Cronbach’s Alpha
It is very common in psychological research to
collect multiple measures of the same construct.
For example, in a questionnaire designed to
measure optimism, there are typically many items
that collectively measure the construct of
optimism. To have confidence in a measure such as
this, we need to test its reliability, the degree to
which it is error-free. The type of reliability we'll
be examining here is called internal consistency
reliability. the degree to which multiple measures
of the same thing agree with one another.
1
Cronbach’s Alpha
As an example we consider the “Benevolent
Sexism Scale” part of the scale developed by
Peter Glick and Susan Fiske (1996). Details are
given in the Appendix to the print version of the
notes.
2
Reverse Scoring
Most of the items are phrased so that strong
agreement indicates a belief that men should
protect women, that men need women, and that
women have positive qualities that men lack.
However, three of the items are phrased in the
reverse #3, #6, and #13. In order to make those
items comparable to the other items, we will need
to reverse score them.
3
Reverse Scoring
In this questionnaire, participants responded to
the items using a 7 point Likert scale (the original
scale had only 5 points) ranging from 1 (“Strongly
Disagree”) to 7 (“Strongly Agree”). When we
reverse score an item, we want 1's to turn into
7's, 7's to turn into 1's, and all the scores in
between to become their appropriate opposite
(6's into 2's, 5's into 3's, etc.).
4
Reverse Scoring
Fortunately, there is a simple mathematical rule
for reverse scoring.
reverse score(x) = max(x) + 1 – x
Where max(x) is the maximum possible value for
x. In our case, max(x) is 7 because the Likert
scale only went up to 7. To reverse score, we take
7 + 1 = 8, and subtract our scores from that
8 - 7 = 1, 8 - 1 = 7.
5
Reverse Scoring
To get SPSS to reverse score.
Transform > Compute Variable
6
Reverse Scoring
You will be creating a new variable for each of the
variables you need to reverse score. #3, #6, and
#13. The original variables are called ASI3, ASI6
and ASI13. For simplicity preserve the names for
the new reverse scored variables. Name the first
variable (the “Target Variable”) ASI3, and set it
equal to 8 ASI3.
Repeat the exercise for the remaining variables
(ASI6, and ASI13).
7
Reverse Scoring
8
Reliability
Now you're ready to compute the reliability of
this scale, select
Analyze > Scale > Reliability Analysis
9
Reliability
Move all the scored items into the 'Items' box.
10
Reliability
Click on the box labelled Statistics and select
Scale if item deleted (explained below).
11
Reliability
Click on the box labelled Statistics and select
Scale if item deleted (explained below).
Press 'Continue' and
then 'OK.' You
should get the
following output.
12
Reliability
Look at the top of the output and you will see
“.741” under “Cronbach's Alpha.” This is the most
common statistic used to describe the internal
consistency reliability of a set of items. If you are
using a questionnaire in your research, your
results should include a report of the Cronbach's
alpha for your questionnaire.
Reliability Statistics
Cronbach's
Alpha
N of Items
.741
11
13
Reliability
Item-Total Statistics
Scale
Scale Mean if Variance if
Corrected
Cronbach's
Item-Total
Alpha if Item
Item Deleted Item Deleted Correlation
Deleted
ASI1
42.76
67.173
.598
.690
ASI3
42.77
77.166
.281
.736
ASI6
43.23
73.467
.371
.725
ASI8
43.69
72.984
.434
.716
ASI9
41.81
80.566
.255
.737
ASI12
42.30
69.993
.514
.704
ASI13
42.49
74.829
.370
.725
ASI17
43.28
73.740
.385
.723
ASI19
43.93
74.036
.411
.719
ASI20
43.05
77.805
.257
.739
ASI22
43.39
74.680
.362
.726
14
Reliability
Item-Total Statistics
Scale
Scale Mean if Variance if
Corrected
Cronbach's
Item-Total
Alpha if Item
Item Deleted Item Deleted Correlation
Deleted
ASI1
42.76
67.173
.598
.690
ASI3
42.77
77.166
.281
.736
ASI6
43.23
73.467
.371
.725
ASI8
43.69
72.984
.434
.716
ASI9
41.81
80.566
.255
.737
ASI12
42.30
69.993
.514
.704
ASI13
42.49
74.829
.370
.725
ASI17
43.28
73.740
.385
.723
ASI19
43.93
74.036
.411
.719
ASI20
43.05
77.805
.257
.739
ASI22
43.39
74.680
.362
.726
The first two
columns (Scale
Mean if Item
Deleted and
Scale Variance if
Item Deleted) of
the next table
generally aren't
all that useful.
