Posted: December 16th, 2022

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Part 1

- A variable that has a relationship with (in terms of covariance), or has the potential to be related to the outcome variable we’ve measured, is
- Which of the following sentences best describes a covariate?
- Which of the following assumptions must be met when conducting an ANCOVA?
- ANCOVA is:
- What are the two main reasons for including covariates in ANOVA?
- In the context of analysis of covariance, this is the value of the group mean adjusted for the effect of the covariate.
- A researcher is interested in examining individuals’ attitudes toward three computer programs. Each participant rates one of three programs. The researcher controls for previous experience with computers. This could utilize:
- Participants were randomly allocated to one of two stress management therapy groups, or a waiting list control group. Their baseline levels of stress were measured before treatment, and again after 3 months of weekly therapy sessions. The researcher decided to run an ANCOVA on her data. What was the covariate?
- A health psychologist was interested in the effects of vitamin supplements on the immune system. Three groups of adults were exposed (in a highly ethical way) to the cold virus; one group took no supplements for a week before exposure, another had vitamin C supplements, and a third had multivitamins (excluding C). The severity of the cold was measured as a percentage (0% = not contracted, 100% = very severe symptoms). The psychologist also measured the number of cigarettes that each person smoked per day, as smoking suppresses the immune system. The psychologist was interested in the differences in the severity of the illnesses across different vitamin groups accounting for cigarette usage. What technique should be used to analyze these data?
- You are conducting a study. The IV is attachment style. There are three groups of individuals with different attachment styles; these are secure, dismissing, and fearful. You want to explore whether these differ on their scores of relationship satisfaction. The DV is relationship satisfaction. You are aware, however, that relationship satisfaction is known to covary with depression. You conduct an ANCOVA with this data. The formula will remove the variance due to the association between which two variables?
- Imagine we wanted to investigate the effects of three different conflict styles (avoiding, compromising and competing) on relationship satisfaction, but we discover that relationship satisfaction is known to covary with self-esteem. Which of the following questions would be appropriate for this analysis?

Part 2

A marketing manager was interested in the therapeutic benefit of certain soft drinks for curing hangovers. He took **15 people** out on the town one night and got them drunk. The next morning as they awoke, feeling dehydrated, he gave five of them water to drink, five of them Lucozade (a very nice glucose-based UK drink) and the remaining five a leading brand of cola (this variable is called **drink**). He measured how well they felt (on a scale from “0 = I feel like death” to “10 = I feel really full of beans and healthy”) two hours later (this variable is called **well**). He wanted to know which drink produced the greatest level of wellness. However, he realized it was important to control for how drunk the person got the night before, and so he measured this on a scale of “0 = as sober as a nun” to “10 = flapping about like a haddock out of water on the floor”(this variable is called **drunk**). The data are in the file HangoverCure.sav under **Resources for Quizzes >> Quiz 4**. Conduct an ANCOVA to see whether people felt better after different drinks when controlling for how drunk they were the night before. Let’s identify type of variables in the data to conduct data analyses.

Let’s run an ANOVA WITHOUT the covariate using the HangoverCure.sav in SPSS. You will have the SPSS output as below when the covariate is not included.

Before including a covariate in an analyses, we should check that the covariate is independent from the experimental manipulation (NO INTERACTION). In this case, we need to check out that the proposed covariate (CV) is roughly equal across the levels of our independent variable (IV). We can test this by running an ANOVA using SPSS, with the proposed covariate (CV) as the outcome and the independent variable (IV) as the predictor. You will have the SPSS output as below that shows the results of the one-way ANOVA.

Next, we can conduct the ANCOVA in SPSS: [Analyze] – [General Linear Model] – [Univariate…].

· First, specify the variables for Dependent Variable (DV), Fixed Factor(s) (IV), and Covariate(s).

· Second, click on [Options] to assess the Options dialog box. Then, check on Descriptive Statistics, Estimates of effect size, Parameter Estimates, and Homogeneity tests.

· Next, click on [Contrasts…] to assess the Contrasts dialog box. Then, Change the type of contrast from None to Simple, and Change Reference Category from Last (which is default) to First.

· Finally, click on [Continue] to return to the main dialog box and click on [OK] in the main dialog box to run the ANCOVA.

· Among the tables in the SPSS output, what does Leven’s Test of Equality for Error Variances inform us?

According to the ANCOVA table below, which of the following statements **best** reflects what the effect of the type of **drink **tells us?

According to the ANCOVA table below, which of the following statements **best** reflects what the effect of drunkenness tells us?

The SPSS output below shows the Parameter Estimates that are calculated using a regression analysis with **drink **split into two dummy coding variables. Here, the beta values literally represent the differences between the means of the drink groups and so the significances of the *t*-tests tell us whether the group means differ significantly. First, identify which drink was coded as a reference group in the comparisons.

Based on the SPSS output below on the Parameter Estimates, we can conclude as below.

The SPSS output below shows the descriptive statistics and the adjusted values of the group means. **While the descriptive statistics shows no mean differences in X and Y drink groups, the adjusted means show that the significant ANCOVA reflects a difference between the X and Z groups.**

The SPSS output below also shows the effect sizes in terms of partial eta squared calculated using sums of squares for the effect of drink, drunk, and the error. Now we can report the main findings as follows. Report **three decimal places** for * F*,

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