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Chapter 12 Factorial Designs 12.1 Factorial Designs 1) Factorial designs include A) one independent variable. B) at least three independent variables. C) two or more independent variables. D) as many factors as there are extraneous variables. Answer: C Rationale: Factorial designs involve the manipulation of two or more independent variables, allowing researchers to study the main effects of each variable as well as their interactions. 2) If two independent variables have an effect on each other in a factorial research design, we are primarily concerned about their A) contradictory cohort effect. B) interactive effect. C) cohort effect. D) None of the above. Answer: B Rationale: In factorial designs, when two independent variables have an effect on each other, we are primarily concerned about their interactive effect, which refers to how the effects of one variable change depending on the level of the other variable. 3) In factorial designs, the independent variables are called A) matrices. B) factorials. C) factors. D) cohort variables. Answer: C Rationale: In factorial designs, the independent variables are referred to as factors. These factors represent the variables that are manipulated to observe their effects on the dependent variable(s). 4) What are the factors in a factorial design? A) the independent variables B) the dependent variables C) the organismic variables D) the experimental variables Answer: A Rationale: The factors in a factorial design are the independent variables, as they are the variables that are systematically manipulated by the researcher to observe their effects on the dependent variable(s). 5) Which of the following statements is correct about interactions? A) They are enhancements of the effect. B) They are additive effects. C) They are spurious effects. D) They occur only in interaction with organismic dependent variables. Answer: A Rationale: Interactions in factorial designs refer to situations where the effects of one independent variable are enhanced or attenuated by the presence of another independent variable. They are not simply additive effects but rather modifications or enhancements of the main effects. 6) Factorial experiments A) include two or more dependent variables. B) include two or more independent variables. C) focus on unmeasured factors. D) focus on organismic factors. Answer: B Rationale: Factorial experiments involve the manipulation of two or more independent variables to examine their main effects and interactions on one or more dependent variables. 7) What term refers to the situation in which two independent variables have an enhanced effect when they are in combination? A) artifact B) confound C) dependency D) interaction Answer: D Rationale: The term that refers to the situation in which two independent variables have an enhanced effect when they are in combination is "interaction." Interactions occur when the effects of one independent variable depend on the level of another independent variable. 8) Research designs that include two or more independent variables are called A) factorial designs. B) multiplicative designs. C) between-subjects designs. D) correlated-groups designs. Answer: A Rationale: Research designs that include two or more independent variables are called factorial designs because they involve the manipulation of multiple factors or independent variables. 9) An effect between two variables that is different than the sum of the effects of the two variables is termed A) an additive effect. B) an interactive effect. C) a multiplicative effect. D) a holistic effect. Answer: B Rationale: An effect between two variables that is different than the sum of the effects of the two variables is termed an interactive effect. Interactive effects in factorial designs occur when the effect of one independent variable is modified by the presence of another independent variable. 10) A phenomenon in which two variables enhance each other is termed A) a bifurcation. B) an enhancement. C) an interaction. D) a crossover effect. Answer: C Rationale: A phenomenon in which two variables enhance each other is termed an interaction. Interactions in factorial designs occur when the effects of one independent variable are modified by the presence of another independent variable. 11) A true interaction is not simply ________; it is a(n) ________. A) additive; multiplication B) factorial; addition C) multiplicative; matrix D) additive; enhancement Answer: D Rationale: Option D correctly describes a true interaction as not simply additive but rather enhancing or amplifying the effect of one variable on another. This aligns with the concept that interactions involve the joint influence of multiple variables on the outcome. 12) Factorial designs are used when A) only one independent variable is included in the study. B) more than one independent variable is included, and interactions as well as main effects are expected. C) only main effects are expected. D) there is no possibility of extraneous variables. Answer: B Rationale: Factorial designs are utilized when more than one independent variable is included, and interactions as well as main effects are anticipated. This allows for the examination of how different variables jointly influence the dependent variable. 13) The primary focus in factorial designs is typically on A) interaction effects. B) sequence effects. C) cohort effects. D) Both A and B Answer: A Rationale: The primary focus in factorial designs is usually on interaction effects, as they indicate how the effects of one variable depend on the levels of another variable. Option A accurately reflects this emphasis. 14) The essential issue in interactions is A) to determine whether two factors influence the dependent variable differently when they co-occur than when they occur separately. B) to understand how two main effects can cause an interaction. C) to determine how two co-occurring factors influence the independent variable. D) to determine which of the factors occurs first. Answer: A Rationale: The essential issue in interactions, as described in option A, involves determining whether the effects of two factors on the dependent variable differ when they occur together compared to when they occur separately. This is fundamental to understanding interaction effects. 15) In most factorial studies, the primary focus is on A) the main effects of the independent variables on the dependent variables. B) the main effects of the dependent variables on the independent variables. C) the interaction effects of the dependent variables on the independent variables. D) the interaction effects of the independent variables on the dependent variables. Answer: D Rationale: In most factorial studies, the primary focus is on the interaction effects of the independent variables on the dependent variables, as these indicate how the effects of one variable are modified by the presence of another variable. 