Microsoft Office Tutorials and References

In Depth Information

**Comparing Results to an Estimate**

Comparing Results to an Estimate

The Chi Square test is a statistical method for determining whether observed

results are within an acceptable range compared with what the results were

expected to be. In other words, the Chi Square is a test of how well a before

and after compare. Did the observed results come close enough to the

expected results that we can safely assume there is no real difference? Or

were the observed and expected results far enough apart that we must

conclude there is a real difference?

A good example is flipping a coin 100 times. The expected outcome is 50

times heads, 50 times tails. Figure 10-2 shows how a Chi Square test statistic

is calculated in a worksheet without using any functions.

Figure 10-2:

Calculating

a Chi

Square.

Cells B5:B6 are the expected results — that heads and tails will each show

up 50 times. Cells C5:C6 show the observed results. Heads appeared 44

times, and tails appeared 56 times. With this information, here is how the Chi

Square test statistic is calculated:

1.Foreachexpectedandobservedpair,calculatethedifferenceas

(Expected
–
Observed
).

2.Calculatethesquareofeachdifferenceas
(Expected
–
Observed
)
2
.

3.Dividethesquaresfromthepreviousstepbytheirrespective

expectedvalues.

4. Sum the results of the previous step.

Of course, a comprehensive equation can be used for the first three steps,

such as =(expected - observed)^2/expected.

The result in this example is 1.44. This number — the Chi Square value — is

then looked up in a table of Chi Square distribution values. This table is a