Statistics Module 5: Chapter 9-10

The item below is based on the following scenarios.The scenarios below are possible results of a study in which participants completed a measure of how important religion was to them personally. Participants are either from a Rural or Urban area, and are either Poor or Rich.Which of the following interpretations is consistent with Scenario A? a) Religion is more important to poor people when they live in rural areas. In the urban areas, poor people are socialized to be more like rich people, who are less religious, regardless of where they live. b) Rich people, regardless of where they live, value religion moderately. Poor people value religion more in urban centers than in rural areas because it is more accessible. c) People who live in the urban areas need religion more than people in rural areas, regardless of how rich or poor they are. d) Poor people in urban areas have a harder time than people in rural areas, so they value religion more. Rich people who move to rural areas are trying to get away from their materialistic lifestyle and tend to be more religious.

Rich people, regardless of where they live, value religion moderately. Poor people value religion more in urban centers than in rural areas because it is more accessible.

The item below is based on the following scenarios.The scenarios below are possible results of a study in which participants completed a measure of how important religion was to them personally. Participants are either from a Rural or Urban area, and are either Poor or Rich. A sociologist said, "As far as how important religion is to people, it doesn't matter where they live. What matters is how much money they make." If this conclusion was based on one of these scenarios, which scenario was being considered? a) scenario A b) scenario B c) scenario C d) none of the above

Scenario B

When an interaction effect is present, significant main effects a) should not be interpreted b) should be interpreted, but cautiously c) should be interpreted in the usual manner, as they are unaffected by interactions d) will never occur

Should be interpreted, but cautiously

When sample sizes are equal, MSWithin is figured by a) summing the population variance estimates figured within each group and dividing by the total number of participants (over all groups). b) summing the population variance estimates figured within each group and dividing this sum by the number of groups. c) multiplying the within-groups sum of squares (SSWithin) by the size of each sample (n). d) dividing the within-groups sum of squares (SSWithin) by the size of each sample (n).

Summing the population variance estimates figured within each group and dividing this sum by the number of groups.

Given four populations with equal means and equal variances, an F distribution for situations with samples of 10 scores each could be created by a) applying the t test formula to each pair of samples, squaring the results to obtain F ratios, then repeating this process a large number of times. b) applying the analysis of variance formula to a set of four samples (one from each of the four populations) of 10 scores each, determining the degrees of freedom, and repeating this process a large number of times. c) taking 10 samples from each of the four populations, figuring the F ratio, and repeating this process a large number of times d) taking samples of 10 scores from each of the four populations, figuring an F ratio for each set of samples, and repeating this process a large number of times.

Taking samples of 10 scores from each of the four populations, figuring an F ratio for each set of samples, and repeating this process a large number of times.

Advanced topic: If you were to use a "signal-noise" analogy to explain the structural model, you could say that "signal" represents a) the between-groups population variance estimate b) the within-groups population variance estimate c) the total population variance estimate d) degrees of freedom

The between-groups population variance estimate

Marginal means are a) the means of one grouping variable alone b) used to identify interaction effects c) always reported in research articles d) the means of both grouping variables, minus the interaction

The means of one grouping variable alone

"S2Within" equals a) the sum of squares within each group. b) the square root of the standard within-groups deviations from the mean. c) the squared variance within groups d) the population variance estimate based on the variation within each of the groups.

The population variance estimate based on the variation within each of the groups.

Advanced topic: When considering the power of a main effect in a factorial analysis of variance, all of the following must be taken into account EXCEPT a) the number of scores per cell b) the number of levels of the other grouping variable c) the predicted effect size for this main effect d) the predicted effect size for the other grouping variable

The predicted effect size for the other grouping variable

The cutoff F used to evaluate the significance of the Scheffé test for any particular comparison between two group means is a) the same cutoff F used for the overall study b) the cutoff based on df = 1 for the numerator and the overall dfBetween for the denominator. c) the cutoff based on df = 2 for the numerator and the overall dfWithin for the denominator d) the cutoff based on df = 1 for the numerator and df = overall dfWithin / 2 for the denominator.