16) The treatment combinations in a factorial design are represented in A) statistical terms. B) dependent variables. C) a matrix of cells. D) boxes. Answer: C Rationale: Treatment combinations in a factorial design are typically represented in a matrix of cells, with each cell representing a unique combination of levels of the independent variables. Option C correctly identifies this representation. 17) In a factorial design, the notation "2 X 3 X 2" tells us that the design has ________ independent variables. A) 3 B) 12 C) 7 D) 9 Answer: A Rationale: The notation "2 X 3 X 2" indicates that the factorial design has 3 independent variables, each with 2, 3, and 2 levels, respectively. Option A accurately reflects this interpretation. 18) Factorial designs allow us to study both ________ effects of the independent variables on the dependent variable. A) individual and interactive B) dependent and independent C) symbiotic and dichotomous D) rank order and correlational Answer: A Rationale: Factorial designs enable the study of both individual (main) effects and interactive (interaction) effects of the independent variables on the dependent variable. Option A correctly identifies this capability. 19) A 2 X 3 factorial design results in a ________ cell matrix. A) 6 B) 2 C) 8 D) 5 Answer: A Rationale: A 2 X 3 factorial design results in a 6-cell matrix, as it involves 2 levels of one independent variable and 3 levels of another independent variable, yielding 6 unique combinations. Option A accurately represents this outcome. 20) In factorial designs, the notation "3 X 3" tells us that the design has ________ independent variables. A) 3 B) 9 C) 6 D) 2 Answer: D Rationale: The notation "3 X 3" indicates that the factorial design has 2 independent variables, each with 3 levels. Option D correctly interprets this notation. 21) A 2 X 2 factorial design A) is called a one-way ANOVA. B) results in a four-cell matrix. C) will yield four interactions. D) must include an organismic independent variable. Answer: B Rationale: In a 2 X 2 factorial design, there are two independent variables, each with two levels. When these levels are crossed, they result in a total of four unique conditions or cells in the design, hence a four-cell matrix. 22) The design notation for a factorial design shows the number of ________ and the number of ________. A) participants; independent variables B) participants; conditions C) dependent variables; levels of each independent variable D) independent variables; levels of each independent variable Answer: D Rationale: The design notation for a factorial design indicates the number of independent variables followed by the number of levels each independent variable has. For example, a 2 X 3 factorial design indicates two independent variables, each with 2 and 3 levels respectively. 23) As factorial designs become more complex through addition of more independent variables, results are generally A) easier to interpret. B) more difficult to interpret. C) less scientifically valid. D) Both B and C Answer: B Rationale: With the addition of more independent variables, factorial designs become more complex, making interpretation more difficult. Managing multiple independent variables and their interactions can complicate the analysis and interpretation of results. 24) A factorial design study has two independent variables with three levels of each variable. This would be expressed as ________. A) 3 X 2 B) 2 X 3 C) 2 X 3 X 1 D) 3 X 3 Answer: D Rationale: In a factorial design with two independent variables, each having three levels, the notation is expressed as 3 X 3, indicating three levels for each of the two independent variables. 25) The 3 X 4 factorial design produces a ________ cell matrix. A) 2 B) 4 C) 12 D) 7 Answer: C Rationale: A 3 X 4 factorial design, with two independent variables having 3 and 4 levels respectively, results in a total of 12 unique conditions or cells in the design. 26) Which of the following statements is true? A) No more than four factors can be included in a factorial design. B) Interactions with up to ten factors can be readily interpreted. C) Any number of factors can be included, but interpretation of interactions is more difficult as the number of factors increases. D) The number of factors has no bearing on the interpretation of results. Answer: C Rationale: While factorial designs can accommodate multiple factors, interpreting interactions becomes increasingly difficult as the number of factors increases. This complexity arises from the intricate relationships among multiple variables, making interpretation challenging. 27) What information is given in the factorial design notation, 2 X 3 X 2? A) Interactions will be found. B) The design has 12 independent variables. C) The design has three independent variables. D) The design has two independent variables, three dependent variables, and two organismic variables. Answer: C Rationale: The notation 2 X 3 X 2 indicates that the factorial design has three independent variables, with the first having 2 levels, the second having 3 levels, and the third having 2 levels. 28) A factorial design with a notation of 3 X 3 X 2 tells us that the design has ________ independent variables. A) 2 B) 6 C) 3 D) 18 Answer: C Rationale: The notation 3 X 3 X 2 indicates that the factorial design has three independent variables. 29) The primary reason for limiting factorial designs is A) to make data entry easier. B) that complicated factorial designs are unwieldy and difficult to interpret. C) that data analysis is very expensive for complicated designs. D) to prevent participant loss due to attrition. Answer: B Rationale: Factorial designs become increasingly complex as more factors are added, making them unwieldy and difficult to interpret. Limiting the number of factors helps to manage this complexity and facilitates clearer interpretation of results. 30) A 4 X 3 factorial design has ________ factors. A) 2 B) 3 C) 4 D) 12 Answer: A Rationale: In a 4 X 3 factorial design, there are two independent variables, one with 4 levels and the other with 3 levels, resulting in a total of two factors. 31) The impact of each independent variable in a factorial design on the dependent variable is termed the A) interactive effects. B) within-subjects effects. C) main effects. D) matrix effects. Answer: C Rationale: Main effects in factorial designs refer to the effects of each independent variable individually on the dependent variable, regardless of other variables. Options A, B, and D are incorrect because they do not accurately describe the effects of individual variables. 32) The notation 3 X 3 indicates that the design has _____ _____ variables with three _____ of each. A) nine independent; repetitions B) three dependent; levels C) two independent; repetitions D) two independent; levels Answer: D Rationale: The notation 3 X 3 in a factorial design indicates that there are two independent variables, each with three levels. Option A incorrectly describes the number of independent variables and repetitions. Option B refers to dependent variables, which is not specified in the notation. Option C incorrectly describes the number of independent variables. 