Consider the One-Way ANOVA table (some values are intentionally left blank) for

Question

Consider the One-Way ANOVA table (some values are intentionally left blank) for the amount of food (kidney, shrimp, chicken liver, salmon and beef) consumed by 50 randomly assigned cats (10 per group) in a 10-minute time interval.

H0: All the 5 population means are equal   H1: At least one population mean is different.

Population: 1 = Kidney, 2 = Shrimp, 3 = Chicken Liver, 4 = Salmon, 5 = Beef.

ANOVA

Source of Variation

SS

df

MS

F

P-value

F crit

Between Groups

3.65896

-----

0.91474

--------

9.15E-10

2.578739

Within Groups

------

-----

0.043966

Total

5.63745

49

What is the sum of squares 'within groups' value (SSW) or error sum of squares?

ANOVA

Source of Variation

SS

df

MS

F

P-value

F crit

Between Groups

3.65896

-----

0.91474

--------

9.15E-10

2.578739

Within Groups

------

-----

0.043966

Total

5.63745

49

Explanation / Answer

First we need to find the df column

For between groups df=5-1=4, Since, there are 5 gruops

For within groups df=10-1 =9, Since, there are 10 per group.

For error df= 49-9-4=36 {total- all other df}

ss of within group =

SSW=Ms of within group × df of within group

=0.043966×9=0.395694

error sum of square = TSS-SSB -SSW

=5.63745-3.65896-0.395694 = 1.582796

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