# How to analyse data collected by multiple choice questions? Is it possible to apply any statistical test ? Can we Use SPSS/PASW for it?

I could not find any specific statistical tool to analyse MCQs, does anybody know how to?

Question

I could not find any specific statistical tool to analyse MCQs, does anybody know how to?

- Yes you can. I think the best tool is weighted mean and weighted variance. You can look at the weighted ( mean, variance) in wiki to find formulae for them. The last question, you can use SPSS and Excel to analyse them
- In such type of research, the first step is to find out reliability of the respondents. I suggest to use psychometric test of true score. It will help you to minmise respondent-bias. Latter, you may use SPSS or Excel for your analysis.
- Nearly any sastatistical package can analyze multiple choice data. It is certainly possible to apply a statistical test. However, it is essential to first formulate null and alternative hypotheses before attempting to apply a statistical test. The nature of the hypotheses and so the nature of the statistical test depends greatly on the level of measurement (e.g., continuous, ordinal, nominal or categorical, binary) and whether the intent is to compare two groups or to assess relationships within one group. Multiple choice variables will not be continous so there is no reason to consider them here. Suppose the multiple choice question is nominal. Then the null hypothesis is that the (relative) frequency distributions in the two groups are equal. A chi-square test with degrees-of-freedom equal to the number of categories minus 1 is used to test this hypothsis. If chi-square is large enough so that p<0.05 then the null hypothesis is rejected in favor of the alternative hypothesis that that the frequency distributions are unequal. Another example is if the responses are ordinal. In that case, a Mann-Whitney U test or a Wilcoxon rank sum test may be used to test the hypothesis. This test would have more 'statistical power' than the usual chi-square test because the research hypothesis is sharper or narrower. The null is that the distributions are equal. The alternative is that the distribution of scores is shifted to the left or to the right for one population relative to the other. If the response is dichotomous, then the null and alternative hypopotheses can be stated in terms of proportions. The null hypothesis is that the proportion of 'yes' responses is equal between groups. The alternative hypothesis is that these proportions are unequal. A chi-square test with one degree-of-freedom or a (large sample normal) z-test are typically used to test these hypotheses unless the sample sizes are very small. In such cases, Fisher's exact test is often used. There are other types of responses, for example, 'check all that apply'. There are potentially a number of ways to handle such data; but probably most of these ways involve turning the situation into one or more response variable as described above.
- @Al-Saadnoy thanks, weighted averages have its own limitations. Sometimes even we cannot assign weights to the points.

@Khan :- no doubt reliability is base of any research

@Gerg : thanks for the suggestion. actually I have to analyse the data like 'check all that apply' e.g If I will ask a question to the manufacturer- Facilities given by you for your workers. with an option

Medical Benefits

Rest rooms

Sufficient break for lunch & Tea

Paid holidays as per norms

Paid weekly leaves

Loan and advance

Adequate wages as per norms

Clean lunch room

Mediclaim/ Insurance facility

Transportation facility

Uniform/ Safety Shoes/ Helmets/ Gloves etc...

How exactly the test will be, I have searched in PASW help, I wont find anything related to this - I think that you can use the model of random vector to describe your test results. The random vector should consist of 11 descete random variables, one random variable for each option in the test. So random variables will have rather easy distribution - their values will be 0 or 1 depending on the answer, 1- for marking this option, 0 for not marking.

This way you'll be able to estimate the correlation between these random variables, to estimate the probability of becoming 1 or 0 for each variable in vector etc. - I agree with Petr that multiple response (check all that apply) questions, like your example, are essentially the same as a corresponding collection of yes/no questions from an analysis point of view. The one area where you might need to be careful is in the treatment of no response (no item checked). This would likely correspond to all responses missing not to all responses no.
- @ Thanks Petr I will try to implement the random vector model

@Thanks David - yes multiple response... how the spreadsheet designed? is it yes or no for each one or tall var in one cell.

it yes or no for each response you can follow the following on spss

From the menus choose:

Analyze

Multiple Response

Define Sets...

NB: The new variable is a virtual variable. it means that will be lost after closing the program

then after you create your new set either you can go through frequency or cross tab

good luck - @Thanks Mohamed
- Simple, try Rasch Analysis. I would recommend RUMM by David Andrich. Rasch analysis uses logits so that you can then after this analysis run more tradational tests using SPSS. See my paper on Rasch analysis on categorial variables, similar to multiple choice question test analysis for which Rasch was developed for. The reference is:

Cornish-Ward, Steven and Soutar, Geoff (1997) "Consumer Acquisition patterns for Durable Goods and Financial Assets: A Rasch Analysis" Applied Economics, vol. 29(7), pp 903-911 ISBN: 0003-6846 (ISI ranked journal , impact factor=.845, Tier A, Economics), Cited 43 times. - @PAN. I will suggest you to download and install a very beautiful, public domain software specially designed for Survey data collection, organisation, analysis and graphical plotting of the same. A person with your background should have such a programme. Pl send your e-mail and I will send you the link as well as my lecture on this software (PPT file) to give you an idea about the usage of the same.
- Thanks Prof. Ravi.
- Multiple Correspondence Analysis (related to Principal Components) provides a nice and comprehensive exploratory approach to this kind of data.
- I agree with Juan Modroño, in addition is a highly interesting and useful procedure available in most commercial and open source statistical software (R statistical system)

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