1. Two Variable Statistics
The Formal Test For Independence

2. Correlation
Finding the relationship between two quantitative variables without being able to infer causal relationships
Correlation is a statistical technique used to determine the degree to which two variables are related

3. Example: The Scenario
This contingency table shows the responses of a randomly chosen sample of adults regarding the person’s weight and whether they have diabetes.
At a 5% significance level, the critical value of χ2 is 5.99.

4. The alternative hypothesis:
Step 1: Stating….
What we need to find: Test at a 5% level whether there is a link between weight and suffering diabetes.
The null hypothesis:
H0 is that diabetes and weight are independent.
The alternative hypothesis:
H1 is that diabetes and weight are not independent.

5. Step 2: df and critical value
The degrees of freedom is:
df = (r – 1)(c – 1)
df = (2 – 1)(3 – 1) = 2
With a significance level of 5% we use the table to find the critical value.
We reject H0 if χ2 calc > 5.99.

6. Step 3: Expected Frequency Table
Use your GDC to calculate this for you.
Weight
light
medium
heavy
Diabetic
18.529
17.912
19.559
Non-Diabetic
71.471
69.088
75.441

7. Step 4: Calculate χ2
Use your GDC to calculate this for you.

8. Step 5: Conclude your result…
Since χ2 = 6.61 and 6.61 > 5.99 then we reject the null hypothesis.
We can conclude that there is a relationship between weight and diabetes.

9. The p-Value
When finding χ2 on your calculator, a p-value is also provided. This can be used, together with the χ2 value and the critical value, to determine whether or not to accept that the variables are independent.
For a given contingency table, the p-value is the probability of obtaining observed values as far or further from the expected values, assuming the variables are independent.

10. The p-Value….
Based on our calculations we found the p-value to be or 3.7%.
Because this is less that the significance level of 5% or 3.7% < 5%, we then can reject the null hypothesis.
In other words there is a relationship between weight and diabetes.

11. Using Technology to Calculate χ2
Chi-Square Independence Test on TI-84 Calculator
TI-NSPIRE Chi Square Test on 2 Way Tables
Chi-Square Test for 2-Way Tables using Casio fx-9750GII

12. Thank
You