STP 420 Midterm 3

Steps of ANOVA

1. Hypotheses

2. Calculate overall mean, group means

3. Degrees of freedom between groups, within groups

4. Compute SSG: mean of squares among groups

5. Compute SSE: mean of squares within groups

6. Compute MSG and MSE

7. Calculate F stat

8. Use F table for critical value

9. Make decision

N

number of total observations of data (3 groups, 4 observations each, N = 12)

k

number of groups

DF between groups

k-1

DF among groups

N-k

SSG (mean among groups)

sum of n(group mean - total mean)². (n is the same for each group; number of groups does not change)

formula: sum of n_i * (x_i bar - x bar)²

SSE (mean within groups)

sum of (individual value - total mean)² for each group.

(ex: should have sum of 4 values per group if we have 3 groups of 4 observations)

formula: (x - x bar)²

MSG (mean of squares among groups)

SSG/(k-1)

MSE (mean of squares within groups)

SSE/(N-k)

F statistic

MSG/MSE

critical value

find f critical value using (k-1, N-k)

What do we do when we reject null hypothesis?

use fisher’s LSD to find out which groups are different

power of the test

correctly rejecting null hypothesis

what influences the power of the test?

• increase sample size

• increase alpha

• decrease population sd

• increase difference between hypothetical mean and population mean

which factors related to the power of the test can we control?

• increase alpha

• increase sample size