i. One characteristic of the F distribution is that computed F can only range be
ID: 3179806 • Letter: I
Question
i. One characteristic of the F distribution is that computed F can only range between -1 and +1.
ii. The shape of the F distribution is determined by the degrees of freedom for the F-statistic, one for the numerator and one for the denominator.
iii. The F distribution's curve is positively skewed.
A) (i), (ii), and (iii) are all false statements.
B) (i), (ii), and (iii) are all correct statements.
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i) and (ii) are correct statements but not (iii).
Explanation / Answer
F-statistics is always positive, since F(m,n)X21(m)/mX22(n)/n which is always positive
The F distribution is the distribution of the ratio of two estimates of variance. It is used to compute probability values in the analysis of variance. The F distribution has two parameters: degrees of freedom numerator (dfn) and degrees of freedom denominator (dfd). The dfn is the number of degrees of freedom that the estimate of variance used in the numerator is based on. The dfd is the number of degrees of freedom that the estimate used in the denominator is based on. The dfd is often called the degrees of freedom error or dfe. In the simplest case of a one-factorbetween-subjects ANOVA,
dfn = a-1
dfd = N-a
where "a" is the number of groups and "N" is the total number of subjects in the experiment. The shape of the F distribution depends on dfn and dfd. The lower the degrees of freedom, the larger the value of F needed to be significant. For instance, if dfn = 4 and dfd = 12, then an F of 3.26 would be needed to be significant at the.05 level. If the dfn were 10 and the dfd were 100, then an F of 1.93 would be significant at the .05 level
As F is always positive we will have positive skewness
So answer is
D) (ii) and (iii) are correct statements but not (i).
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