
5. (a) Consider a hypothetical two-way layout with three factors (A, B, C) each at two levels (I,...
Lesson: -Factorial designs have more than one independent variable or factors. -A two way factorial design has two independent variables, a three-way factorial design has three independent variables and so forth. -A 2x2 design has two factors and two levels of each. -A 2x3 design also has two factors but one has two levels and one has three. -A 3x3 design has two factors and each factor has 3 levels. Each example has 2 independent variables or factors. Comparison of...
Consider the following hypothetical outcome of a three-way
factorial design.
Draw a line graph for each of the two-way interactions (i.e.,
AxB, AxC, BxC) and label each point in the graphs with its data
value—you MUST show the numbers used in the graph.
[Remember: marginal means are NOT graphed; this problem requires
collapsing across the third variable…]
Question 71 (4 points)
Show the cell means and graph for the 2-way AxB
interaction.
Part A:For a three-way factorial ANOVA, how many interactions will be included in the ANOVA table? A. 6 B. 5 C. 7 D. 4 E. 3 Part B: In ANOVA, the interaction of two variables is certainly present when A. the difference between means across levels of one variable varies across levels of the other variable. B. the two variables are negatively correlated. C. the two variables are positively correlated. D. the main effects do not account for all of...
Saved Help Consider the following partially completed two-way ANOVA table. Suppose there are 5 levels of Factor A and 4 levels of Factor B. The number of replications per cellis 3. Use the 0.01 significance level. (Hint: estimate the values from the Ftable.) 1. Complete an ANOVA table. (Round MS and Fto 2 decimal places.) Source MSF Factor A Factor B Interaction 2. Find the critical values to test for equal means. (Round your answers to 2 decimal places.) Critical...
Consider the following partially completed two-way ANOVA table. Suppose there are four levels of Factor A and two levels of Factor B. The number of replications per cell is 4. Use the 0.01 significance level. (Hint: Estimate the values from the Ftable.) a. Complete an ANOVA table. (Round MS and Fto 2 decimal places.) ANOVA SS df MS F Source Factor A 70 3 1.40 Factor B 50 11 23.33 50.00 70.00 3.00 Interaction 210 3 4.20 Error 24 16.67...
just for part b c e
Consider the following experiment of the effects of eight factors on the taste of a 1985 Pinot Noir, as assessed by a panel of five experts. Each expert ranked the sixteen samples of wine, with rank "1" denoti the best and "16" the worst. The final outcome for a treatment- level combination is the average rank for that particular wine over all the experts, which we shall treat as a continuous outcome. Descriptions of...
Consider a two-way analysis of variance experiment with treatment factors A and B. The results are summarized below. Source of Variation df SS Factor A 4 86 Factor B 5 75 Interaction 20 75 Error 90 300 Total 119 536 What are the levels of factor A and factor B?
For Problems 9 and 10: In a three-factor experiment suppose that factor A has 3 levels, factor B has 2 levels, and factor C has 3 levels. Also, for each of the combination of levels of the factors, 3 observations were measured. The researcher fitted the full model with main effects, all two-factor interactions, and all three-factor interactions. 9. How many possible treatments are there? A. 8 B. 11 C. 18 D. 54 10. If all treatments were applied, what...
For the following scenario, identify the design (e.g,. two-way independent), name the factors, name the levels name the dependent variable, give the # of cells, give the # of possible simple effects, and total N. An educational psychologist is studying student motivation in elementary school. She follows males and females from urban and rural communities for three years, from grades 4 to 6 (n=5). Each year, they complete a questionnaire measuring their motivation and enthusiasm for school.
3. Consider the two-factor model with interaction Suppose that there are a and b levels of the factors respectively. Now consider the set of equations (a) Show that the equations are not redundant. (b) Show that these equations are equivalent to the hypothesis of no interaction. (c) Thereby calculate the rank of the hypothesis of no interaction. (d) Show that the hypothesis is testable, provided there exists at least one sample from each combination of factor levels.