Although it tests a claim about group means, ANOVA reaches its decision by comparing two estimates of the population variance.
Missing Word
variance
Variance measures spread as the average squared deviation. ANOVA compares a variance estimate based on how far apart the group means are with one based on spread inside the groups.
Category: ANOVA Basics
Question 2
To find the F statistic, take the factor mean square and divide it by the error mean square.
Missing Word
divide
F = MS between / MS within, so the factor (between-groups) mean square is divided by the error (within-groups) mean square. When H0 is true both estimate the same population variance and F is near 1; F grows as the group means spread apart.
Category: F-Ratio
Question 3
Every F distribution is skewed to the right, with a long tail toward large values.
Missing Word
right
A distribution skewed to the right has its long tail on the side of large values. F curves start at zero and trail off to the right.
Category: F Distribution
Question 4
One-way ANOVA assumes that each population being sampled has a normal distribution.
Missing Word
normal
Normal populations are one of the conditions for ANOVA, together with equal standard deviations and independent random samples. The F distribution of the test statistic depends on these conditions.
Category: ANOVA Assumptions
Question 5
The samples drawn from the different groups in a one-way ANOVA must be independent of one another.
Missing Word
independent
Independent samples means that which individuals end up in one group has no effect on which end up in another. Paired or matched data violate this condition.
Category: ANOVA Assumptions
Question 6
In the notation F(4, 10), the second number, 10, gives the denominator degrees of freedom.
Missing Word
denominator
The second number in F(df1, df2) is the denominator degrees of freedom. In ANOVA it equals n - k, the within-groups degrees of freedom.
Category: F Distribution
Question 7
For an ANOVA comparing k groups, the k - 1 degrees of freedom belong to the mean square that sits in the numerator of the F statistic.
Missing Word
numerator
The numerator degrees of freedom belong to the between-groups mean square, which sits on top of the F statistic. With k groups there are k - 1 of them.
Category: ANOVA Table
Question 8
Because sums of squares cannot drop below zero, an F statistic is never negative.
Missing Word
negative
Mean squares are sums of squared deviations divided by positive degrees of freedom, so both are zero or positive. Their quotient, F, is therefore zero or positive.
Category: F Distribution
Question 9
The F test for two variances is very sensitive to departures from normality, so its p-values can be misleading for skewed data.
Missing Word
sensitive
A test that is sensitive to an assumption can give unreliable results when that assumption fails. For this reason many statisticians avoid the F test for two variances unless the populations are clearly normal.
Category: Two Variances
Question 10
In one-way ANOVA, the sum of squares for the factor plus the sum of squares for error equals the total sum of squares.
Missing Word
total
The total sum of squares measures all the variation in the data around the grand mean. ANOVA splits it into a between-groups part and a within-groups part.
Category: ANOVA Table
Question 11
The F distribution is named for the English statistician Sir Ronald Fisher.
Missing Word
Fisher
Ronald Fisher developed analysis of variance, and the F distribution carries the first letter of his name in his honor. It is the distribution of a ratio of two independent variance estimates, which is why ANOVA and the test for two variances both use it.
Category: F Distribution
Question 12
In ANOVA, the factor that sorts individuals into groups is a categorical (also called qualitative) variable.
Missing Word
categorical
A categorical variable places each individual into one of several groups, such as a diet or a teaching method. The response measured on each individual must be numerical so that group means can be compared.
Category: ANOVA Assumptions
Question 13
The mean square within groups, also called the error mean square, measures how much values vary inside their own groups.
Missing Word
within
The mean square within is SS within divided by n - k. It estimates the population variance whether or not H0 is true, so it serves as the denominator of F.
Category: ANOVA Table
Question 14
In one-way ANOVA, if the p-value of the F test is less than alpha, the decision is to reject H0.
Missing Word
reject
A p-value below alpha means a result this extreme would be unlikely if all the population means were equal, so H0 is rejected. Rejecting H0 supports the claim that at least two population means differ, without saying which ones.
Category: ANOVA Basics
Question 15
Besides ANOVA, the F distribution is used to test whether 2 populations have the same spread.
Missing Word
2
The F test for two variances compares the spread of 2 populations by dividing one sample variance by the other. It uses n1 - 1 and n2 - 1 degrees of freedom.
Category: Two Variances