33) Effects of a single factor in a factorial design are known as A) main effects. B) the interaction. C) matrix effects. D) cell effects. Answer: A Rationale: Effects of a single factor in a factorial design are referred to as main effects, representing the influence of each independent variable on the dependent variable individually. Options B, C, and D are incorrect because they do not accurately describe the effects of individual factors. 34) Conducting a factorial experiment is A) more complex than conducting single-variable designs. B) simpler than conducting single-variable designs. C) rarely done in modern psychological research. D) easier because we can omit operational definitions and research hypotheses. Answer: A Rationale: Factorial experiments are more complex than single-variable designs because they involve examining the effects of multiple independent variables simultaneously, which requires careful consideration of interactions between variables. Options B, C, and D are incorrect because they do not accurately describe the complexity of factorial experiments. 35) A 2 X 2 factorial A) is essentially two designs that have been combined into a single study. B) contains four factors. C) does not have enough factors to show interactions. D) is extremely difficult to interpret if interactions are found. Answer: A Rationale: A 2 X 2 factorial design combines two independent variables, each with two levels, resulting in a total of four experimental conditions. Option B incorrectly describes the design as containing factors. Options C and D are incorrect because they do not accurately describe the nature of 2 X 2 factorial designs. 36) In a 2 X 2 factorial design, there are ________ null hypotheses for each dependent measure. A) 2 B) 3 C) 4 D) 6 Answer: B Rationale: In a 2 X 2 factorial design, there are three null hypotheses for each dependent measure: one for each main effect and one for the interaction effect between the two independent variables. Options A, C, and D do not accurately describe the number of null hypotheses. 37) If we have three factors in a factorial design, we have ________ possible effects. A) 3 B) 7 C) 4 D) 11 Answer: B Rationale: With three factors in a factorial design, there are seven possible effects: three main effects (one for each factor) and four interaction effects (combinations of two or three factors). Options A, C, and D do not accurately describe the number of possible effects. 38) Factorial designs A) include no more than one research hypothesis. B) cannot test participants across more than one condition. C) are ineffective when matched participants are included. D) contain more than one null hypothesis. Answer: D Rationale: Factorial designs typically involve testing multiple research hypotheses, as each independent variable and interaction may have its own hypothesis. Options A, B, and C incorrectly describe factorial designs. 39) In a 2 X 2 factorial design, threats to internal validity A) are nonexistent. B) are considerably less than in a single-variable design. C) are more complex than in a single-variable design. D) can be controlled by randomly assigning matched pairs (2 X 2) of participants to conditions. Answer: C Rationale: In a 2 X 2 factorial design, there can be increased complexity in identifying and controlling threats to internal validity due to interactions between the independent variables. Options A, B, and D incorrectly describe the threats to internal validity in factorial designs. 40) How many null hypotheses does a single-variable experimental design contain? A) one for each independent variable B) three for each dependent measure C) one for each independent variable and one for each dependent variable D) one for each dependent measure Answer: D Rationale: A single-variable experimental design typically contains one null hypothesis for each dependent measure being tested, reflecting the comparison of groups or conditions on that particular measure. Options A, B, and C incorrectly describe the number of null hypotheses in single-variable designs. 41) How many null hypotheses does a 2 X 2 factorial have for each dependent measure? A) three B) two times two C) one D) none Answer: A Rationale: In a 2 X 2 factorial design, there are three null hypotheses for each dependent measure: one for each main effect (Factor A, Factor B) and one for the interaction between Factor A and Factor B. 42) Which of the following is NOT one of the three null hypotheses for each dependent measure in a 2 X 2 factorial? A) There is no difference between the levels of factor A. B) There are significant main effects for either factor A or B but not both. C) There are no main effects for factor B D) There is no significant interaction of factors A and B. Answer: B Rationale: The null hypotheses for a 2 X 2 factorial include no difference between the levels of each factor (A and B) and no significant interaction between factors A and B. Option B does not accurately represent one of the null hypotheses. 43) The major difference between the hypothesis-testing procedures in factorial versus singlevariable designs is that A) single-variable designs, although less complicated in terms of design, are more difficult to interpret. B) there are more dependent variables in the factorial design. C) the reasoning is very different in each type of design. D) there is more chance for confounding to occur in factorial designs. Answer: D Rationale: The major difference between factorial and single-variable designs in hypothesis testing is the potential for confounding due to the interaction between multiple independent variables in factorial designs, as stated in option D. 44) In a factorial design with two factors, how many possible effects can there be? A) four B) two C) three D) two to the third power Answer: C Rationale: In a factorial design with two factors, there can be main effects for Factor A and Factor B, as well as an interaction effect between Factor A and Factor B, totaling three possible effects. 45) The 2 X 2 factorial combines two designs into a single study, with the result that the 2 X 2 factorial A) is much weaker than a single-variable design. B) contains more than one null hypothesis. C) is impervious to threats to internal validity. D) requires far fewer participants than a single-variable design. Answer: B Rationale: The 2 X 2 factorial combines two designs into one, resulting in multiple null hypotheses and increased complexity compared to single-variable designs, as described in option B. 46) In a matrix for a factorial design, the row means represent the effects of A) extraneous factors. B) individual differences. C) an interaction. D) a single factor. Answer: D Rationale: In a factorial design matrix, the row means represent the effects of a single factor (e.g., Factor A or Factor B) across the levels of the other factor(s). 