Exam 14: One-Factor Fixed-Effects Ancova With Single Covariate

If the dependent variable, math score (Y), is about the same for persons with higher scores in writing (X) and for those with lower scores in writing, one would expect that

A market researcher wanted to know whether different package designs for the same yogurt product would affect consumers' purchase intention. There were four different versions of package designs. Each package was viewed by eight participants, who then rated their likelihood to purchase the product. A one-factor ANCOVA was used to analyze the data where the covariate was the participants' liking of the yogurt product in general. Complete the following ANCOVA summary table ( $\alpha$ = .05): Source SS df MS F Critical Value Decision Between adjusted 10.5 - - - - - Within adjusted - - - Covariate - - 5.6 - - - Total 35 -

In ANCOVA, suppose Y is the dependent variable, X is the covariate, and the factor has two levels. Also all assumptions of ANCOVA are met. Which of the following situations is the most desirable?

In which of the following situations is the assumption of linearity violated?

A researcher wanted to examine whether people remembered information better with auditory cues or with visual cues. Ten participants were randomly assigned to each of the two groups: one group heard a list of words from headphones, and the other group saw the same list of words from a screen. The participants were then asked to write down as many words as they could remember. The dependent variable was the number of words remembered. -Suppose out of budget concerns, the researcher included only five participants in each group, tested each participant twice, and used each time as separate observations. It seems likely that

A researcher wanted to examine whether people remembered information better with auditory cues or with visual cues. Ten participants were randomly assigned to each of the two groups: one group heard a list of words from headphones, and the other group saw the same list of words from a screen. The participants were then asked to write down as many words as they could remember. The dependent variable was the number of words remembered. -For which of the following situations is it appropriate to use ANCOVA?

A researcher wanted to examine if soil type had any effects on the heights of daylilies (Y). The thickness of the soil (X) in the pot was used as the covariate X. Given the data that follow, where there are three types of soil (n = 10 in each group), (a) calculate the adjusted mean values assuming that b_w = 0.5, and (b) determine what effects the adjustment had on the posttest results. soil type heights of daylilies (Y) thickness of soil 1 =20 =21 2 =25 =18 3 =30 =15

Mike wanted to examine whether people remembered information better with auditory cues or with visual cues. He recruited 14 participants and randomly assigned seven participants to each of the two groups: one group heard a list of words from headphones, and the other group saw the same list of words from the screen. The participants were then asked to write down as many words as they could remember. The dependent variable was the number of words correctly remembered (Y), and the covariate was the participants' score on a memory test (X) administered before the experiment. Using the data below, conduct an ANOVA on Y, an ANCOVA on Y using X as a covariate, and compare the results ( $\alpha$ = .05). Determine the unadjusted and adjusted means. Auditory cue (headphone) X Y 80 10 75 9 95 16 60 4 70 11 65 8 90 15 Visual cue (screen) X Y 75 13 90 20 65 8 70 9 80 15 85 13 75 12

based on the following scenario: A researcher wanted to examine if soil type had any effects on the heights of daylilies. Ten bulbs of daylilies were planted in each of the three different types of soil. The thickness of the soil (X) was also measured for each pot. After three months, the heights of the plants (Y) were measured. Below are the group means of the study. soil type n heights of daylilies (Y) thickness of soil (X) 1 10 =20 =21 2 10 =25 =18 3 10 =30 =15 -If the correlation between X and Y is 0.5 for soil type 1, 0.1 for soil type 2, and -0.5 for soil type 3, it seems likely that

based on the following scenario: A researcher wanted to examine if soil type had any effects on the heights of daylilies. Ten bulbs of daylilies were planted in each of the three different types of soil. The thickness of the soil (X) was also measured for each pot. After three months, the heights of the plants (Y) were measured. Below are the group means of the study. soil type n heights of daylilies (Y) thickness of soil (X) 1 10 =20 =21 2 10 =25 =18 3 10 =30 =15 -If ANCOVA is used, which group will have the highest adjusted mean height?