Calculating the C ²

C ² = S (d²/e)

The chi-square is the sum of (S ) the deviation of the observed from the expected (squared), divided by the expected value. Just follow
this basic example and "Plug-n-Chug."

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                                 Class 1         Class 2            Class 3

Observed (o)          34                  24                      42

Expected (e)           33.3               33.3                  33.3

Deviation (d=o-e)   0.7                -9.3                    8.7

Deviation ² (d²)      0.49             86.49                 75.69

D²/e                         0.015            2.6                     2.27

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C ² =                       0.015     +      2.6         +         2.27

C ² = 4.89

Using the C ² Value

So, now you have a C ² value, but what do you do with it? Remember that you are attempting to use statistics to have an unbiased
mechanism by which you can tell whether the data support or reject your hypothesis or hypotheses.

Thankfully this is a snap. You merely count the number of classes (or categories) and subtract one. In the example above, the
d.f. would be 2.

D.f. = # of classes - 1

So, for our example, this is where we stand:

C ² = 4.89, d.f. = 2

You take this information and look at table of critical values and see if this chi-square value equals or exceeds the critical value for these degrees of freedom.

If the critical value is exceeded, then the observed and expected distributions are statistically significantly different from each other at an alpha level of 0.05.

However, the critical value turns out to be 6.0; therefore, the deviations we see between our Expected and Observed data appear to be due merely to chance.

© Cody Arenz and Garry Duncan and Nebraska Wesleyan University