47) Which of the following is an accurate statement? A) There are many possible outcomes of a factorial design. B) Factorial designs can only demonstrate the presence of interactions but not main effects. C) It is not possible to have an interaction effect without at least one strong main effect. D) It is not possible to have both interactions and main effects in the same factorial design. Answer: A Rationale: Option A is accurate. Factorial designs can have multiple outcomes depending on the presence or absence of main effects and interactions. 48) A four-cell factorial matrix shows that the mean scores of all groups in all conditions are the same. This would indicate that there are A) no main effects or interactions. B) interactions, but no main effects. C) main effects, but no interactions. D) both main effects and interactions. Answer: A Rationale: If the mean scores of all groups in all conditions are the same, it indicates that there are no main effects or interactions present, as described in option A. 49) In a graph representing results in a factorial design, a line with a steep slope probably indicates A) a main effect. B) an interaction. C) a nonaffected factor. D) no effects. Answer: A Rationale: A steep slope in a graph typically indicates a strong main effect for one of the factors being plotted. 50) In a graph representing data from a factorial design, parallel lines would indicate that A) there is no interaction. B) there is at least one interaction present. C) there is a significant interaction. D) there are at least two main effects. Answer: A Rationale: Parallel lines in a factorial design graph indicate that there is no interaction between the factors being studied. 51) In a graph of a 2 X 2 factorial design, the two lines are parallel. From the information given, which of the following statements is true? A) There are no main effects. B) There is an interaction between A and B. C) There is a main effect for factor A. D) There is no interaction. Answer: D Rationale: When the lines representing different levels of one factor (A or B) are parallel, it indicates the absence of an interaction effect between those factors. Therefore, option D is correct. 52) A graph of a factorial design has two intersecting lines. From the information given, which of the following is true? A) The interaction between A and B is not significant. B) There is no interaction. C) There is an interaction, which may be significant. D) The null hypothesis can be rejected. Answer: C Rationale: Intersecting lines on a factorial design graph suggest the presence of an interaction effect between the factors. Option C indicates this possibility correctly. 53) In a randomized 2 X 2 factorial design, we test for main effects by A) comparing mean scores for the matrix of cells. B) comparing mean scores of the various levels of each factor. C) comparing the raw scores of each participant. D) finding the mean scores for the entire sample. Answer: B Rationale: To test for main effects in a factorial design, we compare the mean scores of the different levels of each factor independently. This process helps determine if there are significant differences in the outcome variable based on the levels of each factor. 54) In a 2 X 2 factorial design represented on a graph, a main effect for factor B is indicated (the x-axis labeled with the levels of factor A) but no interaction is present. The graphed lines should be A) perpendicular. B) parallel. C) vertical. D) intersecting. Answer: B Rationale: If there's a main effect for one factor but no interaction, the lines representing different levels of the other factor should be parallel. This arrangement allows for the visualization of the main effect while indicating the absence of an interaction. 55) In graphing the results of a 2 X 2 factorial, we can conclude that, if the two lines are parallel, then there is A) an interaction between factor A and factor B. B) no interaction between factor A and factor B. C) a main effect for both factor A and factor B. D) is no main effect for either of the factors. Answer: B Rationale: Parallel lines in a factorial design graph indicate the absence of an interaction effect between the factors. This suggests that the factors do not interact with each other in influencing the outcome variable. 56) If two lines intersect on a graph of a 2 X 2 factorial, we can conclude that A) there must be a main effect for one of the factors. B) there is probably no interaction. C) there is probably an interaction between A and B. D) there is probably a main effect for both A and B. Answer: C Rationale: Intersecting lines in a factorial design graph suggest the presence of an interaction effect between the factors, indicating that the effects of one factor depend on the level of the other factor. 57) What are the factors in the children's dark-fears research discussed in Chapter 12? A) heart rate and frightening images B) illumination and frightening images C) the participants and the dependent variables D) the independent and dependent variables Answer: B Rationale: In the children's dark-fears research, the factors are illumination (level of light) and frightening images. These factors are manipulated to study their effects on children's fear responses. 58) The appropriate statistical test for factorial designs is A) an analysis of variance. B) an analysis of covariance. C) an analysis of bivariance. D) None of the above. Answer: A Rationale: Factorial designs typically use analysis of variance (ANOVA) to analyze the main effects and interactions among factors. ANOVA is suitable for comparing means across multiple groups or conditions. 59) What type of statistical test is usually used to test null hypotheses in factorial designs? A) a correlated t-test B) a simple t-test C) an analysis of variance D) a chi-square test Answer: C Rationale: Analysis of variance (ANOVA) is commonly used to test null hypotheses in factorial designs. ANOVA allows for the simultaneous comparison of multiple group means to determine if there are significant differences among them. 60) What is the appropriate statistical test for a factorial design? A) the Modes test B) ANOVA C) t-test D) chi-square Answer: B Rationale: The appropriate statistical test for a factorial design is analysis of variance (ANOVA). ANOVA is used to analyze the main effects and interactions among factors in factorial designs by comparing means across different groups or conditions. 61) Which of the following statements is accurate? A) Science is defined, not by the use of computers and lab equipment, but by the process of systematic thinking that guides the use of such aids. B) Statistical analyses for factorial designs are impossible to do by hand. C) It is not necessary to understand experimental design or statistical principles in order to interpret computer analyses of factorial designs. D) For modern researchers, knowledge of computer technology has taken the place of knowledge of research design and statistical principles. Answer: A Rationale: This statement accurately reflects that the essence of science lies in systematic thinking and methodology rather than merely relying on tools or technology. 