# Chi-square independence in political sciences

I've been assigned to do a cross-class project between political science and math about the behavior of voters in a democratic state. More specifically, I'm focusing on a party from a national election in 2007, where I have made a table consisting of two rows – mandates and news about that party – and one column for each election day:

    Day        1   2   3   4   5   6...
Mandates  11   8  11  13  12  12
News      30  46  12  33  48  42


I would like to check whether the appearence of news in the media about this party have affected the number of mandates given to the party in the daily opinion surveys. Would it be legitimate to perform a chi-square-independence test on this data or would I not be able to conclude anything? Why/why not?

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To get a little more advanced, I was thinking if it is possible to evaluate if the news have affected some days particularly than others with the chi-square-independence test (yes it has to be this method). I would then calculate the change in the mandates for each day which would make my table look like this:

    Day        1   2   3   4   5   6...
Mandates  11  -3   3   2  -1   0
News      30  46  12  33  48  42


Then for each column, I would manually calculate the expected result. Example for column "Day 2":

The observed results are that there has been 46 news and the party has lost three mandates. We assume that the news haven't affected the number of mandates and thus they would stay equal and the change will be zero:

Observed data:

    Day        2
Mandates  -3
News      46


Expected data:

    Day        2
Mandates   0
News      46


If I do so for every column, would I then be able to evaluate that the news has affected the number of mandates one day, but not another, mathematically? I would really like to test for this, because then I would be able to pin point some days to focus on from which I can extract articles and look upon the positiv/negative rhetorics made by the party.

Sorry for the bad tables, but I was not able to post images. Thanks in advance.

/Brinck10

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In both cases I think a good starting point is thinking through explicitly what your null hypothesis from the Chi square test is, and how you would describe and interpret that null hypothesis. Does it make sense? –  Peter Ellis May 28 '12 at 6:14
In your second question you have some problems you don't in the first. If your expected value for a cell is zero, your Chi square statistic will not be defined (think through why). –  Peter Ellis May 28 '12 at 6:16
Hi Peter, thanks for your answer. Well, in both cases my null hypothesis would be something like: "The news don't influence the number of mandates at all." Regarding your answer, would you please elaborate on the first part which ignores the time-series? Secondly, I interpreted the assignment incorrectly: I'm able to do a plain chi-square test, it is not limited to an independence test. –  Frederik Brinck Jensen May 28 '12 at 9:03
I think the null hypothesis you would actually test if you followed your original question is "Is 'day' related to the relative mix of news and mandate?" Which isn't the null hypothesis you want to test... hence I suggest another approach. –  Peter Ellis May 28 '12 at 21:22

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Here's a suggestion that still meets the (odd) limitation that you can only use a Chi square test. Treat "day" as your unit of analysis, and set up a cross-tab where each cell is the number of days that that fits into a bin of mandate-news combinations eg 0:10 News, +1:2 Mandates. Then see what relationship there is between those two variables.

This ignores the time-series aspect of your data, but if you have been restricted to a Chi square test might be a better approach.

It won't meet your need of identifying which are the interesting days however - I think you'd need something more sophisticated for that. So this would only be a starting point for you...

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So you mean something like this (Rows and columns are separated by comma)? Columns: -3M, -2M, -1M, 0M, +1M, +2M, +3M Rows: 00:10 News, 11:20 News, 21:30 News, 31:40 News And then do a chi-square test on these data? –  Frederik Brinck Jensen May 28 '12 at 11:08
Yes, that's it. The reason I say it ignores the time series is that it doesn't pay regard to the sequence the days are in, just counts them and puts them in cells. But it does allow a meaningful test of the independence of mandate from news. This is what you want to test, not whether "day" is independent from the mandate-news combination. –  Peter Ellis May 28 '12 at 21:21
Perfect. But how would I calculate the end points? For instance, it wouldn't make sense to say that the number of mandates has increased with 11 on the first day (though that would be correct). –  Frederik Brinck Jensen May 29 '12 at 7:06
– And should I include a column saying "No change"? –  Frederik Brinck Jensen May 29 '12 at 7:29
Re the end points. Normally if you are using "differenced" data like this you need to miss out on one point - so you'd start with the difference from day 1 to 2, if you are using that approach. And yes, a "no change" column would be a good idea. As this is a chi square test you can have any categories you want. If you find the answer useful you can click on the upwards thing (and/or the tick next to it, if you want to accept it as the answer), and the question will be removed from the list of "questions with no upvoted answers". –  Peter Ellis Jun 5 '12 at 21:08