PSYC 202 Chapter Notes - Chapter 11: Variance, F-Distribution, Null Hypothesis
WEEK 11 VIDEO NOTES
f-tests – way to test for the ratio of sample variance that are coming from two populations
- Form the set of statistical methods (ANOVA)
Ratio of variances
- F distribution
- Sample variances are estimates just like sample means
- Not a normal distribution
- Given by an F-distribution with df1 and df2
o 2 degrees of freedom bc of the two populations
o Df=sample size - 1
-
-
o Skewed to the right – NOT normally distributed
o All values are positive – can’t have anything less than 0
- When comparing populations – look at the ratio of variances
o Each population has its own distribution of population variance
o If we took one sample from pop1 and one from pop2, what would the value of the
ratio of the two variances be?
o If we took multiple samples, what would the sampling distribution of the ratio of
the variances be?
-
-
o Low sampling intensity = green line
o As sample size increases, the peak of the distribution centers around a variance of
1
F-Test
- Evaluate the hypothesis that two variances are equal
- Null hypothesis is that the variances are equal – pop 1 is less than or equal to pop2
- Alternative hypothesis is that the variances are not equal – pop1 is larger than pop2
- F-distribution is given by the ratio of the sample variances – s12/s22 s = standard
deviation
- Deciding which population goes on top depends on the question you are interested in
o Want to set it up in the direction so that if you reject the null hypothesis, then the
population with the larger variance is in the numerator
- There are two degrees of freedom df= (n1-1)(n2-1)
- To construct null hypothesis for F distribution:
o First degree of freedom is for the groups (number of groups -1) or (k-1)
o Second degree of freedom is for the error or residuals. (total number of data
points– number of categories in categorical variable) or (n-k)
- ALL F TESTS ARE ONE TAILED
-
VIDEO 2
For an ANOVA F-test → comparing a measured numerical value against a categorical value,
usually with 3 or more levels.
While an ANOVA can be used to compare the means of just two levels of a categorical variable
(e.g. sex - male or female), usually a t-test with two independent samples is used in that case
Single factor analysis of variance
- Framework to test multiple questions while controlling type 1 error
- Asks is the variation among group means greater than by chance alone?
- Have categorical and numerical data. In the categorical data you want to compare more
than two groups
- Can’t use t tests because the tests are not independent
o The data is shared among the tests
- Have to control the type one error rate for the entire set of questions – called the family
wise error rate
-
Document Summary
Week 11 video notes f-tests way to test for the ratio of sample variance that are coming from two populations. Form the set of statistical methods (anova) Sample variances are estimates just like sample means. Evaluate the hypothesis that two variances are equal. Null hypothesis is that the variances are equal pop 1 is less than or equal to pop2. Alternative hypothesis is that the variances are not equal pop1 is larger than pop2. F-distribution is given by the ratio of the sample variances s1. There are two degrees of freedom df= (n1-1)(n2-1) For an anova f-test comparing a measured numerical value against a categorical value, usually with 3 or more levels. While an anova can be used to compare the means of just two levels of a categorical variable (e. g. sex - male or female), usually a t-test with two independent samples is used in that case. Framework to test multiple questions while controlling type 1 error.