Question

ANOVA calculations and rejection of the null hypothesis

The following table summarizes the results of a study on SAT prep courses, comparing SAT scores of students in a private preparation class, a high school preparation class, and no preparation class. Use the information from the table to answer the remaining questions.

Treatment	Number of Observations	Sample Mean	Sum of Squares (SS)
Private prep class	60	650	132,750.00
High school prep class	60	645	147,500.00
No prep class	60	625	162,250.00

QUESTION: Using the data provided, complete the partial ANOVA summary table that follows. (Hint: T, the treatment total, can be calculated as the sample mean times the number of observations. G, the grand total, can be calculated from the values of T once you have calculated them.)

Source	Sum of Squares (SS)	df	Mean Square (MS)
Between treatments
Within treatments

QUESTION: ANOVA summary tables typically have a “Total” row not included in the partial table you just completed. Which of the following is a possible reason for including this row?

A) The SStotal is used in the calculation of the F test statistic.

B) The SStotal is sometimes easier to calculate than SSbetween Since SSwithin + SSbetween = SStotal you can use SStotal to calculate SSbetween

C) The total sums of squares is the sometimes called the “error term.”

D) The MS total is used in the calculation of the F test statistic.

QUESTION: In ANOVA, the F test statistic is the ___________ of the between-treatments variance and the within-treatments variance. The value of the F test statistic is ____________ .

When the null hypothesis is true, the F test statistic is ___________ . When the null hypothesis is false, the F test statistic is most likely __________. In general, you should reject the null hypothesis for ____________ .

Answer 1

Group	ni	x̅i	S2i	ni*(Xi-Xgrand)2	(ni-1)*S2i
A	60	650.000	2250.00	6000.000	132750.0000
B	60	645.000	2500.00	1500.000	147500.0000
C	60	625.000	2750.00	13500.000	162250.0000
	grand mean=	640.00		21000.0000	442500.0000
				SSTr	SSE
Source	SS	df	MS
between	21000.0000	2	10500.0000
within	442500.0000	177	2500.0000

The SStotal is sometimes easier to calculate than SSbetween Since

SSwithin +SSbetween = SStotal you can use SStotal to calculate SSbetween

in ANOVA the F statisitc is the ratio of the between,,,,,,,,,,the value of the F test statisitc is 4.20

when the null hypothesis is true , the F test statistics is closer to 1, when the null hypothesis is false, the F test statistic is most likely high

in general , you should reject,,,,,for larger F values