The same cutoff F used for the overall study

The most serious violation of an assumption for an analysis of variance occurs when a) the populations are strongly skewed in the positive direction b) the scores between and within groups are dependent c) the variance estimate of the group with the largest estimate is twice that of the smallest d) the number of scores in each group is less than 10

The scores between and within groups are dependent

Advanced topic: The sum of the squared deviations of each score from the mean of its group plus the sum of the squared deviations of each score's group's mean from the grand mean equals a) the grand mean divided by dfTotal b) the portion of the grand mean's deviation accounted for by the score itself. c) the portion of the grand mean's deviation accounted for by the score's group. d) the sum of squared deviations of each score from the grand mean

The sum of squared deviations of each score from the grand mean

If a research article reports that "The mean performance scores for the Normal Sleep, Reduced Sleep, and No Sleep groups were 18.0, 16.6, and 15.6, respectively, F (2, 36) = 2.95, p < .05," the most accurate conclusion is that a) people who get no sleep perform significantly worse than people who sleep a reduced amount. b) people who get no sleep perform significantly better than people who sleep a normal amount. c) the three groups do not all come from populations with the same mean, although it is not clear which population means are different. d) conclusions about the relationship between amount of sleep and performance cannot be drawn from these results.

The three groups do not all come from populations with the same mean, although it is not clear which population means are different.

In a 2 × 2 analysis of variance, the basis for estimating the numerator of the F ratio for the column effects is a) the variance among the four cell means b) the variance between the two column marginal means c) the variance between the two row marginal means d) the variance between the means of the two diagonals

The variance between the two column marginal means

In an analysis of variance, if the null hypothesis is false, then a) the variation between sample means reflects the variation within the populations as well as the variation between the population means b) the within-groups variance is significantly larger than the between-groups variance c) the variance within each sample is larger than if the null hypothesis were true d) the variance between sample means is no greater than the variance within the population with the largest variance.

The variation between sample means reflects the variation within the populations as well as the variation between the population means.

Ann conducts a study, and finds that the estimated population variances for the groups are 12.8, 16.3, 15.1, and 19.9. What is the within-groups estimate of the population variance? a) (12.82 + 16.32 + 15.12 + 19.92) / (4 - 1) = 351.18 b) (12.82 + 16.32 + 15.12 + 19.92) / 4 = 263.39 c) (12.8 + 16.3 + 15.1 + 19.9) / (4 - 1) = 21.37 d) (12.8 + 16.3 + 15.1 + 19.9) / 4 = 16.03

(12.8 + 16.3 + 15.1 + 19.9) / 4 = 16.03

How many F ratios are figured in a two-way analysis of variance a) 1 b) 2 c) 3 d) as many as there are cells in the design

3

If a research article presented the results of an analysis of variance as, "F (2, 38) = 3.60, p < .05," then how many groups were there in the study? a) 2 b) 3 c) 40 d) 41

3

In a 2 × 3 analysis of variance, the number of null hypotheses is a) 1 b) 2 c) 3 d) 6

3

In a 3 × 3 analysis of variance, the number of null hypotheses is a) 1 b) 3 c) 6 d) 9

3

Joe conducts an analysis of variance. If he rejected the null hypothesis, the most likely F value is a) 0.64 b) 1.01 c) 3.57 d) -5.12

3.57

In an analysis of variance with a between-groups population variance estimate of 30 and a within-groups estimate of 25, the F ratio is a) 25 / (30-25) = 5.00 b) (30-25) / 30 = 0.17 c) 25 / 30 = 0.83 d) 30 / 25 = 1.20

30 / 25 = 1.20

Advanced topic: According to the structural model of the two-way analysis of variance, each score's overall deviation from the grand mean is divided into a) 2 components b) 4 components c) 7 components d) as many components as there are cells in the design

4 components

In an analysis of variance with a within-groups variance estimate of 8.5 and a between-groups variance estimate of 5.3, the F ratio is a) 5.3/8.5=0.62 b) 8.5/5.3=1.60 c)sq root 5.3/8.5=0.27 d)sq root 8.5/5.3=0.55

