CK-12 Probability and Statistics - Advanced

11.2. The One-Way ANOVA Test http://www.ck12.org

SSB=

k

∑

k= 1

Tk^2

nk

−

T^2

N

≈ 1 , 364. 57 −

( 194 )^2

31

≈ 150. 5

Since there are four Degrees of Freedom for this calculation (the number of groups minus one), the mean squares
between groups is

MSB=

SSB

K− 1

≈

150. 5

4

≈ 37. 6

Next we calculate the mean squares within groups(MSW)which is also known as the estimation of the pooled
variance of a population(σ^2 ).

To calculate the mean squares within groups, we use the formula

SSW=

k

∑

k= 1

nk

∑

i= 1

Xik^2 −

k

∑

k= 1

Tk^2

nk

Using our summary statistics from above, we can calculate that the within groups mean square(MSW)is equal to:

SSW=

k

∑

k= 1

nk

∑

i= 1

Xik^2 −

k

∑

k= 1

Tk^2

nk

≈ 1 , 452 − 1 , 364. 57

≈ 87. 43

And so we have

MSW=

SSW

N−K

≈

87. 43

26

≈ 3. 36

Therefore, ourF-Ratio is

F=

MSB

MSW

≈

37. 6

3. 36

≈ 11. 18

We would then analyze this test statistic against our critical value (using theF-distribution table and a value of
(α=. 02 ), we find our critical value equal to 4.14. Since our test statistic( 11. 18 )exceeds our critical value( 4. 14 ),
we reject the null hypothesis. Therefore, we can conclude that not all of the population means of the five programs
are equal and that obtaining anF-ratio that extreme by chance is highly improbable.

Technology Note - Excel

Here is the procedure for performing a One-way ANOVA in Excel using this set of data.

1. Copy and paste the table into an empty Excel worksheet