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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...
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 ...
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?...
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...
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...
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...
Consider the following experiment of the effects of eight factors on the taste of a 1985 Pinot No...
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...
For the following scenario, identify the design (e.g,. two-way independent), name the factors, name the levels...
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.
Transistor Manufacturing Study: A transistor manufacturer conducted an experiment to investigate the effects of three factors...
Transistor Manufacturing Study: A transistor
manufacturer conducted an experiment to investigate the effects of
three factors on PRODUCTivity (measured in thousands of dollars of
items produced) per 40-hour week. The factors were as follows:
Length of work week in DAYS (two levels): Five consecutive
8-hour days or four consecutive 10-hour days
SHIFT (two levels): day or evening shift
Number of coffee BREAKS (three levels): 0, 1, or 2
The experiment was conducted over a 24-week period with the 2 ×...
3. Consider the two-factor model with interaction Suppose that there are a and b levels of...
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.
1.- Consider an experiment with two factors: Instructors (3 levels) and Teaching Methods (2 level...
1.- Consider an experiment with two factors: Instructors (3 levels) and Teaching Methods (2 levels). Each instructor teaches a topic using each of the two methods, say A and B. The response is the mean score in each of the six cells. Draw a plot of the mean scores under the following different situations: (a) method B is much better than method A (better means 3 times higher scores) but without noticeable difference from instructor to instructor. (b) method B...
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.
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...
Transistor Manufacturing Study: A transistor
manufacturer conducted an experiment to investigate the effects of
three factors on PRODUCTivity (measured in thousands of dollars of
items produced) per 40-hour week. The factors were as follows:
Length of work week in DAYS (two levels): Five consecutive
8-hour days or four consecutive 10-hour days
SHIFT (two levels): day or evening shift
Number of coffee BREAKS (three levels): 0, 1, or 2
The experiment was conducted over a 24-week period with the 2 ×...
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.
1.- Consider an experiment with two factors: Instructors (3 levels) and Teaching Methods (2 levels). Each instructor teaches a topic using each of the two methods, say A and B. The response is the mean score in each of the six cells. Draw a plot of the mean scores under the following different situations: (a) method B is much better than method A (better means 3 times higher scores) but without noticeable difference from instructor to instructor. (b) method B...
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