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I am trying to understand the statistical test of the chi-square in Excel. I already made the test but I still don't know how to compute the χ² value and what it means, how to compute the degrees of freedom and how to write a propper APA approved result section. Can anyone help me and explain this in a simple way?

I have a population of n=76. 'Left' = 25 and 'Right' = 51. The hypothesis is you would expect a normal distribution ('Left' =38 and 'Right' = 38). So the question is 'is this distribution a coincidence?' The p < .029. By seeing this outcome I thought there is that is no coincidence that there isn't a normal distribution and it must be due to a variable.

Is it true in this case the degress of freedom is just n-1?

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up vote 2 down vote accepted

This is really more of a statistical question (except perhaps the bit about APA style). As such it probably belongs on stats.stackexchange.com .

A binary variable does not have a "normal distribution". A normal distribution is bell shaped and is relevant to continuous data.

Your null hypothesis is that the population proportions for left and right handers are equal. Thus, if your chi-square value is sufficiently large, then you might reject the null hypothesis and conclude that the population proportions are unequal.

If $k$ is the number of categories (you have two categories), then degrees of freedom for the one sample chi-square test is $k-1$ (i.e., $2-1 = 1$).

To calculate chi-square check out the example here.

The following formula in Excel should give you a p-value. For example if your chi-square value was 22, and your degrees of freedom was 3:

 =1-CHISQ.DIST(22, 3,TRUE)
  • the first argument is the chi-square value
  • The second argument is the degrees of freedom
  • The third argument indicates that a cumulative distribution (CDF) is desired
  • Thus by taking 1 minus the value of the CDF you get the probability of getting a chi-square value as large or larger than the observed value.

You can check your formula by looking at existing calculated tables. http://home.comcast.net/~sharov/PopEcol/tables/chisq.html

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Thank you very much Jeromy! This was very helpful! –  NinaM Mar 11 '13 at 12:32
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