5.3/8.5=0.62

A consumer psychologist is interested in the effects of Annual Income and Motivations to Shop on shopping patterns of consumers. If Annual Income is divided into two levels (High and Moderate) and Motivation to Shop is divided into three levels (Escape, Necessity, and Socializing), and both are considered in one study, the number of cells will be a) 2 b) 3 c) 4 d) 6

6

In a 3 x 3 analysis of variance, the number of cells is a) 1 b) 3 c) 6 d) 9

9

In a 3 x 3 analysis of variance, the number of populations is a) 2 b) 3 c) 6 d) 9

9

A repeated measures analysis of variance is to an ordinary analysis of variance as a t test for dependent means is to a) a t test for a single sample b) a t test for independent means c) a two-way analysis of variance d) any factorial analysis of variance

A t test for independent means

In an analysis of variance, if the null hypothesis is true, then a) the research hypothesis can also be true b) fewer participants can be included in the experiment c) there is less variance among means of samples than if the null hypothesis were not true d) the within-groups estimate of the population variance is smaller than the between-groups estimate.

There is less variance among means of samples than if the null hypothesis were not true

If a research article reports "F (2, 36) = 2.95, p < .05," you know that a) there were two groups b) there were 39 participants c) there were 36 participants d) there were 36 participants per group

There were 39 participants

In a two-way analysis of variance, what is the population variance estimate for the denominator of the F ratios for the main and interaction effects a) All effects are tested using the same estimate based on averaging the estimates of the variance of scores within each cell b) Each effect is tested using a variance estimate based on the variation within the appropriate groupings c) Each effect is tested using a variance estimate based on the variation among the appropriate marginal means d) The row and column effects are tested using an estimate based on the variation within the appropriate groupings, but the interaction effect is tested based on averaging the estimates based on variance of scores within each cell.

All effects are tested using the same estimate based on averaging the estimates of the variance of scores within each cell

All of the following are advantages of factorial designs EXCEPT a) they automatically provide and indicator of effect size for the measured variable b) they are more fficient c) the combined influences of variables can be studied d) more than one grouping variable can be considered in the same study

They automatically provide an indicator of effect size for the measured variable

In an analysis of variance, if the within-groups variance estimate is about the same as the between-groups variance estimate, then a) the null hypothesis should be rejected b) any difference between sample means is probably due to random sampling error c) an error has been made in computing the between-groups and the within-groups variance estimates d) any difference between sample means is probably due to a real difference caused by experimental conditions.

Any difference between sample means is probably due to random sampling error

For a factorial analysis of variance, the assumptions that were necessary for a one-way analysis of variance a) are no longer required b) are necessary for each cell c) are unchanged d) are unchanged, but less important, because factorial analysis of variance is more robust than on-way analysis of variance

Are necessary for each cell

In a three-way factorial design, there can be a) four main effects and three interactions b) three main effects and three interactions c) two main effects and three interactions d) three main effects and four interactions

Three main effects and four interactions

An interaction effect can be identified in all of the following ways EXCEPT a) through inspecting cell means b) through inspecting marginal means c) by using graphs d) by a verbal description of results

Through inspecting marginal means

The correct order of post hoc comparison procedures following an analysis of variance from the least conservative to the most conservative is a) Bonferroni, Scheffe, Tukey b) Scheffe, Tukey, Bonferroni c) Tukey, Scheffe, Bonferroni d) Bonferroni, Tukey, Scheffe

Tukey, Scheffe, Bonferroni

A 2 x 3 factorial design has a) two variables that divide the groups b) six variables that divide the groups c) three variables that divide the groups d) five variables that divide the groups

Two variables that divide the groups

If an experimenter "crosses Intelligence with Attractiveness" in a factorial design in which intelligence has three levels (high, medium, and low) and attractiveness has two levels (high and low), the study will a) be a three-way analysis of variance b) be a 3 x 2 analysis of variance c) have eight cells to the third power d) have five cells

Be a 3 x 2 analysis of variance

Which statistical procedure ensures that the alpha level for any given planned contrast will not exceed .05? a) Tukey b) Scheffe c) Bonferroni d) Gosset

