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I have a survey which contains 13 variables in total. For each variable I asked 3 similar questions in order to test the internal consistency.

Now I performed 13 Cronbach's alpha tests, one for each variable, to see whether people filled in the 3 questions per variable on a consistent basis. The results are presented below:

Variables ______________ Cronbachs Alpha ______ Cronbachs alpha if item deleted
Accessibility__________________0.416_______________Not possible to get a higher CA
Accuracy
____________________0.680_______________Not possible to get a higher CA
Completeness
________________0.681_______________Not possible to get a higher CA
Consistency
__________________0.604_________________________0.718
Information Quality
_____________0.832_______________Not possible to get a higher CA
Quantity
_____________________0.566_______________Not possible to get a higher CA
Relevance
___________________0.327_________________________0.490
Reliability
____________________0.617_________________________0.689
Satisfaction
__________________0.747_________________________0.752
Timeliness
___________________0.398_________________________0.487
Understandability
______________0.569_______________Not possible to get a higher CA
Use
_________________________0.530________________________0.556
Usefulness
___________________0.655________________________0.721

My questions are the following:
If possible, do I need to delete an item in order to get a higher CA? Or should I only do this when the increase in CA is relatively high?
Can I use all the variable displayed above or are some of them worthless because of the low CA score?

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  • $\begingroup$ How did you get from 39 questions to 13 variables? $\endgroup$ – Peter Flom Nov 8 '12 at 10:34
  • $\begingroup$ I used averages of the three questions relating to one variable. But before I merged the 39 questions into these 13 variables I performed the Chronbach Alpha test with the results displayed above. $\endgroup$ – Laurens Nov 8 '12 at 10:46
  • $\begingroup$ So, these are results from 13 different runs of Cronbach's alpha? $\endgroup$ – Peter Flom Nov 8 '12 at 10:53
  • $\begingroup$ Yes that is correct. $\endgroup$ – Laurens Nov 8 '12 at 10:54
  • $\begingroup$ OK, then you should edit your question to make it clearer, but I will post an answer. $\endgroup$ – Peter Flom Nov 8 '12 at 11:04
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What is your real goal/question to be answered? If your only goal is to get high values of CA then you can just generate random noise and replicate it a couple of times, nice high alpha value, but otherwise useless.

In my experiance Cronback's alpha is usually not the end goal and sometimes more of a distraction than a help. It could very well be that the most interesting part of the whole dataset is a variable that acts to pull down an alpha value (why is it not measuring what you thought it would?) and deleting that variable to get a high alpha would be the opposite of the best strategy.

So focus first on what you are trying to accomplish with this study (if high CA is really what is important then you need to go back and redesign the survey and possibly other data collection processes and collect new data), but it could also be that the CA values are only an interesting footnote to much more interesting results.

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  • $\begingroup$ To build a little on this perceptive answer: if you are planning to use these 13 variables as predictors of some outcome, then you may find that within each of a given set of 3 items, there is a tradeoff between their internal consistency (a form of reliability) and the extent of the domains that they cover (a form of validity). $\endgroup$ – rolando2 Dec 9 '12 at 13:52
  • $\begingroup$ More on this topic and related ones is at stats.stackexchange.com/questions/21119/… . $\endgroup$ – rolando2 Dec 9 '12 at 13:58
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Per the comments, these are 13 results from 13 runs of Cronbach's alpha on sets of 3 questions each.

The original question is whether to delete items (from sets of 3) if alpha can be improved by much. However, I think that, considering that these are sets of 3 items that are supposed to be on the same variable, none of these alphas are great and only a few are really acceptable. I would say those with alpha under .7 need to be reworked in more ways than just deleting a question. One way to get a better sense of what's going on with the 39 items might be a factor analysis. Another, simpler, method would be to find the differences between the 3 sets of questions in each variable and see which differences are large. Such low alphas where there ought to be high alphas could be some fundamental problem like data entry or something.

However, on the original question: I would say delete items only if they raise alpha by a reasonable amount. Otherwise, you are potentially taking advantage of qualities of this particular sample.

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