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What Is the Formula for the Chi-Square Statistic and How Do You Use It?

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How to Use the Chi-Square Statistic Formula
What Is the Formula for the Chi-Square Statistic and How Do You Use It?
C.K.Taylor

To see how to compute a chi-square statistic using the formula, suppose that we have the following data from an experiment:

  • Expected: 25 Observed: 23
  • Expected: 15 Observed: 20
  • Expected: 4 Observed: 3
  • Expected: 24 Observed: 24
  • Expected: 13 Observed: 10

Next, compute the differences for each of these. Because we will end up squaring these numbers, you may subtract them in any order. Staying consistent with our formula, we will subtract the observed counts from the expected ones:

  • 25 – 23 = 2
  • 15 – 20 =-5
  • 4 – 3 = 1
  • 24 – 24 = 0
  • 13 – 10 = 3

Now square all of these differences: and divide by the corresponding expected value:

  • 22/25 = 0 .16
  • (-5)2/15 = 1.6667
  • 12/4 = 0.25
  • 02/24 = 0
  • 32 /13 = 0.5625

Finish by adding the above numbers together: 0.16 + 1.6667 + 0.25 + 0 + 0.5625 = 2.693

Further work involving hypothesis testing would need to be done to determine what significance there is with this value of χ2.

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