Lecture 12.docx - October 31 2022 Analysis part 2 T-test ●...

October 31, 2022
Analysis part 2
T-test
● T distribution
● 2 groups
Anova
● More than 2 groups
Variance
● Sum of squares
● (n-1) vs n
○ Sample is the population divide by n
○ When it is not use (n-1)
Why variance?
● Cannot distinguish groups based on just the mean, need to use variance as well

October 31, 2022
Degrees of Freedom
● How many values in a data set can be varied
● mean= sum of the outcomes/ the total number of outcomes
● 5 variables that are free to vary
F Statistic
● F refers to Fisher
● Ratio of mean square among groups to the mean square within groups
● Mean squares= sum of squares/ degrees of freedom
Anova ‘Ingredients’
● At least 3 groups
● Sum of squares among groups

October 31, 2022
● Dispersion within each group compared to the dispersion among each group
Anova Example
● 4 groups, is there a difference among the groups
● Yi: any of the groups, average value of each group
● Ni: sample sizes
● Anova tells us if there is a greater different within or among each group
Grand Mean
● Sum of all the values divided by the total sample size
Sum of Squares Among groups
● Average value subtract the grand mean and square it and multiply by the sample