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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.

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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.

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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.

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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.).

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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.

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Reverse Scoring

To get SPSS to reverse score.Transform > Compute Variable

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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).

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Reverse Scoring

9

Reliability

Now you're ready to compute the reliability of this scale, select

Analyze > Scale > Reliability Analysis

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Reliability

Move all the scored items into the 'Items' box.

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Reliability

Click on the box labelled Statistics and select Scale if item deleted (explained below).

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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.

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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

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ReliabilityItem-Total Statistics

Scale Mean if

Item Deleted

Scale

Variance if

Item Deleted

Corrected

Item-Total

Correlation

Cronbach's

Alpha if Item

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

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Reliability

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.

Item-Total Statistics

Scale Mean if

Item Deleted

Scale

Variance if

Item Deleted

Corrected

Item-Total

Correlation

Cronbach's

Alpha if Item

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

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ReliabilityThe 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.

Item-Total Statistics

Scale Mean if

Item Deleted

Scale

Variance if

Item Deleted

Corrected

Item-Total

Correlation

Cronbach's

Alpha if Item

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

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ReliabilityIn 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).

Item-Total Statistics

Scale Mean if

Item Deleted

Scale

Variance if

Item Deleted

Corrected

Item-Total

Correlation

Cronbach's

Alpha if Item

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

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ReliabilityIf 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.

Item-Total Statistics

Scale Mean if

Item Deleted

Scale

Variance if

Item Deleted

Corrected

Item-Total

Correlation

Cronbach's

Alpha if Item

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

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Alpha if Item DeletedNow 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.

Item-Total Statistics

Scale Mean if

Item Deleted

Scale

Variance if

Item Deleted

Corrected

Item-Total

Correlation

Cronbach's

Alpha if Item

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

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Alpha if Item DeletedFor 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.

Item-Total Statistics

Scale Mean if

Item Deleted

Scale

Variance if

Item Deleted

Corrected

Item-Total

Correlation

Cronbach's

Alpha if Item

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

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Alpha if Item DeletedBecause a higher alpha indicates more reliability, it would be a bad idea to get rid of the first item.

Item-Total Statistics

Scale Mean if

Item Deleted

Scale

Variance if

Item Deleted

Corrected

Item-Total

Correlation

Cronbach's

Alpha if Item

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

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Alpha if Item DeletedIn 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.

Item-Total Statistics

Scale Mean if

Item Deleted

Scale

Variance if

Item Deleted

Corrected

Item-Total

Correlation

Cronbach's

Alpha if Item

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

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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.

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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.

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Computing a mean score for a

questionnaireThe 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.

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Computing a mean score for a

questionnaireTo 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.

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Computing a mean score for a

questionnaire

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Computing a mean score for a

questionnaireSelect Graphs > Legacy Dialogs > Histogram and put your new ASI variable into the variable box. Press OK. You should get output like this.

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Computing a mean score for a

questionnaireSelect Graphs > Legacy Dialogs > Histogram and put your new ASI variable into the variable box. Press OK. You should get output like this.

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Computing a mean score for a

questionnaireA 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.