**The Chi-Square Test**

[Table of Critical
Values]

** **
In combination with discussion of **fundamentals**,
note in the above especially the concepts of **Model**,
**Categorical (Count) Data**, **Degrees of
Freedom**, & **Significance Level**.
Consult the **Table of Critical Values** for a
discussion of that concept.

**
HOMEWORK**: The **Power **of a
statistical test is related to the sample size
necessary to detect what may be a small but
significant deviation from expectation. The numbers
presented show that with **n = 50**, an outcome of
**29:21** is *insufficient *to demonstrate a
significant deviation from equality. This begs the
question, what outcome *would *be significant,
or stated another way, what is the *minimum
deviation* from expectation that could be
detected with a sample of 50? From the formula above,
and given a critical value of *X*^{2}
= 3.84, *show ***algebraically ***what
that minimum deviation is for this simple case*.

If you are feeling energetic, use **Excel
**to calculate a table of the range of such values
over a range of sample sizes 50, 100, 200, 500, and
1000. What does this tell you about the importance of
sample size in testing biological hypotheses?

** **

Customization of the **Chi-Square Test for Nucleotide data**

Box © 2013
Sinauer Associates; Text material © 2022 by Steven M. Carr