15
Reliability
Item-Total Statistics
Scale
Scale Mean if Variance if
Corrected
Cronbach's
Item-Total
Alpha if Item
Item Deleted Item Deleted Correlation
Deleted
ASI1
42.76
67.173
.598
.690
ASI3
42.77
77.166
.281
.736
ASI6
43.23
73.467
.371
.725
ASI8
43.69
72.984
.434
.716
ASI9
41.81
80.566
.255
.737
ASI12
42.30
69.993
.514
.704
ASI13
42.49
74.829
.370
.725
ASI17
43.28
73.740
.385
.723
ASI19
43.93
74.036
.411
.719
ASI20
43.05
77.805
.257
.739
ASI22
43.39
74.680
.362
.726
The third column
is the correlation
between a
particular item
and the sum of
the rest of the
items. This tells
you how well a
particular item
“goes with” the
rest of the
items.
16
Reliability
Item-Total Statistics
Scale
Scale Mean if Variance if
Corrected
Cronbach's
Item-Total
Alpha if Item
Item Deleted Item Deleted Correlation
Deleted
ASI1
42.76
67.173
.598
.690
ASI3
42.77
77.166
.281
.736
ASI6
43.23
73.467
.371
.725
ASI8
43.69
72.984
.434
.716
ASI9
41.81
80.566
.255
.737
ASI12
42.30
69.993
.514
.704
ASI13
42.49
74.829
.370
.725
ASI17
43.28
73.740
.385
.723
ASI19
43.93
74.036
.411
.719
ASI20
43.05
77.805
.257
.739
ASI22
43.39
74.680
.362
.726
In the output
above, the best
item appears to
be ASI1, with an
item total
correlation of
r = .598. The
item with the
lowest item total
correlation is
ASI9 (r = .255).
17
Reliability
Item-Total Statistics
Scale
Scale Mean if Variance if
Corrected
Cronbach's
Item-Total
Alpha if Item
Item Deleted Item Deleted Correlation
Deleted
ASI1
42.76
67.173
.598
.690
ASI3
42.77
77.166
.281
.736
ASI6
43.23
73.467
.371
.725
ASI8
43.69
72.984
.434
.716
ASI9
41.81
80.566
.255
.737
ASI12
42.30
69.993
.514
.704
ASI13
42.49
74.829
.370
.725
ASI17
43.28
73.740
.385
.723
ASI19
43.93
74.036
.411
.719
ASI20
43.05
77.805
.257
.739
ASI22
43.39
74.680
.362
.726
If this number is
close to zero,
then you should
consider
removing the
item from your
scale because it
is not measuring
the same thing
as the rest of
the items.
18
Alpha if Item Deleted
Item-Total Statistics
Scale
Scale Mean if Variance if
Corrected
Cronbach's
Item-Total
Alpha if Item
Item Deleted Item Deleted Correlation
Deleted
ASI1
42.76
67.173
.598
.690
ASI3
42.77
77.166
.281
.736
ASI6
43.23
73.467
.371
.725
ASI8
43.69
72.984
.434
.716
ASI9
41.81
80.566
.255
.737
ASI12
42.30
69.993
.514
.704
ASI13
42.49
74.829
.370
.725
ASI17
43.28
73.740
.385
.723
ASI19
43.93
74.036
.411
.719
ASI20
43.05
77.805
.257
.739
ASI22
43.39
74.680
.362
.726
Now look in the
last column.
“Alpha if item
deleted.” This is
a very important
column. It
estimates what
the Cronbach's
alpha would be if
you got rid of a
particular item.
19
Alpha if Item Deleted
Item-Total Statistics
Scale
Scale Mean if Variance if
Corrected
Cronbach's
Item-Total
Alpha if Item
Item Deleted Item Deleted Correlation
Deleted
ASI1
42.76
67.173
.598
.690
ASI3
42.77
77.166
.281
.736
ASI6
43.23
73.467
.371
.725
ASI8
43.69
72.984
.434
.716
ASI9
41.81
80.566
.255
.737
ASI12
42.30
69.993
.514
.704
ASI13
42.49
74.829
.370
.725
ASI17
43.28
73.740
.385
.723
ASI19
43.93
74.036
.411
.719
ASI20
43.05
77.805
.257
.739
ASI22
43.39
74.680
.362
.726
For example, at
the very top of
this column, the
number is .690.
