Statistical Tests in Biology - the Chi-Square Test

In the Chi-Square Test, a scientist evaluates data by comparing the actual observed data with expected data from previous studies or models. The data analyzed using the Chi-Square Test is categorical data or ‘yes or no’ data. For ‘yes or no’ data, the Chi-Square Test is often an appropriate statistical test. The method for doing the Chi-Square Test is given below, and the probability or Pvalues are given in the Critical Chi-Square Table.

The Chi-Square Test

Chi-Square Value

=

Σ

(observed - expected) expected 2

for all classes

1. Generate a Chi-Square Value

a) Take the expected number of flies in your first category and subtract it from the observed number of flies for that category. Take the value obtained and square it. Then divide this number by the expected value.

b) Repeat this step for each of the other categories of expected phenotypes.

(observed - expected)2 values have been obtained, expected add them all together to obtain the Chi-Square Value.

c) Once all of the

2. Determine the degrees of freedom (df) for the experiment.

The degrees of freedom is equal to (the number of categories of expected classes) - 1

3. Once you have calculated a Chi-Square Value, and have determined the df, it is time to determine a P-value. The P -value is estimated using a P-value

Table (below). Using the Table, you find the P-value that corresponds to your Chi-Square Value and degrees of freedom (df).

For example, let’s imagine that the degrees of freedom is 5, and the ChiSquare Value is 15.1. Using the Table (below), we find the P-value is approximately of 0.01 which is less than the ‘cut-off’ P-value of 0.05.

1

BIOL 1020 - TUTORIAL 9

Critical Chi-Square Table with Probability

Probability df 0.995

0.99

0.975

0.95

0.90

0.10

0.05

0.025

0.01

0.005

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

---

---

0.001

0.004

0.016

2.706

3.841

5.024

6.635

7.879

0.010

0.020

0.051

0.103

0.211

4.605

5.991

7.378

9.210

10.597

0.072

0.115

0.216

0.352

0.584

6.251

7.815

9.348

11.345

12.838

0.207

0.297

0.484

0.711