# Statistical Test for multiple choice questions

#### Prats

##### New Member
I Iaunched a survey recently where I have the following types of questions -
1) A multiple choice question (where users can mark more than one correct answer), let's call it variable a.
2) A single choice answer type question (radio button type), let's call it categorical variable b.
3) A continuous variable, let's call it variable c.

What is the best statistical test or method to analyze if a has an effect on b, and if a has an effect on c? I am particularly looking to understand how to deal with the multiple choice answer question.

#### Karabiner

##### TS Contributor
Could you please describe what "variables a b c" actually stand for?
And what the particular research questions are, with respect to these
variables? And how large your samle size is?

With kind regards

Karabiner

#### Prats

##### New Member
Sure @Karabiner! Thank you for your response.
1) The question for variable a (though I am not sure if I can call it a variable), is - "What drawing tool do you use?", with multiple choices - like tool A, tool B, tool C, tool D. Survey respondents can select multiple tools.
2) Categorical variable b is job category of the respondent.
3) Variable c measures perceived-difficulty of drawing.

My research question is
a) Is there is a relation between job category and type of drawing tool users use?
b) Does the type of drawing tool have an effect on perceived-difficulty of drawing?

Had it been a multiple choice question with a single correct answer, I would have used a chi square test for my research question a) and used Anova test or multiple regression for question b). However, in this case since there could be different combinations of choices for the multiple choice question, I can't seem to figure out how I should treat this data.

I am targeting a sample size of 200.

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#### Karabiner

##### TS Contributor
One could crosstabulate Jobs * Tool Combinations (something like: A-only, A&B, A&C, C only ... etc). I don't know how many tools and how many jobs there are, or whether some or all combinations of tools are important. If there are many different jobs and/or many different combinations of tools, then your Job*Tool table will soon become too large and some cell frequencies will become too low.

One alternative approach could be a) to count number of tools used by each subject and compare this variable between Jobs (Kruskal-Wallis H-test or oneway analysis of variance [ANOVA]), and in addition b) perform tool-wise crosstabulations (Jobs * tool A used yes/no, Jobs * tool B used yes/no ...etc.), with Chi² test. But as mentioned before, I do not know what is important for you to know in particular, or whether there might be only a handful of combinations. And there could be issues with multiple testing.

The Tools * Difficulty Score problem could be solved by using H test, or oneway ANOVA (if the score is interval scaled ), with "tool combination" as grouping variable, and/or correlation (Spearman or Pearson) between number of tools and score, and/or a series of tool-wise comparisons (grouping variables: Tool A used yes versus no,; Tool B used yes versus no ...), using U-test (if score is ordinal) or t-test (if score is interval).

With kind regards

Karabiner

#### Prats

##### New Member
Thank you so much. I was looking for this answer - converting the multiple choice question (with more than one correct answer) to binary variables (Tool A used yes versus no, Tool B used yes versus no), and then applying the tests you mentioned.