62) ANOVAs are used to test for A) confounding. B) statistically significant differences in single-variable designs. C) statistically significant differences in situations in which more than one independent variable is being studied. D) Both B and C Answer: D Rationale: ANOVAs are utilized to test for statistically significant differences in both single-variable designs (option B) and situations where multiple independent variables are being studied simultaneously (option C). 63) What does an A X B interaction mean in a two-way ANOVA? A) There must be significant main effects for Factors A and B. B) The main effects for Factors A and B must be short of significance. C) The effect of A was different depending on the level of B. D) If there are significant main effects, they must be interpreted first, before interpreting the interaction. Answer: C Rationale: An A x B interaction indicates that the effect of one independent variable (Factor A) is influenced by the level of another independent variable (Factor B), demonstrating that the effect of Factor A differs depending on the level of Factor B. 64) The results of an ANOVA are typically presented in A) a Latin square. B) an ANOVA summary table. C) reverse order. D) a table of correlations. Answer: B Rationale: ANOVA results are commonly presented in a summary table that includes information such as sums of squares, degrees of freedom, mean squares, and F-values. 65) In cases in which there is both a main effect and an interaction, it is important to A) conduct further statistical tests. B) be highly suspicious of the main effect. C) interpret the main effect first. D) interpret the interaction first. Answer: D Rationale: When both a main effect and an interaction are present, it is crucial to interpret the interaction first as it provides information about how the effects of the independent variables combine, which may influence the interpretation of the main effects. 66) What is listed in the first column of an ANOVA summary table? A) degrees of freedom B) sums of squares C) source of variation D) significance level Answer: C Rationale: The first column of an ANOVA summary table typically lists the source of variation, which includes factors such as between-groups, within-groups, and interaction effects. 67) When we find an interaction and a main effect, all of the effects are interpreted in terms of the A) main effect. B) interaction. C) column means. D) row means. Answer: B Rationale: When both an interaction and a main effect are present, all effects are interpreted in terms of the interaction because the presence of an interaction implies that the effects of the independent variables are not simply additive. 68) In performing an ANOVA, the total degrees of freedom are calculated by taking A) one more than the total number of participants. B) the product of the number of participants and the number of conditions. C) one less than the total number of participants. D) the number of conditions minus one. Answer: C Rationale: The total degrees of freedom in ANOVA are calculated by subtracting one from the total number of participants, reflecting the constraint imposed by calculating group means. 69) In performing a 2 X 2 ANOVA, the degrees of freedom for an interaction are calculated by taking A) the number of participants minus one. B) the number of participants plus one. C) the product of the number of columns and the number of rows. D) the product of the degrees of freedom for the main effects. Answer: D Rationale: The degrees of freedom for an interaction in a 2 X 2 ANOVA are calculated by taking the product of the degrees of freedom for the main effects, which is a fundamental principle in factorial ANOVA designs. 70) In performing an ANOVA, the degrees of freedom associated with the error variance are calculated by A) taking the total number of participants and subtracting the number of cells. B) multiplying the total number of participants by the number of cells. C) subtracting one from the total number of participants. D) taking the product of the degrees of freedom for the main effects. Answer: A Rationale: The degrees of freedom associated with the error variance in ANOVA are calculated by taking the total number of participants and subtracting the number of cells, reflecting the degrees of freedom available to estimate within-group variability. 71) Which of the following is correct? A) If there are no main effects, there can be no interactions. B) Whenever interactions are found, there must be main effects. C) Whenever main effects are found, there must be at least one interaction. D) When both interactions and main effects are found, the interactions are interpreted first. Answer: D Rationale: When both interactions and main effects are found, it is recommended to interpret the interactions first to avoid potentially erroneous conclusions about the relative explanatory power of main effects versus interactions. 72) The reason for beginning data interpretation with the interaction rather than the main effect is A) that it is more convenient to do it that way. B) to avoid reaching the erroneous conclusion that the main effect has more explanatory power than it warrants. C) that it is traditional to begin with the interaction. D) that it is easier to rule out the effects of the interaction this way. Answer: B Rationale: Beginning data interpretation with the interaction rather than the main effect helps avoid erroneously attributing more explanatory power to the main effect than it actually has, as interactions can modify the interpretation of main effects. 73) The F-ratio in a single-independent-variable between-subjects design is calculated by A) dividing the sum of squares by the degrees of freedom. B) dividing the between-groups variance by the within-groups variance. C) multiplying the degrees of freedom by the error term. D) dividing the mean square between by the degrees of freedom. Answer: B Rationale: The F-ratio in a single-independent-variable between-subjects design is calculated by dividing the between-groups variance by the within-groups variance, which provides a measure of whether the observed differences between groups are larger than what would be expected by chance. 74) To find out if a p-value value is significant, a researcher must A) consult prior research. B) compare it with the designated alpha value. C) consult the t-table. D) rely on consensus. Answer: B Rationale: To determine if a p-value is significant, a researcher compares it with the designated alpha value (typically 0.05), and if the p-value is smaller than alpha, the result is considered statistically significant. 75) In the dark-fears study, A) the main effects seemed to be due to the interaction. B) there were no main effects. C) there were no interactions. D) the main effects were not due to the interaction. Answer: A Rationale: In the dark-fears study, the main effects appeared to be due to the interaction between variables, indicating that the relationship between variables was not straightforward and was influenced by the interaction effect. 