That means that
the Cronbach's
alpha of this
scale would drop
from .741 to
.690 if you got
rid of that item.
20
Alpha if Item Deleted
Item-Total Statistics
Scale
Scale Mean if Variance if
Corrected
Cronbach's
Item-Total
Alpha if Item
Item Deleted Item Deleted Correlation
Deleted
ASI1
42.76
67.173
.598
.690
ASI3
42.77
77.166
.281
.736
ASI6
43.23
73.467
.371
.725
ASI8
43.69
72.984
.434
.716
ASI9
41.81
80.566
.255
.737
ASI12
42.30
69.993
.514
.704
ASI13
42.49
74.829
.370
.725
ASI17
43.28
73.740
.385
.723
ASI19
43.93
74.036
.411
.719
ASI20
43.05
77.805
.257
.739
ASI22
43.39
74.680
.362
.726
Because a higher
alpha indicates
more reliability,
it would be a bad
idea to get rid of
the first item.
21
Alpha if Item Deleted
Item-Total Statistics
Scale
Scale Mean if Variance if
Corrected
Cronbach's
Item-Total
Alpha if Item
Item Deleted Item Deleted Correlation
Deleted
ASI1
42.76
67.173
.598
.690
ASI3
42.77
77.166
.281
.736
ASI6
43.23
73.467
.371
.725
ASI8
43.69
72.984
.434
.716
ASI9
41.81
80.566
.255
.737
ASI12
42.30
69.993
.514
.704
ASI13
42.49
74.829
.370
.725
ASI17
43.28
73.740
.385
.723
ASI19
43.93
74.036
.411
.719
ASI20
43.05
77.805
.257
.739
ASI22
43.39
74.680
.362
.726
In fact, if you look
down the "Alpha if
item deleted"
column, you will see
that none of the
values is greater
than the current
alpha of the whole
scale: .741. This
means that you
don't need to drop
any items.
22
Improving Reliability
If you are using an accepted scale obtained from a
published source, you do not need to worry about
improving reliability. You should use the whole
scale, even if it has problems, because if you start
changing the scale you will be unable to compare
your results to the results of others who have
used the scale. You only want to improve the
reliability of a scale if it is a scale you are
developing.
23
Improving Reliability
If one of the “Alpha if item deleted” values is
greater than the overall alpha, you should re run
Analyze > Scale > Reliability Analysis after moving
the offending item from the “Items” box back
over to the unused items box. Repeat this process
until there are no values in the “Alpha if item
deleted” column that are greater than the alpha
for the overall scale.
24
Computing a mean score for
a questionnaire
The goal of this whole procedure is to produce a
single score for your questionnaire. Once you've
used reliability analysis to identify the items that
will produce the most reliable measure, you can
use those items to create an average score for
your questionnaire, as described below.
25
Computing a mean score for
a questionnaire
To compute a mean score, select Transform >
Compute. In the Target Variable box, type in the
name of your scale, ASI.
In the Numeric Expression box, type the word
MEAN, followed by “(” and then a list of the
variables you want to average together, separated
by commas. Make sure you only put in the
variables that you decided were the best for the
scale. At the end, close the expression with a “)”.
Press OK to compute the new variable.
26
Computing a mean score for
a questionnaire
27
Computing a mean score for
a questionnaire
Select Graphs > Legacy Dialogs > Histogram and
put your new ASI variable into the variable box.
Press OK. You should get output like this.
28
Computing a mean score for
a questionnaire
Select Graphs >
Legacy Dialogs >
Histogram and
put your new
ASI variable into
the variable box.
Press OK. You
should get
output like this.
29
Computing a mean score for
a questionnaire
A histogram is a plot of how often possible values
occurred. It's one way to see if there is anything
really strange in your data - any extreme values, or all
the scores piled up on one side. If you've done
everything correctly, you should find that the values
on the right side of the image above correspond to
the values in your output, standard deviation of .851,
mean of 4.30, and N of 74.
30