basic statistics question


Lets say I was conducting a very basic educational research study (not to be published but for interest) and I was wondering if different pupil personality types preferred different types of practical work. Each pupil has been assigned to one of four personality types (this assignment is crude and is in itself unreliable). I then ask each pupil which of 4 types of practical work they prefer. what type of statistical analysis can I perform, if any, to see if there is any significance in my answers?  

I am presuming if there was no significance then pupils from category A, for example, would pick practical types 1-4 at random giving roughly 25% in each practical type. If 75% or 90% of pupils in category A picked practical type 1, can I do any analysis to show how meaningful this is, if at all?

I only remember working with numerical data and not categorical data like this. Having a brief look around for 'assocations between categorical variables' (e.g. personality type and practical type) I have seen residual analysis suggested. I have also seen odds and odds ration suggested.

I have also seen on wikipedia that I might need a 4*4 contingency table.

If you suggest a method, please can you say whether it can be done in Excel or something else free!!

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"can I do any analysis to show how meaningful this is"
Unfortunately you will have to hope that somebody more familiar with probability than I will give more details. The fact that the personality assignment is uncertain is not too important, If it were perfectly random you would get 25% in each catagory anyway.
You want to find the probability that the actual % differs from 25% assuming random selection.
I cannot give you that calculation now
You can do statistical analysis, yes. The question would be whether or not it had relevance.

Four personality types might choose differently from four work types, or they might choose the same. All four personality types might, for example, have a 70% preference for work type #1. If there is no factor that ties a personality type to a work type, then any distribution will be related to something other than personality. Maybe 70% of the students saw the same TV show the night before, and that show had an event that closely resembled something about work type #1.

"Statistics" is easy enough. "Meaning" is where things get tricky.

It can require large populations and experiments with strongly controlled variables.

For styles of learning, I'm familiar with three fundamental ones -- visual, auditory and tactile. Most students can learn well by seeing, i.e., watching demonstrations. Of the rest, fewer learn by hearing, or listening to explanations. And of the remainder, nearly all learn by doing, actually experiencing the activity.

Much of teaching style in past decades involves lecture, which can tend to be inefficient. It can also tend to reward only that fraction that is suited to auditory learning while effectively punishing a majority.

Your thoughts about linking personality types to work types seems to step in a good direction, IMO.


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andiejeAuthor Commented:
i've looked up how to do the chi squared test on nominal variables and it seems that that test will tell me if there is dependence or independence between the variables. I am now wondering if there is any way to tell the strength of the association or which variable values are associated

andiejeAuthor Commented:
Hi Tom, thanks for your answer. i'm thinking of expanding the questions a little. I will get the following information about each pupil: age, gender, year group, ability set, and personality type. I will then be able to find out by asking which type of practical they prefer best. I was going to look if there is an association between personality type and practical preferences. But now I'm thinking why not look at that question for all variables (gender, age etc.).

However i do not have any tools to do multiple regression with categorical variables. Is it still valid to look at the relationship between each explanatory variable and each response variable independently rather than looking at them all together?
FWIW, There is a very readable book that explains how to do this stuff, although it needs some math: Applied Regression Analysis by Harry Smith and Norman R. Draper.  The 1980 edition was considered the definitive text at the time and is available on ebay for cheap.

On the internet you should look for "analysis of variance" or anova.
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