RESEARCH METHODS F/ BEHAV.(LL)-W/MINTAP
6th Edition
ISBN: 9781337755016
Author: GRAVETTER
Publisher: CENGAGE L
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Chapter 11.2, Problem 2LO
Define a main effect for one factor and an interaction between factors, and be able to identify main effects and interactions in the results from a two-factor design.
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Students have asked these similar questions
A two-factor research study is used to evaluate the effectiveness of a new blood-pressure medication. In this two-factor study, factor A is medication versus no medication and factor B is male versus female.
The medicine is expected to reduce blood pressure for both males and females, but it is expected to have a much greater effect for males. What pattern of results should be obtained if the medication works as predicted?
A significant main effect for factor A (medication)
A significant interaction
A significant main effect for factor A and a significant interaction
An insignificant main effect for factor A (medication)
In a two factor factorial design with two design factors A and B, why do we generally include the interaction term in the model? What is the major concern if the model ignores the interaction effect?
A researcher wants to see if gender and / or income affects the total amount of help given to a stranger who is sitting on the side of a busy road with a sign asking for help. The independent variables are gender, income, and the interaction of gender and income. The dependent variable is total help. He wants to know if one or both factors – or the interaction of the two - affects the total amount of help offered. Because he is analyzing two independent variables (gender and income), he used a factorial ANOVA. His results show the main effect of each of the independent variables on the dependent variable (total help) and the interaction effect. The researcher is using a 95% confidence interval which means that he wants to be at least 95% sure that his independent variables affected total help if he rejects the null hypothesis. Below is the data set followed by the results:
Chapter 11 Solutions
RESEARCH METHODS F/ BEHAV.(LL)-W/MINTAP
Ch. 11.1 - Define a factorial research design, including the...Ch. 11.2 - Define a main effect for one factor and an...Ch. 11.2 - Explain how the existence of an interaction can...Ch. 11.2 - Describe and explain the independent relationship...Ch. 11.3 - Explain how a factorial study can combine...Ch. 11.3 - Identify the statistical analyses that are...Ch. 11.4 - Describe three specific applications of the...Ch. 11 - In addition to the key words, you should also be...Ch. 11 - In a classic study, Shrauger (1972) examined the...Ch. 11 - Suppose a researcher conducts a two-factor study...
Ch. 11 - The following matrix represents the results (the...Ch. 11 - The following data show the pattern of results...Ch. 11 - Explain why the main effects in a factorial study...Ch. 11 - Explain what is meant by the concept that main...Ch. 11 - In Figure 11.5, we show three combinations of main...Ch. 11 - For a two-factor research study with two levels...Ch. 11 - A researcher would like to use a factorial study...Ch. 11 - A two-factor analysis of variance is used to...Ch. 11 - A researcher has demonstrated that a new...
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- Write a report of the different research design with exceptional of experimental research design.arrow_forwardPlease look at the picture and explain all three examples (a, b, c). Explain what is the main effect of factor A and factor B and why do we have/do not have interaction in each examplearrow_forwardThe Minister of National Security in Trinidad and Tobago is interested in determining the factors that influence the number of crimes that are reported. You are tasked to develop a model using the appropriate variables. The following variables are utilized: X1 = total overall reported crime rate per 100,000 residents X2 = reported violent crime rate per 100,000 residents X3 = % of people 25 years+ with 4 yrs. of high school X4 = % of 16 to 19-year-olds not in high school and not high school graduates. X5 = % of 18 to 24-year-olds in college X6 = % of people 25 years+ with at least 4 years of college X1 X2 X3 X4 X5 X6 478 184 74 11 31 20 494 213 72 11 43 18 643 347 70 18 16 16 341 565 71 11 25 19 773 327 72 9 29 24 603 260 68 8 32 15 484 325 68 12 24 14 546 102 62 13 28 11 424 38 69 7 25 12 548 226 66 9 58 15 506 137…arrow_forward
