Clarifying the Concepts
What are the four assumptions for a within-
What are order effects?
Explain the source of variability called “subjects.”
What is the advantage of the design of the within-
What is counterbalancing?
Why is it appropriate to counterbalance when using a within-
How do we calculate the sum of squares for subjects?
How is the calculation of dfwithin different in a between-
How could we turn a between-
What are some situations in which it might be impossible—
How is the calculation of effect size different for a one-
What is a matched-
Calculating the Statistics
For the following data, assuming a within-
Person | ||||
---|---|---|---|---|
1 | 2 | 3 | 4 | |
Level 1 of the independent variable | 7 | 16 | 3 | 9 |
Level 2 of the independent variables | 15 | 18 | 18 | 13 |
Level 3 of the independent variable | 22 | 28 | 26 | 29 |
dfbetween = Ngroups − 1
dfsubjects = n − 1
dfwithin = (dfbetween)(dfsubjects)
dftotal = dfbetween + dfsubjects + dfwithin, or dftotal = Ntotal − 1
SStotal = Σ(X − GM)2
SSbetween = Σ(M − GM)2
SSsubjects = Σ(Mparticipant − GM)2
SSwithin = SStotal − SSbetween − SSsubjects
The rest of the ANOVA source table for these data
The effect size
The Tukey HSD statistic for the comparisons between level 1 and level 3
For the following data, assuming a within-
Person | ||||||
---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | 6 | |
Level 1 | 5 | 6 | 3 | 4 | 2 | 5 |
Level 2 | 6 | 8 | 4 | 7 | 3 | 7 |
Level 3 | 4 | 5 | 2 | 4 | 0 | 4 |
dfbetween = Ngroups − 1
dfsubjects = n − 1
dfwithin = (dfbetween)(dfsubjects)
dftotal = dfbetween + dfsubjects + dfwithin, or dftotal = Ntotal − 1
SStotal = Σ(X − GM)2
SSbetween = Σ(M − GM)2
SSsubjects = Σ(Mparticipant − GM)2
SSwithin = SStotal − SSbetween − SSsubjects
The rest of the ANOVA source table for these data
The critical F value and your decision about the null hypothesis.
If appropriate, the Tukey HSD statistic for all possible mean comparisons
The critical q value; then, make a decision for each comparison in part (k)
The effect size
For the following incomplete source table below for a one-
Source | SS | df | MS | F |
---|---|---|---|---|
Between | 941.102 | 2 | — | — |
Subjects | 3807.322 | — | — | — |
Within | — | 20 | — | |
Total | 5674.502 | — |
Complete the missing information.
Calculate R2.
Assume that a researcher had 14 individuals participate in all three conditions of her experiment. Use this information to complete the source table below.
Source | SS | df | MS | F |
---|---|---|---|---|
Between | 60 | — | — | — |
Subjects | — | — | — | — |
Within | 50 | — | — | |
Total | 136 | — |
Applying the Concepts
Fear of dogs and one-
Person | ||||
---|---|---|---|---|
1 | 2 | 3 | 4 | |
Small dog | 7 | 16 | 3 | 9 |
Medium dog | 15 | 18 | 18 | 13 |
Large dog | 22 | 28 | 26 | 29 |
State the null and research hypotheses.
Determine whether the assumptions of random selection and order effects were met.
In Exercise 13.13, you calculated the effect size for these data. What does this statistic tell us about the effect of size of dog on fear levels?
In Exercise 13.13, you calculated a Tukey HSD test for these data. What can you conclude about the effect of size of dog on fear levels based on this statistic?
Chewing-
Person | |||||
---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | |
Gum 1 | 4 | 6 | 3 | 4 | 4 |
Gum 2 | 8 | 6 | 9 | 9 | 8 |
Gum 3 | 5 | 6 | 7 | 4 | 5 |
Gum 4 | 2 | 2 | 3 | 2 | 1 |
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Conduct all six steps of the hypothesis test.
Are any additional tests warranted? Explain your answer.
