Could anyone, please, suggest a way to find out how to calculate Difficulty Index of a research instrument (i.e., test) using SPSS?
Hemn Adil Karim Can you elaborate on what you mean by "Difficulty Index"? In general, the difficulty of a test would be reflected in the average (mean) score. (The lower the mean of the test scores, the more difficult the test.)
Dear Hemn Adil Karim,
If you are talking about IRT analysis the answer is no. But in R is is possible and free.
Here an article that describes how to do it in R:
Rizopoulos, D. (2006). ltm: An R package for latent variable modeling and item response theory analyses. Journal of Statistical Software, 17(5), 1–25. https://doi.org/10.18637/jss.v017.i05
I hope I could help you.
Christian Geiser, thanks for the informative and precise answer. I have designed a test comprising 35 items. To check the reliability of the test items and the Difficulty Index (i.e., how difficult the test is for the respondents), I have used KR20 for the reliability using SPSS; my point here is that, how can I know the difficulty of the test items using SPSS. What I have got from your answer is that, I have to rely on the mean of test scores gained from the respondents. Could you please, give me an example for Low and High Mean?
Amalia Raquel Pérez Nebra, thank you so much for your impressive recommendation. I will check it.
Hemn Adil Karim
Let's say each of your 35 items is measured on a 5-point scale ranging from "completely disagree" (scored as 1) to "completely agree" (scored as 5). Further assume that you compute your test summary score as the mean across the 35 item scores for each participant. A summary (mean) value close to 1 would indicate that a respondent on average finds it rather difficult to agree with the test items, whereas a mean near 5 would indicate that they find it rather easy. You could also compute the mean of the summary score across participants ("mean of means") to see whether overall the test is rather "easy" or rather "difficult."
For a sum score (summing rather than averaging the item scores), this is more difficult to see (more relative) unless you compare means across different groups (different populations), different subscales (subtests, test halves etc.), or different time points.
Christian Geiser many thanks with appreciation. Your clarification, of course, brightens the ways I want to take.
To add to Amalia Raquel Pérez Nebra 's answer, I agree that it is hassling to do even simple IRT models to measure item difficulty, and I usually recommend mirt over ltm in R because it is faster, does more models, etc. (though the default parameterization is different, so careful going back and forth between the two!), but if there is a reason that you are required to use SPSS or can't afford R ;o), then the Chapter Creating Latent Variables: Computing Supplementary Material ...
goes through a couple of approaches (and there are others) on pp. 73--75.
Hemn Adil Karim , I think it will be useful if you define difficulty. In the psychometrics literature in education difficulty often refers to the probability of correctly answering a question (or as Christian Geiser says, for a test it could be the number of fails). But of course difficulty can mean many things. If this were a survey and you mean difficulty some respondents have understanding an item, obviously this requires something different (e.g., response times, think alouds).
Daniel Wright Thanks a lot for the informative answer. The test is a comprehension test in which students have to take the test as an experiment. That is, it isn't a survey. So, I have decided to use Excel at first, then I asked myself whether there is a better way in SPSS to find out the Difficulty Index and Discrimination Index, or not?
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