12.2 Variations of Basic Factorial Design 1) The increased use of factorial designs in research has come about largely because they are A) less complicated to analyze. B) more sensitive than other designs to the effects of the independent variable. C) better at testing several causal hypotheses within a single design. D) used by all important psychologists. Answer: C Rationale: Factorial designs are preferred in research because they allow researchers to test multiple causal hypotheses within a single design, enhancing efficiency and providing more comprehensive insights into the relationships between variables. 2) An important reason for the increased popularity of factorial designs in psychological research is that A) factorials are much less expensive to conduct. B) factorial designs are easier to conceptualize than single-variable designs. C) factorials come closer than do single-variable designs to the way behavior in natural environments is determined (i.e., influenced by multiple factors). D) factorials require the use of many fewer participants than do single-variable designs. Answer: C Rationale: Factorial designs are popular in psychological research because they better reflect the complexity of behavior in natural environments by considering multiple factors simultaneously, leading to more ecologically valid findings. 3) In a within-subjects factorial design, we need ten participants in each of the four cells. In total, we need A) 40 participants. B) 20 participants. C) 30 participants. D) 10 participants. Answer: D Rationale: In a within-subjects factorial design, each participant experiences all levels of the independent variables, so the total number of participants needed is equal to the number of cells. 4) In a 2 X 2 between-subjects factorial design, we wish to run ten participants in each of the four cells. In total, we will need A) 40 participants. B) 10 participants. C) 20 participants. D) 80 participants. Answer: A Rationale: In a between-subjects factorial design, each participant is only exposed to one level of each independent variable, so the total number of participants needed is equal to the number of cells multiplied by the number of participants per cell. 5) In a repeated-measures factorial design, A) there must be at least two independent groups. B) participants must be matched on at least two potentially confounding variables. C) there is no problem of sequence effects. D) sequence effects must be controlled. Answer: D Rationale: In a repeated-measures factorial design, sequence effects must be controlled because participants are exposed to multiple conditions, which could lead to order effects influencing the results. 6) A repeated-measures ANOVA adjusts for the effects of A) variations in the dependent variable. B) using the same participants in each condition. C) researcher bias. D) randomization. Answer: B Rationale: A repeated-measures ANOVA is designed to analyze data where the same participants are measured under different conditions. It adjusts for the effects of using the same participants in each condition by accounting for the correlation between repeated measures from the same participant. 7) A within-subjects factorial design A) requires more participants than a between-subjects design. B) assures equivalence of groups at the start of the study. C) takes longer to carry out than a between-subjects design. D) is a contradiction in terms. Answer: B Rationale: In a within-subjects factorial design, each participant experiences all levels of each independent variable, ensuring equivalence of groups at the start of the study because participants serve as their own controls. 8) Within-subjects factorials A) must include independent groups of participants. B) are also called repeated-measures factorials. C) use statistics that take into account the correlated nature of the data. D) Both B and C Answer: D Rationale: Within-subjects factorials involve repeated measurements from the same participants across different conditions, often referred to as repeated-measures factorials. They utilize statistical methods that account for the correlated nature of the data, such as repeated-measures ANOVA. 9) An important reason for the increased popularity of within-subjects designs in psychological research is that A) within-subjects designs are generally more sensitive to the effects of the dependent variable. B) within-subjects designs come closer to the multiple determined nature of behavior than do between-subjects designs. C) within-subjects experiments are easier to get published. D) within-subjects designs are generally more sensitive to the effects of the independent variable. Answer: D Rationale: Within-subjects designs are often preferred because they tend to be more sensitive to the effects of the independent variable, allowing researchers to detect smaller differences or effects more easily compared to between-subjects designs. 10) An important reason for the increased popularity of within-subjects designs in psychological research is that A) within-subjects designs require fewer participants than between-subjects designs. B) within-subjects designs are less sensitive to sequence effects than between-subjects designs. C) within-subjects designs are less sensitive to the effects of the independent variable. D) such an increase reflects a current research trend. Answer: A Rationale: Within-subjects designs often require fewer participants compared to between-subjects designs because each participant serves as their own control, reducing the necessary sample size to achieve statistical power. 11) The use of a within-subjects design in a factorial experiment can do all of the following EXCEPT A) provide greater sensitivity to the effects of the independent variable. B) assure equivalence of groups at the start of the experiment, because the participants in each condition are identical. C) require fewer participants and, as a result, be more efficient. D) reduce confounding due to sequence effects. Answer: D Rationale: Within-subjects designs are susceptible to sequence effects, such as order or carryover effects, which can confound the results. Therefore, they do not necessarily reduce confounding due to sequence effects. 12) We have two factors in a study; one is a between-subjects factor and the other is a withinsubjects factor. This design is called a A) within-subjects design. B) mixed design. C) between-subjects design. D) factorial within-subjects design. Answer: B Rationale: A mixed design includes both between-subjects and within-subjects factors, allowing researchers to examine the effects of both manipulated and nonmanipulated variables within the same study. 13) Mixed designs are A) factorial designs that include a between-subjects factor and a within-subjects factor. B) factorial designs that include a manipulated factor and a nonmanipulated factor. C) factorial designs that include only nonmanipulated factors. D) Either A or B Answer: D Rationale: Mixed designs encompass factorial designs that combine both manipulated and nonmanipulated factors, which could include both between-subjects and within-subjects factors. 