The F is calculated by:
dividing a measure of between-groups variability by a measure of within-groups variability.
When F is significant:
we do not know which specific means differ significantly
Within-groups variance reflects:
the amount of difference between means that we would expect to occur by chance alone.
In which of the following situations would it be necessary to use within-groups ANOVA?
A longitudinal study follows a group of kindergarten children through high school and assesses their intelligence at three time points.
In a between-subjects ANOVA, SSbetween = 225, SSwithin = 47, dfbetween = 2, and dfwithin = 19. What is the value for MSbetween?
112.5
FORMULA:
MSbetween= SS between / DF between
In a within-groups ANOVA, MSbetween = 10, MSwithin = 5, dfbetween = 2, and dfwithin = 35. What is the value of F?
2
FORMULA:
F=MS between / MS within
Jonah conducts an ANOVA comparing the life satisfaction scores of those with low IQ, average IQ, and high IQ. He is able to reject the null hypothesis and decides to conduct a Tukey HSD post hoc test. The MSwithin for his ANOVA is 2.1. If the low IQ group
-13.09
FORMULA:
Jonah conducts an ANOVA comparing the life satisfaction scores of those with low IQ, average IQ, and high IQ. He is able to reject the null hypothesis and decides to conduct a Tukey HSD post hoc test. The MSwithin for his ANOVA is 2.1. If the low IQ group
8.73
(M1-M2)/? (MSwithin/N)
Within-groups degrees of freedom is calculated by:
multiplying the between-groups degrees of freedom by the subjects degrees of freedom.
A researcher reports that dfbetween = 4 and dfwithin = 20.
How many treatment conditions are in this study?
5
FORMULA:
df between 4+1=5
Which of the following is the CORRECT formula for calculating R2 in a one-way within-groups ANOVA?
Within group
R2= ss between / (ss total - ss subjects)
Which of the following is the CORRECT formula for calculating R2 in a one-Way Between-Groups ANOVA?
Between group
R2 = ss between / ss total
In a within-groups ANOVA, SSbetween = 1100, SSwithin = 250, SSsubjects = 557, and SStotal = 1907. What is the value of R2?
0.81
FORMULA:
R2 = ss between / (ss total - ss subjects)
A professor wants to know whether critical-thinking skills change as a student progresses through college. He compares critical-thinking skills for a group of 100 students at three time points: during the students' first semester, fifth semester, and eigh
-3.87
FORMULA:
SM= ? (MS within/N)
HDS = (M1 - M2) / sm
_____ can be interpreted as the proportion of variance in the dependent variable that is accounted for by the independent variable.
R2
When calculating a Tukey HSD test for a within-groups ANOVA, under what conditions should you use the harmonic mean?
You never use the harmonic mean since the groups always have equal sample sizes
When calculating a Tukey HSD test, if the samples sizes are unequal, we must first calculate a weighted sample size known as:
the harmonic mean
the harmonic mean
...
What is the primary advantage of the within-groups ANOVA as compared to the between-groups ANOVA?
Within-groups ANOVA reduces the amount of error due to differences between groups.
Reducing within-groups variability will impact the F ratio by making it:
larger.
Given dfwithin = 14, 3 groups, and HSD = 4.1, which of the following is TRUE?
At a p level of 0.05, the researcher can reject the null hypothesis
Tiffany is interested in the effects of different kinds of instructions on exam performance. She asks 60 college freshmen to study regularly for an upcoming exam, which they will have 1 hour to take. Participants are randomly assigned to one of three inst
between-groups variance.
Tiffany is interested in the effects of different kinds of instructions on exam performance. She asks 60 college freshmen to study regularly for an upcoming exam, which they will have 1 hour to take. Participants are randomly assigned to one of three inst
within-groups variance.
The F ratio in ANOVA is a ratio of:
two estimates of population variance
In which of the following situations would it be necessary to use a between-groups ANOVA?
A researcher is interested in the effects of distraction on listening comprehension and randomly assigns participants to one of three distraction groups.
