Is Spatial Memory Age-Related?
Using Save in the previous regression. Remove the
selections under Residuals and Distances, and under
Prediction Intervals, select Mean and Individual.
231
Is Spatial Memory Age-Related?
SPSS repeats the regression analysis and creates new
columns in the data viewer. These columns show the
predicted city block score (PRE_1), confidence limits
for the predicted mean city block score (LMCI_1,
UMCI_1) and confidence limits for individual
predictions (LICI_1, UICI_1) associated with the
study times listed in the dataset.
232
Is Spatial Memory Age-Related?
Question - What can you say about the mean city
block score of participants with a study time of 60
seconds?
233
Is Spatial Memory Age-Related?
Answer - We are 95% confident that the mean lies
between 21.21 and 28.17.
234
Is Spatial Memory Age-Related?
Question - What city block score can Mrs. Smith
expect if she takes 60 seconds to study the grid?
235
Is Spatial Memory Age-Related?
Answer - We are 95% confident that Mrs. Smith’s
city block score will be between 7.54 and 41.85.
236
Is Spatial Memory Age-Related?
Question - What can you say about the city block
score of participants with a study time of 160
seconds?
237
Is Spatial Memory Age-Related?
Answer - The 95% confidence interval is given as
(-8.11, 9.13). However, the longest study time used
here was 145 seconds. Therefore, predicting a city
block score for a study time of 160 seconds is
extrapolating beyond the range of our observations,
which is unreliable.
238
Is Spatial Memory Age-Related?
th-th-th-that's all folks!
Or is it!!
239