6.4 Tests of Variance, Correlation and Independence Flashcards
What test do you use to test a single variance?
The Chai-squared test
What are the key properties of the Chai-squared distribution?
It is asymmetrical
It’s symmetry increases with the degrees of freedom
it is bounded from below by zero & it cannot be negative (cannot be lower than -100%)
At which point do you reject a Chai-squared test?
Reject if the test statistic is in the tails
What are the critical values for a Chai-squared test?
For a two tailed test, the critical value is significance level divided by 2
For a 5% significance level
The upper tail would be 2.5%
The left lower tail would be 97.5%
What is the formula for the Chai-squared distribution?
Which test is used if you are testing the equality of two population variances?
An F-test with (n1-1) and (n2-1) degrees of freedom
What are the key properties of the F-distribution?
It is asymmetrical
It is bounded from below by zero
It has two separate degrees of freedom
How do you calculate the F-test?
It is the sample variance of sample 1 divided by the sample variance of sample 2
Note… the greater variance is always the numerator (on top)
How do you interpret the F-test?
Reject if the test value is in the tails of the test
What is a parametric test?
They test something about a population parameter
What is a nonparametric test?
They test things other than parameter values
When is the null hypothesis rejected when using a parametric test to determine correlation? Which test is used?
Using a t-test with n-2 degrees of freedom
Reject if test statistic is in the tails
When is the hypothesis rejected for a nonparametric test?
The non-parametric test will produce a correlation coefficient that can be used as an input in a parametric test
If sample size is large, degrees of freedom is n-2 using t-test
Reject if test statistic is in the tails
What test is used for a test of independence?
A chai-squared test with [R-1] x [C-1] degrees of freedom
R = row categories
C = column categories
What is the test stat value for a test of independence?
It is the sum of the squared differences divided by the expected frequency
I.e. it is the sum of the contingency table totals