Changes in within-groups variance result in changes in the _____ of the F ratio.
denominator
Changes in between-groups variance result in changes in the _____ of the F ratio
numerator
If you calculate an F statistic and find that it is smaller than your critical value, you would:
fail to reject the null hypothesis.
By convention, an R2 value of 0.05 would be considered:
medium.
A post hoc test is warranted when:
the F is significant and we have more than two groups.
A within-groups ANOVA has less variability between the groups than a between-groups ANOVA because:
the same participants are in each condition of the study.
In addition to the sources of variability calculated for a between-subjects ANOVA, the within-subjects ANOVA also calculates:
SSsubjects.
A measure of variability that is essentially an average of the sample variances is:
within-groups variance
Within-groups variance reflects:
the amount of difference between means that we would expect to occur by chance alone.
What does the "one" in one-way ANOVA refer?
...
The F ratio is a ratio of:
There is only one independent variable.
F is obtained by dividing _____ by _____.
MSbetween; MSwithin
Leo is interested in the effects of sleep deprivation usage on number of calories consumed. He asks a group of 20 college students to spend the night in the sleep lab under one of the following conditions: no sleep, 2 hours of sleep, 4 hours of sleep, 6 h
He knows that there is a difference among the groups somewhere, but he does not know where
In a within-groups ANOVA, SSbetween = 49.5, SSwithin = 115, dfbetween = 3, and dfwithin = 49. What is the value of MSwithin?
2.35
FORMULA:
MSwithin = ss within/df within
There is a different F distribution for every:
combination of sample size and number of samples.
The grand mean is the:
mean of all the scores in the study, regardless of the condition.
The measure of effect size calculated for ANOVA is _____.
R2
Ultimately, having less variability within-groups will:
make it easier to reject the null hypothesis.
With two groups, the square root of F is equal to _____.
t
The F statistic increases when:
within-groups variance decreases and between-groups variance increases
The symbol for variance in the ANOVA is _____.
MS
The numerator of the Tukey HSD test consists of:
the difference between two means.
If the cutoff q statistic is 3.68, with a p level of 0.05, which of the following would be significant?
HSD = 3.65
HSD = 4.35
F = 4.35
group mean difference = 3.65
HSD = 4.35
Analysis of variance (ANOVA) (p. 276)
Analysis of variance (ANOVA) is 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.
F statistic (p. 276)
The F statistic is a ratio of two measures of variance: (1) between-groups variance, which indicates differences among sample means, and (2) within-groups variance, which is essentially an average of the sample variances.
Between-groups variance (p. 276)
Between-groups variance is an estimate of the population variance, based on the differences among the means.
Within-groups variance (p. 276)
Within-groups variance is an estimate of the population variance, based on the differences within each of the three (or more) sample distributions.
one-way ANOVA (p. 277)
A one-way ANOVA is a hypothesis test that includes both one nominal independent variable with more than two levels and a scale dependent variable.
between-groups ANOVA (p. 277)
A between-groups ANOVA is a hypothesis test in which there are more than two samples, and each sample is composed of different participants.
within-groups ANOVA (p. 277)
A within-groups ANOVA is a hypothesis test in which there are more than two samples, and each sample is composed of the same participants; also called a repeated-measures ANOVA.
Homoscedastic (p. 278)
Homoscedastic populations are those that have the same variance; homoscedasticity is also called homogeneity of variance.
Heteroscedastic (p. 278)
Heteroscedastic populations are those that have different variances.
source table (p. 285)
A source table presents the important calculations and final results of an ANOVA in a consistent and easy-to-read format.
grand mean (p. 287)
The grand mean is the mean of every score in a study, regardless of which sample the score came from.
R2 (p. 294)
R2 is the proportion of variance in the dependent variable that is accounted for by the independent variable.
post hoc test (p. 294)
A post hoc test is a statistical procedure frequently carried out after the null hypothesis has been rejected in an analysis of variance; it allows us to make multiple comparisons among several means; often referred to as a follow-up test.
Tukey HSD test (p. 294)
The Tukey HSD test is 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.