Research Methods for the Behavioral Sciences
5th Edition
ISBN: 9780357231913
Author: Frederick J Gravetter; Lori-Ann B. Forzano
Publisher: Cengage Limited
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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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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:
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Chapter 11 Solutions
Research Methods for the Behavioral Sciences
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 - Under what circumstances will the main effects in...Ch. 11 - Prob. 7ECh. 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 - Prob. 1EACh. 11 - In Figure 11.5, we show three combinations of main...
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- 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_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_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. 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_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. 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 survey of high school students was done to examine whether students had ever driven a car after consuming a substantial amount of alcohol (1=yes, 0=no). Data was collected on their sex (male/female), race (White/non-White), and grade level (9,10,11,12). Researchers realized that the impact of race on consuming alcohol before driving might vary by grade level and decided to fit the following model. Variable Coding = 1 if Intercept Sex () Female Race () Black Grade level ( 9th grade 10th grade 11th grade [Reference = 12th grade] Attached is the logistic model 1. Compute the OR of drinking before driving for students who self-reported as Black versus non-Black in the 9th grade, adjusting for gender. 2. Compute the OR of drinking before driving for students who self-reported as Black versus non-Black in the 12th grade, adjusting for gender. 3. Compute the OR of drinking before driving for someone in the 9th grade versus 12th grade for a student who…arrow_forward
- Explain why a 3 way interaction will have more regression lines than a 2 way interaction.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_forwardExplain, in your own words: What is the purpose of a control matrix?arrow_forward
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