Editing Nomogram (section)

===Chi-squared test computation===
[[Image:chisquarenomo3.png|right|200px|thumb|[[Chi-squared distribution]] nomogram]]
The nomogram below can be used to perform an approximate computation of some values needed when performing a familiar statistical test, [[Pearson's chi-squared test]]. This nomogram demonstrates the use of curved scales with unevenly spaced graduations.

The relevant expression is:

<math display="block">\frac{(OBS - EXP)^2}{EXP}</math>

The scale along the top is shared among five different ranges of observed values: A, B, C, D and E. The observed value is found in one of these ranges, and the tick mark used on that scale is found immediately above it. Then the curved scale used for the expected value is selected based on the range. For example, an observed value of 9 would use the tick mark above the 9 in range A, and curved scale A would be used for the expected value. An observed value of 81 would use the tick mark above 81 in range E, and curved scale E would be used for the expected value. This allows five different nomograms to be incorporated into a single diagram.

In this manner, the blue line demonstrates the computation of:

{{in5}} (9 &minus; 5)<sup>2</sup> / 5 = 3.2

and the red line demonstrates the computation of:

{{in5}} (81 &minus; 70)<sup>2</sup> / 70 = 1.7

In performing the test, [[Yates's correction for continuity]] is often applied, and simply involves subtracting 0.5 from the observed values. A nomogram for performing the test with Yates's correction could be constructed simply by shifting each "observed" scale half a unit to the left, so that the 1.0, 2.0, 3.0, ... graduations are placed where the values 0.5, 1.5, 2.5, ... appear on the present chart.
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