Bonferroni

Advanced topic: each score's deviation from the grand mean represents a) true variation b) measurement error c) both true variation and measurement error d) neither true variation nor measurement error

Both true variation and measurement error

The power of an analysis of variance can be increased by all of the following EXCEPT a) having more participants in each group b) using more groups in an experiment c) using the .01 significance level instead of the .05 significance level d) having equal numbers of participants in the groups

Using the .01 significance level instead of the .05 significance level

If a research article does not report the variance estimates, R2 a) can be figured by [(F)(dfBetween)]/[(F)(dfBetween) + dfWithin]. b) can be figured by F/dfWithin. c) can be estimated by SM/SWithin. d) cannot be figured

Can be figured by [(F)(dfBetween)]/[(F)(dfBetween) + dfWithin].

An analysis of variance differs from a t test for independent means in that an analysis of variance a) is usually used to compare two groups, while a t test for independent means can be used to compare two or more groups b) can be used to compare three or more groups, while a t test for independent means cannot be used to compare more than two groups c) is conducted before the experiment, while a t test for independent means is conducted after the experiment d) includes computation of group variances as part of the analysis, while a t test does not include these computations.

Can be used to compare three or more groups, while a t test for independent means cannot be used to compare more than two groups.

"Proportion of variance accounted for" is also referred to as all of the following EXCEPT a) R^2 b) the correlation ratio c) eta-squared d) chi-squared

Chi-squared

The Scheffé test requires first figuring the F for the comparison as if a planned comparison is being conducting, then adjusting the F from that comparison by a) dividing that F by the study's overall dfWithin b) multiplying that F by the study's overall dfWithin c) dividing that F by the study's overall dfBetween d) multiplying that F by the study's overall dfBetween

Dividing that F by the study's overall dfBetween

In a factorial design, a "cell" is a) each combination of levels of the variables that divide the groups b) the combination of different levels of one variable that divides the groups, ignoring any other variables that divide the groups. c) a study with a single two-level variable that divides the groups d) the same thing as a "main effect.

Each combination of levels of the variables that divide the groups

The results of an analysis of variance would be reported in a research article as a) F(44) = 3.40, significant b) F(2,44) < .05 c) F(2,44) = 3.40, p <.05 d) F = 3.40, p <.05

F(2,44) = 3.40, p <.05

In the formula, Σ(M-GM)2/dfBetween, "GM" is the a) general multiple b) grand mean c) group mean d) group median

Grand mean

The item below is based on the following scenarios.What is the relationship between the amount of time spent shopping, Short (under 15 minutes) or Long (over 15 minutes), and the age of the shopper, Young (under 22) or Old (over 22), and the amount of money spent by shoppers in a music store. Which interpretation is consistent with scenario A? a) more money is spent when people shop for a long time as compared with a short time b) younger buyers spend more money in general than older buyers c) less money is spent when people shop for a long time as compared with a short time d) older buyers spend more money in general than younger buyers

Younger buyers spend more money in general than older buyers

The item below is based on the following scenarios. What is the relationship between the amount of time spent shopping, Short (under 15 minutes) or Long (over 15 minutes), and the age of the shopper, Young (under 22) or Old (over 22), and the amount of money spent by shoppers in a music store. Which interpretation is most consistent with scenario C? a) length of time makes no difference int he amount of money spent b) age makes no different in the amount of money spent c) Younger buyers spend more money when they shop for a shorter time whereas older buyers spend more money when they shop for a longer time d) neither age nor length of time makes a difference in amount of money spent

Younger buyers spend more money when they shop for a shorter time whereas older buyers spend more money when they shop for a longer time

The item below is based on the following scenarios.What is the relationship between the amount of time spent shopping, Short (under 15 minutes) or Long (over 15 minutes), and the age of the shopper, Young (under 22) or Old (over 22), and the amount of money spent by shoppers in a music store. Which interpretation is most consistent with the interaction effect in Scenario B? a) If there is only a short time to shop, age makes no difference, but if there is a long time to shop, younger buyers spend more money than older buyers b) younger buyers spend more money in general than older buyers c) more money is spent when people shop for a long time as compared with a short time d) none, because there is no interaction effect

