In other words, it tests whether discrepancies between the observed frequencies (Oi) and the expected frequencies (Ei) are significant, or whether they might reasonably result from chance. The equation is:

χ 2 = ∑

(Oi

− Ei

)

n

 

 

2

i=1

 

Ei

 

If there is a close agreement between the observed and expected frequencies, χ2 will be small. If the agreement is poor, χ2 will be large.

Solver Equations for χ2 Calculations:

If the expected value is a constant:

name1name1



If the expected values vary:

name1name1

name2name2

(To enter the Σ character, press .)

CHI2 = the final χ2 value for your data.

name1 = the name of the SUM list that contains the observed values. name2 = the name of the SUM list that contains the expected values. EXP = the expected value when it is a constant.

When you create and name the SUM list(s), make sure the name(s) match name1 (and name2, if applicable) in the Solver equation.

To solve the equation, press  once or twice (until you see the message ).

The following example assumes that you have entered the CHI equation into the Solver, using OBS for name1. For instructions on entering Solver equations, see “Solving Your Own Equations,” on page 30.

Example: Expected Throws of a Die. To determine whether a suspect die is biased, you toss it 120 times and observe the following results. (The expected frequency is the same for each number, 120 ⎟ 6, or 20.)

220 14: Additional Examples

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