Pessimism and one-
Person | |||||
---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | |
Past | 18 | 17.5 | 19 | 16 | 20 |
Present | 18.5 | 19.5 | 20 | 17 | 18 |
Future | 22 | 24 | 20 | 23.5 | 21 |
Perform steps 5 and 6 of hypothesis testing. Be sure to complete the source table when calculating the F ratio for step 5.
If appropriate, calculate the Tukey HSD for all possible mean comparisons. Find the critical value of q and make a decision regarding the null hypothesis for each of the mean comparisons.
Calculate the R2 measure of effect size for this ANOVA.
Pessimism and one-
Person | |||||
---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | |
Past | 22 | 23 | 25 | 24 | 26 |
Present | 25 | 26 | 27 | 28 | 29 |
Future | 24 | 27 | 26 | 28 | 29 |
Perform steps 5 and 6 of hypothesis testing. Be sure to complete the source table when calculating the F ratio for step 5.
If appropriate, calculate the Tukey HSD for all possible mean comparisons. Find the critical value of q and make a decision regarding the null hypothesis for each of the mean comparisons.
Calculate the R2 measure of effect size for this ANOVA.
Wagging tails and one-
Dog Participant | Owner | Cat | Other Dog |
---|---|---|---|
1 | 69 | 28 | 45 |
2 | 72 | 32 | 43 |
3 | 65 | 30 | 47 |
4 | 75 | 29 | 45 |
5 | 70 | 31 | 44 |
Memory, post hoc tests, and effect size: Luo, Hendriks, and Craik (2007) were interested in whether people might better remember lists of words if the lists were paired with either pictures or sound effects. They asked participants to memorize lists of words under three different learning conditions. In the first condition, participants just saw a list of nouns that they were to remember (word-
Source | SS | df | MS | F |
---|---|---|---|---|
Between | 0.177 | 2 | 0.089 | 8.900 |
Subjects | 0.002 | 3 | 0.001 | 0.100 |
Within | 0.059 | 6 | 0.010 | |
Total | 0.238 | 11 |
Is it appropriate to perform post hoc comparisons on the data? Why or why not?
Use the information provided in the ANOVA table to calculate R2. Interpret the effect size using Cohen’s conventions. State what this R2 means in terms of the independent and dependent variables used in this study.
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Wagging tails, hypothesis-
Source | SS | df | MS | F |
---|---|---|---|---|
Between | 58.133 | 2 | 29.067 | 0.066 |
Subjects | 642.267 | 4 | 160.567 | 0.364 |
Within | 532.533 | 8 | 441.567 | |
Total | 4232.933 | 14 |
Pilots’ mental efforts and a one-
What is the independent variable in this study?
What are the dependent variables in this study?
Explain why the researchers were able to use a one-
η2 is roughly equivalent to R2. How large are each of these effects, based on Cohen’s conventions?
The researchers drew a specific conclusion beyond that there was some difference, on average, in the dependent variables, depending on the particular levels of the independent variable. What additional test were they likely to have conducted? Explain your answer.
Putting It All Together
Eye glare, football, and one-
Person | Black Grease | Antiglare Stickers | Petroleum Jelly |
---|---|---|---|
1 | 19.8 | 17.1 | 15.9 |
2 | 18.2 | 17.2 | 16.3 |
3 | 19.2 | 18.0 | 16.2 |
4 | 18.7 | 17.9 | 17.0 |
What is the independent variable? What are its levels?
What is the dependent variable?
What kind of ANOVA is this?
What is the first assumption for ANOVA? Is it likely that the researchers met this assumption? Explain your answer.
What is the second assumption for ANOVA? How could the researchers check to see if they had met this assumption? Be specific.
What is the third assumption for ANOVA? How could the researchers check to see if they had met this assumption? Be specific.
What is the fourth assumption, specific to the within-
Perform steps 5 and 6 of hypothesis testing. Be sure to complete the source table when calculating the F ratio for step 5.
If appropriate, calculate the Tukey HSD for all possible mean comparisons. Find the critical value of q and make a decision regarding the null hypothesis for each of the mean comparisons.
Calculate the R2 measure of effect size for this ANOVA.
How could this study be conducted using a between-
How could this study be conducted using a matched-
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