The z, t, and F distributions have something in common: the numerator of the test statistic
contains a measure of difference among means due to treatment
A measure of the differences among group means (due to treatment) is included in
between-groups variance
If between-groups variance is much larger than within-groups variance, we infer that the sample means are ________ one another, and we ________ the null hypothesis.
different from; reject
Within-groups variance reflects the
weighted average of the sample variances
There is a different F distribution for every:
combination of sample size and number of samples
The less overlap there is among sample distributions, the
more confident we are that the samples represent true differences in the population
Changes in within-groups variance result in changes in the ________ of the F ratio.
Denominator
In a z test and a t test, when there is no difference between groups, the test statistic is equal to ________, but in the ANOVA, when there are no differences among groups, the test statistic is equal to ________.
0; 1
If you calculate an F statistic and find that it is negative, then you know that:
you have made a calculation error
MSbetween is obtained by
dividing SSbetween by dfbetween
________ is a term used in ANOVA to refer to an independent variable, especially in a study with more than one independent variable
Factor
In a two-way factorial ANOVA, between-groups variance is partitioned into:
two main effects and a single interaction
In a two-way ANOVA, we account for _______ sources of variability, measuring each with a mean square.
Four
analysis of variance (ANOVA)
A hypothesis test typically used with one or more nominal (and sometimes ordinal) independent variables (with at least three groups overall) and a scale dependent variable.
Tukey HSD test
A widely used post-hoc test that determines the differences between means in terms of standard error; the HSD is compared to a critical value; sometimes called the q test.
R2:
The proportion of variance in the dependent variable that is accounted for by the independent variable.
heteroscedastic:
A term given to populations that have different variances.
within-groups variance:
An estimate of the population variance based on the differences within each of the three (or more) sample distributions.
one-way ANOVA:
A hypothesis test that includes both a single nominal independent variable with more than two levels and a single scale dependent variable.
between-groups ANOVA:
A hypothesis test in which there are more than two samples, and each sample is composed of different participants.
main effect:
A result occurring in a factorial design when one of the independent variables has an influence on the dependent variable.
marginal mean
The mean of a row or a column in a table that shows the cells of a study with a two-way ANOVA design
qualitative interaction:
A particular type of quantitative interaction of two (or more) independent variables in which one independent variable reverses its effect depending on the level of the other independent variable.
two-way ANOVA:
A hypothesis test that includes two nominal independent variables, regardless of their numbers of levels, and a scale dependent variable.
factorial ANOVA:
A statistical analysis used with one scale dependent variable and at least two nominal independent variables (also called factors); also called a multifactorial ANOVA.