14) A research design that has both manipulated and nonmanipulated factors is called a A) within-subjects design. B) between-subjects design. C) mixed design. D) Either A or B Answer: C Rationale: A mixed design includes both manipulated (experimental) and nonmanipulated (nonexperimental) factors within the same study. 15) Which of the following is correct about a mixed design? A) It includes both a within-subjects and a between-subjects component. B) It includes both ANOVA and chi-square statistical analyses. C) It includes both a manipulated and a nonmanipulated variable. D) Either A or C Answer: D Rationale: A mixed design incorporates both within-subjects and between-subjects components, along with both manipulated and nonmanipulated variables, allowing for a comprehensive examination of various factors within the same study. 16) The term mixed design is A) used only in poor research. B) used in only one way. C) never used in research. D) used in two different ways. Answer: D Rationale: The term "mixed design" is used in two different contexts in research methodology. It refers to research designs that incorporate both between-subjects and within-subjects factors. It can also refer to designs that include both manipulated and nonmanipulated factors. Therefore, option D is the correct choice. 17) In the type of mixed design in which both between-subjects and within-subjects factors exist in the same study, the critical issue is A) that the statistical procedures must take into account the correlated nature of some of the data. B) one of interpretation of results rather than statistical procedures themselves. C) making sure that the data are entered in the correct order, with the between-subjects data entered first. D) making sure participants are assigned in a random fashion. Answer: A Rationale: When both between-subjects and within-subjects factors exist in the same study, statistical procedures must consider the correlated nature of some of the data. This is crucial for accurately analyzing the results and drawing valid conclusions. Therefore, option A is the correct choice. 18) In the type of mixed design in which both manipulated and nonmanipulated factors are included, the critical issue is A) a statistical one. B) to use care in interpretation of results. C) to interpret main effects before interactions. D) to make sure the same number of participants is used in each group. Answer: B Rationale: When both manipulated and nonmanipulated factors are included in a mixed design, the critical issue is to use care in the interpretation of results. This is because the presence of both types of factors can complicate the interpretation, requiring researchers to consider various potential influences on the outcomes. Therefore, option B is the correct choice. 19) In a repeated measures ANOVA, participants are tested in A) one condition only. B) each condition. C) independent groups. D) randomly assigned independent groups. Answer: B Rationale: In a repeated measures ANOVA, participants are tested in each condition of the study. This allows researchers to assess how participants' responses vary across different conditions within the same group of individuals. Therefore, option B is the correct choice. 20) Research designs using nonmanipulated factors represent A) experimental research. B) differential research. C) case-study research. D) naturalistic research. Answer: B Rationale: Research designs using nonmanipulated factors are typically associated with differential research, where variables are observed and compared across different groups or conditions without experimental manipulation. Therefore, option B is the correct choice. 21) Interpretation of the main effects of nonmanipulated factors must be carried out cautiously because A) the effect of the other factors is unknown. B) main effects can create interactions. C) confounding variable(s) are likely. D) Either A or B Answer: C Rationale: Interpretation of the main effects of nonmanipulated factors must be carried out cautiously because confounding variables are likely present. Nonmanipulated factors may be associated with other variables that influence the outcome, making it difficult to attribute observed effects solely to the nonmanipulated factor. Therefore, option C is the correct choice. 12.3 ANOVA: A Postscript 1) Analysis of variance (ANOVA) for between-subjects designs operates on the concept of A) correlation. B) matched pairs. C) comparing the error variance to the variability within-groups. D) comparing the variability of the means against a standard based on the variability of the scores within each group. Answer: D Rationale: ANOVA for between-subjects designs operates on the concept of comparing the variability of the means against a standard based on the variability of the scores within each group. This comparison allows researchers to determine whether the observed differences between group means are statistically significant. 2) Which of the following statements is accurate? A) The concepts that underlie analysis of variance differ according to how complicated the analysis is. B) Analysis of variance is conceptually designed to compare correlation coefficients. C) Analysis of variance is a inflexible statistical tool. D) The concepts that underlie analysis of variance remain constant no matter how complicated the analysis is. Answer: D Rationale: The accurate statement is that the concepts that underlie analysis of variance remain constant no matter how complicated the analysis is. The basic principles of ANOVA, such as comparing group means and variability, remain consistent regardless of the complexity of the analysis. 3) The most widely used statistical technique in psychology is A) analysis of covariance. B) the t-test. C) the chi-square test. D) analysis of variance. Answer: D Rationale: The most widely used statistical technique in psychology is analysis of variance (ANOVA). ANOVA is commonly used to compare means across different groups or conditions in experimental and nonexperimental research settings. 4) Which of the following statistical analysis techniques should be used with one dependent variable being analyzed? A) the ANOVA B) the MANOVA C) the CONOVA D) None of the above Answer: A Rationale: The correct choice is ANOVA (Analysis of Variance). ANOVA is used when there is one dependent variable being analyzed to compare means across different groups or conditions. MANOVA (Multivariate Analysis of Variance) is used when there are multiple dependent variables. CONOVA is not a standard statistical analysis technique. 5) If we have four factors in a factorial design, we have ________ possible main effects. A) 4 B) 5 C) 24 D) 15 Answer: A Rationale: In a factorial design, the number of possible main effects is equal to the number of factors involved. Therefore, if there are four factors, there are four possible main effects. 6) Even though there are many different F-ratios, each F-ratio represents A) a comparison of overall variance to within-groups variance. B) a comparison of between-groups variance to within-groups variance. C) a comparison of overall variance to between-groups variance. D) a comparison of main effects to interactions. Answer: B Rationale: Each F-ratio in analysis of variance (ANOVA) represents a comparison of between-groups variance to within-groups variance, providing information about whether the differences between group means are greater than would be expected by chance. 