Two Variable Statistics

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Presentation transcript:

Two Variable Statistics The Formal Test For Independence

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

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.

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.

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.

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

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

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.

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.

The p-Value…. Based on our calculations we found the p-value to be 0.037 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.

Using Technology to Calculate χ2 Chi-Square Independence Test on TI-84 Calculator https://www.youtube.com/watch?v=j4_SuB4qzWE TI-NSPIRE Chi Square Test on 2 Way Tables https://www.youtube.com/watch?v=ln5MVtH3fmM Chi-Square Test for 2-Way Tables using Casio fx-9750GII https://www.youtube.com/watch?v=H0NWHFc0w0o

Thank You