One-way ANOVA uses estimates of variance to decide whether several group means are equal.
Correct Answer
True
True. ANOVA compares the variation between group means with the variation within groups. If the between-group variation is much larger, the means are judged not all equal.
Category: ANOVA Basics
Question 2
The null hypothesis of one-way ANOVA states that at least two of the group means differ.
Correct Answer
False
False. The null hypothesis states that all the group population means are equal. The statement that at least two means differ is the alternative hypothesis.
Category: ANOVA Basics
Question 3
One assumption of one-way ANOVA is that each population being sampled is normally distributed.
Correct Answer
True
True. ANOVA assumes normal populations, equal population standard deviations, and independent random samples. The factor must be categorical and the response numerical.
Category: ANOVA Assumptions
Question 4
One-way ANOVA requires the response variable to be categorical.
Correct Answer
False
False. The response variable in ANOVA must be numerical, because the test compares its means. It is the factor that defines the groups that is categorical.
Category: ANOVA Assumptions
Question 5
If all the group population means are equal, MS between and MS within both estimate the same variance, so F tends to be close to 1.
Correct Answer
True
True. Under H0 both mean squares estimate the common population variance, so their ratio should be near 1. Differences from 1 then come mostly from sampling variability.
Category: F-Ratio
Question 6
The F statistic in one-way ANOVA is computed as MS within divided by MS between.
Correct Answer
False
False. The F statistic is MS between divided by MS within. Putting the between-groups mean square on top makes F large when the group means differ.
Category: F-Ratio
Question 7
In one-way ANOVA, SS total equals SS between plus SS within.
Correct Answer
True
True. ANOVA splits the total variation in the data into a part due to differences among group means and a part due to variation inside the groups. Their degrees of freedom add the same way: (k - 1) + (n - k) = n - 1.
Category: ANOVA Table
Question 8
The numerator degrees of freedom in one-way ANOVA are n - k.
Correct Answer
False
False. The numerator, or between-groups, degrees of freedom are k - 1, where k is the number of groups. The value n - k is the denominator, or within-groups, degrees of freedom.
Category: ANOVA Table
Question 9
An F statistic can never be negative.
Correct Answer
True
True. The F statistic is a ratio of two mean squares, each built from squared deviations, so it is always zero or positive. The F distribution therefore starts at zero.
Category: F Distribution
Question 10
Every F distribution has the same shape regardless of its degrees of freedom.
Correct Answer
False
False. There is a different F curve for each pair of numerator and denominator degrees of freedom. As both grow, the curve becomes less skewed and closer to normal.
Category: F Distribution
Question 11
An F distribution is described by two degrees of freedom values, one for the numerator and one for the denominator.
Correct Answer
True
True. An F distribution is written F(df numerator, df denominator). In ANOVA these are k - 1 and n - k.
Category: F Distribution
Question 12
Rejecting H0 in one-way ANOVA shows that every group mean differs from every other group mean.
Correct Answer
False
False. Rejecting H0 shows only that the group means are not all equal, so at least two of them differ. ANOVA by itself does not identify which means differ.
Category: ANOVA Basics
Question 13
The one-way ANOVA test is right-tailed.
Correct Answer
True
True. Differences among the group means make F large, so the p-value is the area to the right of the observed F. Small F values are not evidence against H0.
Category: F Distribution
Question 14
Large differences between group means compared with the variation inside the groups produce an F statistic close to 0.
Correct Answer
False
False. Large differences between group means make MS between much larger than MS within, which produces a large F value. An F statistic close to 0 means the group means are very close together.
Category: F-Ratio
Question 15
As both the numerator and denominator degrees of freedom grow, the F curve becomes more like a normal curve.
Correct Answer
True
True. With small degrees of freedom the F curve is strongly skewed to the right. As both degrees of freedom increase, the skew decreases and the curve approaches a normal shape.
Category: F Distribution
Question 16
In the F test for two variances, an F value close to 1 is strong evidence that the population variances differ.
Correct Answer
False
False. An F value close to 1 means the two sample variances are similar, which supports the null hypothesis of equal population variances. Values far from 1 are evidence that the variances differ.
Category: Two Variances
Question 17
When H0 states that two population variances are equal, the F statistic reduces to the ratio of the two sample variances.
Correct Answer
True
True. The general statistic is (s1^2 / sigma1^2) / (s2^2 / sigma2^2). If sigma1^2 = sigma2^2, those terms cancel and F = s1^2 / s2^2.
Category: Two Variances
Question 18
In one-way ANOVA, MS within is found by dividing SS within by k - 1.
Correct Answer
False
False. MS within is SS within divided by n - k, the within-groups degrees of freedom. Dividing by k - 1 is how MS between is found from SS between.
Category: ANOVA Table
Question 19
The F test for two variances can be left-tailed, right-tailed or two-tailed.
Correct Answer
True
True. The tail depends on the alternative hypothesis: whether the claim is that the first variance is smaller than, larger than or different from the second. This differs from ANOVA, which is always right-tailed.
Category: Two Variances
Question 20
One-way ANOVA assumes the samples from the different groups are paired with one another.
Correct Answer
False
False. One-way ANOVA assumes the samples are randomly selected and independent of one another. Paired or matched data call for different methods.
Category: ANOVA Assumptions