Chi-Squared

AP Bio

Chi-Squared Formula

χ2 - Chi Squared

∑ - Sum of the values

Oi - Observed Data (data collected)

Ei - Expected Values (values expected before start)

Chi-Squared Test

A way to compare the data you collect and observe if the variation is due to chance or if its due to one of the variables you are testing.

We can use our data to see if there is a statistical difference.

Null Hypothesis

No significant statistical difference between the observed and expected values.

The point of Chi-Squared is to accept or reject the null hypothesis.

Degrees of Freedom

Number of values in the final calculation of a statistic that are free to vary. You find the degrees of freedom by taking the total number of outcomes minus 1.

Critical Value

The cut off values that define regions where the test statistic is unlikely to lie.

Accepting/Rejecting Chi-Squared

When you calculate Chi-Squared and it is over the critical value, you reject the null hypothesis (more than chance, its a variable).

If its under, you accept (no statistical difference between observed and expected).

Steps for Chi-Squared

1. Calculate Oi-Ei for each variable then square answer

2. Put the difference over Ei

3. Add fractions together (∑)

4. Convert to decimal

5. Find degrees of freedom (total # of variables - 1)

6. Use DoF to determine critical value

7. Determine if you are accepting or rejecting null hypothesis.