More on ANOVA

One-Factor ANOVA (Between Subjects)

Answers

False, both t tests and ANOVAs use both. In a t test, the difference between means is in the numerator and the denominator is based on differences within groups. In an ANOVA, the variance of the group means (multiplied by n) is the numerator. The denominator is based on differences within groups.
This is correct. These are the four levels of the variable "Type of Smile".
This is a within-subjects design since subjects are tested multiple times. In a between-subjects design each subject provides only one score.
p = 0.3562
F = 1.3057
variance of the means = 9.717
Multiply the variance of the means by the n of 10. The result is 97.17.
.936
Homogeneity of variance is the assumption that the variances in the populations are equal.
True. When a subject provides more than one data point, the values are not independent, thus violating one of the assumptions of between-subjects ANOVA.
False. If the null hypothesis that all of the population means are equal is true, then both MSB and MSE estimate the same quantity.
When the population means differ, MSB estimates a quantity larger than does MSE. A high ratio of MSB to MSE is evidence that the population means are different.
F is defined as MSB/MSE. Since both MSB and MSE are variances and negative variance is impossible, an F score can never be negative.
k-1 = 7-1 = 6
N-k = 105-7 = 98
The F distribution has a long tail to the right which means it has a positive skew.
F equals t² = 6.25.
Sum of squares total equals sum of squares condition + sum of squares error.
Divide sums of squares by degrees of freedom to get mean squares. Then divide MSB by MSE to get F which equals 42.
F = t²