7) In complex ANOVAs, we interpret the F-ratio A) in a different way than in simpler designs. B) as a preliminary to more complicated statistics. C) in the same way as in simpler designs. D) more cautiously than in simpler designs. Answer: C Rationale: The interpretation of the F-ratio in complex ANOVAs remains the same as in simpler designs. It indicates the ratio of between-groups variance to within-groups variance, providing information about the significance of the observed differences between groups. 8) Analysis of covariance (ANCOVA) is used in the same way as analysis of variance (ANOVA) EXCEPT that A) in ANCOVA, the effects of a powerful variable are statistically removed from the scores of the dependent measure as part of the analysis. B) ANCOVA must be done by hand. C) ANCOVA cannot be used with score data. D) in ANCOVA, the effects of a powerful variable are statistically removed from the scores of the dependent measure after the analysis. Answer: A Rationale: Analysis of covariance (ANCOVA) is similar to ANOVA, but it includes the statistical removal of the effects of one or more covariates from the dependent variable scores as part of the analysis. This helps control for confounding variables and increases the precision of the analysis. 9) The analysis of covariance (ANCOVA) is generally useful for the A) removal of interaction effects. B) statistical removal of variability caused by extraneous variables. C) analyzing more than one independent variable. D) All of the above. Answer: B Rationale: ANCOVA is particularly useful for statistically removing the variability caused by extraneous variables (covariates) from the dependent variable scores. This helps increase the accuracy of the analysis by controlling for potential confounding variables. 10) Which of the following statistical analysis techniques can handle more than one dependent variable in the same analysis? A) the ANOVA B) the ANCOVA C) the MANOVA D) All of the above Answer: C Rationale: Multivariate analysis of variance (MANOVA) is specifically designed to handle more than one dependent variable in the same analysis, allowing researchers to assess the relationships among multiple dependent variables simultaneously. 11) The difference between an analysis of variance (ANOVA) and a multivariate analysis of variance (MANOVA) is A) in the independent variable(s). B) in the dependent variable(s). C) that ANOVA uses the F-test, whereas MANOVA uses the Mann-Whitney U-test. D) that MANOVA removes the effect of a powerful independent variable from the dependent measures. Answer: B Rationale: The primary difference between ANOVA and MANOVA lies in the dependent variables. ANOVA assesses differences between groups on a single dependent variable, whereas MANOVA assesses differences on two or more dependent variables simultaneously. 12) Factorial ANOVAs are to ________ as MANOVAs are to ________. A) independent variables; dependent variables. B) dependent variables; independent variables. C) input; output D) between-subjects; within-subjects Answer: A Rationale: In factorial ANOVAs, the independent variables are manipulated to observe their effects on the dependent variables. Similarly, in MANOVAs, multiple dependent variables are analyzed to observe their relationship with the independent variables. 12.4 Ethical Principles 1) Which of the following does NOT represent an important ethical safeguard in doing research with children? A) assuring that the study is competently designed and carried out B) getting informed consent from the children themselves C) getting informed consent from the children's parents D) getting the children's assent to participate in the research Answer: B Rationale: While obtaining informed consent from children themselves is important in some circumstances, it's not always feasible or appropriate. Instead, parental consent is typically required as an important ethical safeguard when conducting research with children. 2) Why do you need the consent of a parent or guardian when doing research with children? A) Children cannot give legal consent. B) Parents would want to know what is happening to their children. C) Young children often cannot sign their name. D) You need the consent of parents for all research, whether with children or adults. Answer: A Rationale: Children are legally unable to provide informed consent due to their status as minors. Therefore, parental or guardian consent is required to ensure that children are not involved in research without appropriate oversight and protection of their rights. 3) In addition to the consent of a parent, when conducting research with children you should also get the A) child's consent. B) child's assent. C) IRB consent. D) consent of an impartial authority. Answer: B Rationale: While parents or legal guardians provide consent for a child's participation in research, the child's assent, or affirmative agreement to participate, should also be obtained, especially for older children who are capable of understanding the nature of the research and its potential risks and benefits. 4) The dark fears study exposed children to potentially frightening images. What is the responsibility of the researcher if one of the child participants shows extreme distress during the study. A) Complete the trials as quickly as possible to keep the distress to a minimum. B) Reassure the child if necessary and discontinue the procedure if the reassurance is insufficient. C) Ask permission of the parent to continue. D) Ask permission of the child to continue. Answer: B Rationale: The ethical responsibility of the researcher is to prioritize the well-being and safety of participants. If a child shows extreme distress during a study, it is crucial to provide appropriate reassurance and, if necessary, to discontinue the procedure to prevent further harm to the child. 5) Why would a researcher use a delayed-treatment control group instead of a no-treatment control group in a study of fear reduction? A) Because you can learn much more clinically by seeing how both groups respond to treatment. B) Because it doubles the sample size in the treatment group. C) Because it reduces the cost of treatment by spreading it over more people. D) Because the researcher is addressing an ethical issue. Answer: D Rationale: Using a delayed-treatment control group instead of a no-treatment control group in a fear reduction study can be considered ethically preferable because it ensures that all participants eventually receive the treatment, thereby minimizing any potential harm or distress caused by withholding treatment from the control group. This approach aligns with ethical principles of beneficence and justice by ensuring equitable access to treatment for all participants. Test Bank for Research Methods: A Process of Inquiry Anthony M. Graziano, Michael L. Raulin 9780205900923, 9780205907694, 9780135705056