ANOVA Homework

ANOVA

StudentIDMajorExam 1 (xi)()2Exam 2 (yi)()2() ()
001Art8552580000
002Science70-1010075-52550
003Science90101009212144120
004Humanities65-1522575-52575
005Art901010072-864-80
006Humanities8000844160
007Science74-63680000
008Art73-74967-1316991
009Science95152259212144180
010Humanities78-248339-6
N=10 80 86480 596430

ANOVA for Exam 1

1) Find the group means

Mean for Art students

Mean for Science students

Mean for Humanities Students

2) Compute the Between Group Variance

a. subtract each group mean from the overall mean,

b. square the difference

c. multiply by number of group members

d. repeat for each group

Art Students: 21.39

Science Students:

Humanities Students:96.45

e.  Sum the 3 values from above (the result is the between group sums of squares)

f. Divide between group sums of squares by number of groups minus 1 (the result is the between group variance)

3. Find Within Group Variance

a. Subtract each score from its group mean, square the difference

Art Students:

Science Students:

Humanities Students

b.  sum the resulting values (the result is the within group sums of squares)

Art:

Science:

Humanities:

Totals=

c. divide within group sums of squares by number of cases minus number of groups (the result is the within group variance)

3. Compute F:

a. Divide the between group variance by the within group variance

4. Find the degrees of freedom and test the null hypothesis of no association

5. Find the variance explained

SS­­between/ SStotal=  Variance Explained

a. Find the total sums of squares,  this value is the sum of the between and within group sums of squares, and the sums of squares for Y

b. divide between group sums of squares by total.

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