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I am assesing the reliability and validity of an 16-item multuiple choice test supposed to test language skills. Cronbach's apha is "questionable" with .65. I am having troubles interpreting the results. The inter-item correlation is low, while the total-item correlation performs well. What does this mean ?

The inter-item correlation range from 0.6 - 0.16 with an average of .10. I interpreted these results as a low degree of homogeneity, causing the Cronbach's alpha to decrease. This means that the items are not appropriate for measuring a construct unidimensionally.

Further, I also calculated the total-item correlation. These range from .25-.55 with an average of 0.40. This is interpreted as good performance. It assese the performance of questions on the tests, therefore the questions are good in discriminating bad students from good ones.

How can these results be interpreted together?

What can be done to improve the test?

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  • $\begingroup$ Item-total correlation can be one of measures of validity of an item if the total (the sum) is valid measure of a trait. Are you sure it is so in your case? $\endgroup$
    – ttnphns
    Apr 29, 2019 at 13:04
  • $\begingroup$ @ttnphns that is what i am trying to figure out. How can i check if the total sum (test result) is a valid measure of the language skill? Is there a specific test or procedure? $\endgroup$
    – user1607
    Apr 29, 2019 at 15:20
  • $\begingroup$ Correlate with an objective external criterion of language skills? $\endgroup$
    – ttnphns
    Apr 29, 2019 at 16:59
  • $\begingroup$ could you elaborate on objective exterenal criterion? maybe an example? $\endgroup$
    – user1607
    Apr 29, 2019 at 17:03

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Reliability (alpha) is a function of two things: the correlations amongst items, and the length of the test.

There's no issue of interpreting the results together. They are consistent (assuming no error).

You can improve the test by pruning out the items that have low item-total correlation, of by adding items.

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  • $\begingroup$ thanks. However, I am not sure how to interpret the low inter-item correlation adn food item-total correlations. What do these results mean? Does it mean my test is reliable (good item-total correlations) but not valid (poor inter-item correlations)? $\endgroup$
    – user1607
    May 13, 2019 at 18:52
  • $\begingroup$ Validity is used in many ways - most often it means how well your test predicts something, e.g. researchgate.net/publication/8234397_The_Concept_of_Validity. I think your test is OK. $\endgroup$ May 13, 2019 at 20:31

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