In ANOVA, the F statistic is the: difference, product, ratio, or sum The value o
ID: 3219448 • Letter: I
Question
In ANOVA, the F statistic is the: difference, product, ratio, or sum
The value of the F test statistic is: .11, .25, 2.31, 9.23
When the null hypothesis is true, the F stat is: large, close to 0, or close to 1
When the null hypothesis is false, the F stat is: large, close to 1, close to 0
In general, you should reject the null hypothesis for: large values of the F-test statistic; values of the F-test statistic close to 1; values of the F-test statistic close to 0
Aa Aa E, 4. 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. Number of Sum of Treatment observations Sample Mean squares (SS) Private prep class 60 660 135,700.00 High school prep class 60 640 153,400.00 No prep class 171,100.00 60 620 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) Mean Square (MS) Between treatments Within treatments 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? O The SStotal is sometimes easier to calculate than SS between Since SS SS SStobal, you can use within between SStotal to calculate SSbetween. O The total sums of squares is the sometimes called the error term O The MS is used in the calculation of the F test statistic total O The SStotal is used in the calculation of the F test statistic 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 n general, you should reject the null hypothesis foExplanation / Answer
Treatment
No of obs
Sample mean
Sum of squares
Private prep class
60
660
1357000
High school prep class
60
640
1534000
No prep class
60
620
1711000
Sum of squares within treatments = 1357000+1534000+1711000= 460200
X = 1/3(660+640+620) = 640
Sum of squares between treatments = ni(xI - x)2 = 60(660-640)2 + 60(640-640)2 + 60(620-640)2 = 48000
Degrees of freedom :
Between treatments = k -1 =3-1 = 2
Within treatments = N – k -1 = 180 – 2 -1 = 177
Mean square:
Between treatments = 48000/2 = 24000
Within treatments = 460200/177 = 2600
Source
Sum of squares
df
Mean square
Between treatments
48000
2
24000
Within treatments
460200
177
2600
The SStotal is sometimes easier to calculate SSbetween. Since SSwithin + SSbetween = SStotal, you can use SStotal to calculate SSbetween .
In ANOVA, The F test statistic is the ratio of the between-treatment variance and the within treatments variance. The value of the F test statistic is 24000/2600 = 9.23
When the null hypothesis is true, the F test statistic is close to 1 because the null hypothesis states that there is no difference in the variance. When the null hypothesis is false, the F test statistic is most likely large because the numerator will be very large compared to the denominator . In general, you should reject the null hypothesis for large values of the F test statistic.
Treatment
No of obs
Sample mean
Sum of squares
Private prep class
60
660
1357000
High school prep class
60
640
1534000
No prep class
60
620
1711000