Page 279 - Statistics II for Dummies

Chapter 15

Using Chi-Square Tests for

Goodness-of-Fit (Your Data,

Not Your Jeans)

In This Chapter
▶ Understanding what goodness-of-fit really means
▶ Using the Chi-square model to test for goodness-of-fit
▶ Looking at the conditions for goodness-of-fit tests

any phenomena in life may appear to be haphazard in the short term,
Mbut they actually occur according to some preconceived, preselected,
or predestined model over the long term. For example, even though you
don’t know whether it will rain tomorrow, your local meteorologist can give
you her model for the percentage of days that it rains, snows, is sunny, or
cloudy, based on the last five years. Whether or not this model is still relevant
this year is anyone’s guess, but it’s a model nonetheless. As another example,
a biologist can produce a model for predicting the number of goslings raised
by a pair of geese per year, even though you have no idea what the pair in
your backyard will do. Is his model correct? Here’s your chance to find out.

In this chapter, you build models for the proportion of outcomes that fall
into each category for a categorical variable. You then test these models by
collecting data and comparing what you observe in your data to what you
expect from the model. You do this evaluation through a goodness-of-fit test
that’s based on the Chi-square distribution. In a way, a goodness-of-fit test is
likened to a reality check of a model for categorical data.

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