- The Minister of National Security in Trinidad and Tobago is interested in determining the factors that influence the number of crimes that are reported. You are tasked to develop a model using the appropriate variables. The following variables are utilized: X1 = total overall reported crime rate per 100,000 residents X2 = reported violent crime rate per 100,000 residents X3 = % of people 25 years+ with 4 yrs. of high school X4 = % of 16 to 19-year-olds not in high school and not high school graduates. X5 = % of 18 to 24-year-olds in college X6 = % of people 25 years+ with at least 4 years of college X1 X2 X3 X4 X5 X6 478 184 74 11 31 20 494 213 72 11 43 18 643 347 70 18 16 16 341 565 71 11 25 19 773 327 72 9 29 24 603 260 68 8 32 15 484 325 68 12 24 14 546 102 62 13 28 11 424 38 69 7 25 12 548 226 66 9 58 15 506 137 60 13…arrow_forwardConsider a two factor factorial design with two design factors A and B. The significance of each of the main and interaction effects may be examined by an F-test. Explain why those F-tests are all one-sided tests.arrow_forwardA study was conducted to assess the influence of various factors on the start of new firms in the computer chip industry. For a sample of 70 countries the following model was estimated: ŷ = -59.31 + 4.983x1 + 2.198x2 + 3.816x3 – 0.310x4 (1.156) (0.210) (2.063) (0.330) -0.886x5 + 3.215x6 + 0.85x7 (3.055) (1.568) (0.354) R2 = 0.766 where ŷ = new business starts in the industry X1 = population in millions X2 = industry size x3 = measure of economic quality of life measure of political quality of life measure of environmental quality of life measure of health and educational quality of life X4 X5 X6 = x7 = measure of social quality of life The numbers in parentheses under the coefficients are the estimated coefficient standard errors. (a) Determine which coefficients in the model are statistically significant? Provide a justification for your answer. (b) Is the overall regression equation statistically significant at the 1% level? Justify your answer.arrow_forward
- A research has been conducted to determine the factors affecting the tax return preparation period. Accordingly, Y = b0 + b1x1 + b2x2 + b3x3 + b4x4+ ε model containing 4 independent variables was created. 40 accountants were interviewed and the following results were reached: y = 17,2 + 3,8x1 – 1,04x2 + 2,15x3 + 15,1x4 y : Tax filing preparation time (minutes) x1: Income of individuals ($ 1000) x2: Age of individuals x3: Number of people living in the household x4: 1 if individuals are hosts, 0 if not = 5.3, = 0.13, = 0.33, = 1.51, = 4.7, R2 = 0.45. d) Test the zero hypothesis, expressed as b1 = b2 = b3 = b4 = 0, at the level of significance α = 0.01. Interpret the results? already a expert solved first three part can you help me with Darrow_forwardA research has been conducted to determine the factors affecting the tax return preparation period. Accordingly, Y = b0 + b1x1 + b2x2 + b3x3 + b4x4+ ε model containing 4 independent variables was created. 40 accountants were interviewed and the following results were reached: y = 17,2 + 3,8x1 – 1,04x2 + 2,15x3 + 15,1x4 y : Tax filing preparation time (minutes) x1: Income of individuals ($ 1000) x2: Age of individuals x3: Number of people living in the household x4: 1 if individuals are hosts, 0 if not = 5.3, = 0.13, = 0.33, = 1.51, = 4.7, R2 = 0.45. a) Interpret the estimate ? b) interpret the value of R2 c) Whether the coefficient of ?4 is different from 0, by creating the relevant hypotheses, testing at the level of α = 0.01 significance Please. Interpret the results d) Test the zero hypothesis, expressed as ?1 = ?2 = ?3 = ?4 = 0, at the level of significance α = 0.01. Interpret the resultsarrow_forwardIf a researcher found a significant interaction between Factor A and Factor B, what does this mean (in general)? O Both Factor A & Factor B have independent effects. O The effect of Factor A on the dependent variable depends on the level of Factor B. O Only Factor A is significant. none of the above.arrow_forward
- Explain why a 3 way interaction will have more regression lines than a 2 way interaction.arrow_forwardA student was interested in the impact of nutrition and exercise on mental health. She recruited a sample of 80 individuals. She divided the participants into 4 groups. One group was a control group. There was no treatment for this group. The second group was the diet group. These participants followed a strict diet that was designed by a dietitian. The nutrients in the diet were optimized for each individual. The third group was an exercise group. These participants worked with a personal trainer on an individualized exercise plan. The fourth group was the exercise and diet group. This group had both the dietitian and personal trainer intervention. After 3 weeks of treatment (or control), She measured their mental health with the Warwick-Edinburgh Mental Well-being Scale (WEMWBS). Some of the information is included in the ANOVA table below but I spilled a coffee on the output and the student already deleted the raw data...oh, no!! Given the ANOVA table below, what is the F-statistic?…arrow_forwardA researcher wants to see if gender and/or income affect the total amount of help given to a stranger who is sitting on the side of a busy road with a sign asking for help. The independent variables are gender, income, and the interaction of gender and income. The dependent variable is total help. He wants to know if one or both factors – or the interaction of the two - affect the total amount of help offered. Because he is analyzing two independent variables (gender and income), he used a factorial ANOVA. His results show the main effect of each of the independent variables on the dependent variable (total help) and the interaction effect. The researcher is using a 95% confidence interval which means that he wants to be at least 95% sure that his independent variables affected total help if he rejects the null hypothesis. Is there significance for either gender or income?arrow_forward
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