ANSWER ALL QUESTIONS
| 1. | Assume it takes participants an average of 180 seconds to eat a vanilla ice cream cone and it takes different participants an average of 220 seconds to eat a chocolate ice cream cone. |
| a. | Conceptually, what does a 95% percent confidence interval for the vanilla cone consumption time mean? (10 marks) |
| b. | Specify (i.e. make up) a 95% confidence interval for the vanilla cone times and a separate 95% confidence interval on the chocolate cone times consistent with the plausible conclusion that the mean consumption times for these two conditions are significantly different. (10 marks) |
| 2. | The following two sets of ANOVA results are both from single factor designs where that factor had 4 levels, and the experimental manipulations in both designs were the same. |
| a. | How many conditions did these designs have? (2 marks) |
| b. | For the between-participants ANOVA, how many degrees of freedom were there for the between groups variability? (2 marks) |
| c. | For the within-participants ANOVA, how many degrees of freedom were there for the within groups variability? (2 marks) |
| d. | Would you reasonably expect the p value for the within-participants ANOVA to be bigger or smaller than the p value for the between-participants ANOVA AND why? (4 marks) |
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| e. | What is a plausible reason for the mean between group variability to be the same, 100.867, in both the between-participant and the within-participant ANOVA results AND why is this situation fairly strange? (6 marks) |
| f. | Which assumptions of the between-participant and within-participant ANOVA’s used here are the same? (4 marks) |
| 3. | A psychologist was interested in influences on psychological well-being during COVID-19 lockdown. In particular, she assessed sending daily messages to participants’ smart phones for a two week period that were either funny video clips (laughing babies, etc.), videos of short mindfulness exercises (breathing, attention, etc.), short videos of stretching exercises or neutral videos (daily weather reports, how to change the oil on a car, etc.). In addition, she manipulated when participants got the videos, in the morning or in the evening. The key measure of well-being was a judgment following each video of how good the participant felt on a scale from -10, “I feel really awful”, to +10, “I feel really great” where 0 is “I feel neutral”. A given participant always received the same kind of video across days but never the same video twice. In addition, a given participant always received videos at the same time of day and made a total of 14 judgments. The researcher was not interested in assessing differences between videos of a given kind (e.g. not interested in differences between laughing baby versus people falling down videos), so she averaged together a given participant’s 14 judgments to get their average well-being score and did her analyses based on these participant averages. |
| a. | Why is this a between-participant design even though participants all gave multiple well-being ratings? (4 marks) |
| b. | How many conditions did this experiment have? (2 marks) |
| c. | Specify all the relevant factors for an ANOVA based on this design. (4 marks) |
| d. | Draw a summary graph (by hand is fine) with error bars of what data from this scenario might look like if participants’ well-being was significantly higher in the evening than the morning but nothing else was significant. (6 marks) |
| e. | What would the potential advantages and disadvantages have been if the researcher had set up this experiment as a within-participants? (4 marks) |
| 4. | |
| a. | For a simple regression, describe the relationship between the sum of squares of the residuals, the sum of squares of model and the total sum of squares of the dependent variable. Further, describe how these measures can be used to generate a measure of correlation. If a regression was conducted on data that showed a perfect negative correlation (r = -1.0) then describe the relationship you would expect between the sum of squares for the model and the total sum of squares of the dependent variable. (10 marks) |
| b. | A researcher predicts that the relationship between an independent variable and a dependent variable will follow a ‘U’-shaped function. Describe the steps that s/he could take to investigate the presence of such a curvilinearity. How might the expected minimum of the fitted function be found? (10 marks) |
| 5. | A study looked at the correlations between parental educational level (coded in number of years of education for fathers ‘YearsDad’ and number of years of education for mothers ‘YearsMom’) and a person’s educational achievement at age 18 labelled ‘Outcome’. The sample included 1000 people (550 males and 450 females). The SPSS output below is from a linear regression.
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| Explain how it is that the ANOVA is significant but neither predictor is significant (α = 0.05). ALSO, explain what can be concluded from the output. [The critical value for r = 0.0619 when N = 1000]. (20 marks) | |
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