Chapter 11
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
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 hours of sleep, or 8 hours of sleep. Leo measures how many calories are consumed by the student in the sleep lab, which is stocked with various food items. After collecting the data, Leo performs an ANOVA and finds that he can reject the null hypothesis. On the basis of this, what does Leo know?
He knows that there is a difference among the groups somewhere, but he does not know where
Heteroscedastic (p. 278)
Heteroscedastic populations are those that have different variances.
Homoscedastic (p. 278)
Homoscedastic populations are those that have the same variance; homoscedasticity is also called homogeneity of variance.
The symbol for variance in the ANOVA is _____.
MS
F is obtained by dividing _____ by _____.
MSbetween; MSwithin
The measure of effect size calculated for ANOVA is _____.
R2
_____ can be interpreted as the proportion of variance in the dependent variable that is accounted for by the independent variable.
R2
R2 (p. 294)
R2 is the proportion of variance in the dependent variable that is accounted for by the independent variable.
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)
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
A researcher reports that dfbetween = 4 and dfwithin = 20. How many treatment conditions are in this study?
5 FORMULA: df between 4+1=5
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 has a mean score of 76, the average IQ group has a mean score of 80, and the high IQ group has a mean score of 74, and each of his samples consists of 10 individuals. What is the Tukey HSD value for the comparison of average IQ individuals to low IQ individuals?
8.73 (M1-M2)/√ (MSwithin/N)
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.
The F ratio is a ratio of:
There is only one independent variable.
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)
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.
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.
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
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 instruction groups: (1) complete the exam as quickly as possible, (2) complete the multiple choice before the short answers and essays, or (3) complete the short answers and essays before the multiple choice. If Tiffany averages the scores for each instruction group and then compares them, any differences in the means of the instruction groups reflect:
between-groups variance.
There is a different F distribution for every:
combination of sample size and number of samples.
Ultimately, having less variability within-groups will:
make it easier to reject the null hypothesis.
Changes in within-groups variance result in changes in the _____ of the F ratio.
denominator
The F is calculated by:
dividing a measure of between-groups variability by a measure of within-groups variability.
If you calculate an F statistic and find that it is smaller than your critical value, you would:
fail to reject the null hypothesis.
Reducing within-groups variability will impact the F ratio by making it:
larger.
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
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 eighth semester. Students in their first semester have an average score of 56.5, students in their fifth semester have an average score of 58, and students in their eighth semester have an average score of 60. Given MSwithin= 82, what is the Tukey HSD value for the comparison between first-semester students and eighth-semester students?
-3.87 FORMULA: SM= √ (MS within/N) HDS = (M1 - M2) / sm
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 has a mean score of 76, the average IQ group has a mean score of 80, and the high IQ group has a mean score of 74, and each of his samples consists of 10 individuals. What is the Tukey HSD value for the comparison of high IQ individuals to average IQ individuals?
-13.09 FORMULA:
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 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.
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.
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.
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.
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.
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.
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.
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
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
Between-groups variance (p. 276)
Between-groups variance is an estimate of the population variance, based on the differences among the means.
In addition to the sources of variability calculated for a between-subjects ANOVA, the within-subjects ANOVA also calculates:
SSsubjects.
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.
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.
grand mean (p. 287)
The grand mean is the mean of every score in a study, regardless of which sample the score came from.
The grand mean is the:
mean of all the scores in the study, regardless of the condition.
By convention, an R2 value of 0.05 would be considered:
medium.
Within-groups degrees of freedom is calculated by:
multiplying the between-groups degrees of freedom by the subjects degrees of freedom.
Changes in between-groups variance result in changes in the _____ of the F ratio
numerator
With two groups, the square root of F is equal to _____.
t
A post hoc test is warranted when:
the F is significant and we have more than two groups.
Within-groups variance reflects:
the amount of difference between means that we would expect to occur by chance alone.
The numerator of the Tukey HSD test consists of:
the difference between two means.
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
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.
The F ratio in ANOVA is a ratio of:
two estimates of population variance
When F is significant:
we do not know which specific means differ significantly
A measure of variability that is essentially an average of the sample variances is:
within-groups variance
The F statistic increases when:
within-groups variance decreases and between-groups variance increases
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 instruction groups: (1) complete the exam as quickly as possible, (2) complete the multiple choice before the short answers and essays, or (3) complete the short answers and essays before the multiple choice. Obviously, even in a single instruction group, not all students will obtain the same exam score. These differences in an instruction group reflect:
within-groups variance.