If there is only a short time to shop, age makes no difference, but if there is a long time to shop, younger buyers spend more money than older buyers

Advanced topic: Σ(X-GM)2 a) equals the sum of squared deviations of scores from their group's mean b) ignores the group a score is in c) is always smaller than Σ(X-M)2 d) is used to determine the grand mean

Ignores the group a score is in

Advanced topic: Using the structural model of the two-way analysis of variance, the first computation is the overall deviation of the score from the grand mean. Next, the deviation of the score from its cell's mean, the deviation of the score's row's mean from the grand mean, and the deviation of the score's column's mean from the grand mean are computed. The remaining deviation is the basis of a) within-groups variance estimates b) row between-groups variance estimates c) column between-groups variance estimates d) interaction between-groups variance estimate

Interaction between-groups variance estimate

A two-way factorial design a) is "two-way" because there are two variables that divide the groups being studied. b) varies only in name from a one-way analysis of variance c) considers two levels of a single variable d) considers a single level of two variables

Is "two-way" because there are two variables that divide the groups being studied.

Advanced topic: In a factorial analysis of variance, the effect size for each main and interaction effect a) is the same for each effect b) is the same number for row and column effects, but different for the interaction effect c) is different for each row, column, and interaction effect d) cannot be calculated because only an effect size for the overall combination of main and interaction effects can be calculated

Is different for each row, column, and interaction effect

A characteristic of an F ratio is that a) the cutoff F equals the calculated F divided by 2 b) it can never be less than 0 c) it is negatively skewed d) the t distribution for infinitydf is the comparison distribution

It can never be less than 0

Advanced topic: One advantage of using the structural model to understand the analysis of variance (as opposed to the method which involves averaging the variances of each group) is that a) it provides more accurate results b) it makes analyzing the results easier when group sizes are different c) It is more structured, and therefore more rigid d) it is more robust to violations of assumptions of normal population distributions

It makes analyzing the results easier when group sizes are different

According to Cohen's conventions, an R2 of .14 would represent a a) small effect b) medium effect c) large d) none of the above, as there are no standards for interpreting R2

Large effect

An interaction effect can be identified by a) looking at the pattern of cell means b) conducting a series of t tests c) dividing each cell mean by it's marginal mean d) dividing each cell mean by a weight marginal mean

Looking at the pattern of cell means

In an analysis of variance, you reject the null hypothesis when the F ratio is a) negative b) much larger than 1 c) equal to the t score d) smaller than 1

Much larger than 1

The item below is based on the following scenarios. What is the relationship between the amount of time spent shopping, Short (under 15 minutes) or Long (over 15 minutes), and the age of the shopper, Young (under 22) or Old (over 22), and the amount of money spent by shoppers in a music store. A store manager said, "How much money people spend isn't related to age. All that matters is how long they shop." If she said that after seeing the results of one of these studies, which scenario was she probably looking at? a) scenario A b) scenario B c) scenario C d) none of the above

None of the above

An interaction effect in a two-way factorial design a) is the effect of one variable that divides the groups, ignoring the influence of the other variable that divides the groups b) occurs when the influence of one variable that divides the groups changes according to the level of the other variable that divides the groups c) almost never occurs when more than one variable that divides the groups is considered at a time d) is rare in a well-designed study, and usually indicates some error in computation

Occurs when the influence of one variable that divides the groups changes according to the level of the other variable that divides the groups

In a one-way analysis of variance, if the null hypothesis is true, then a) the analysis of variance can never produce a significant F ratio. b) estimates of the population variance will be easier to figure. c) the variance between sample means will be larger than the variance within each sample. d) any difference among sample means reflects variance within the populations.

any difference among sample means reflects variance within the populations.

The item below is based on the following scenarios. The scenarios below are possible results of a study in which participants completed a measure of how important religion was to them personally. Participants are either from a Rural or Urban area, and are either Poor or Rich Which of the following statements is true based on the information presented in Scenario C? a) On the average, religion is more important to rich people than to poor people. b) The column means show that religion is more important to poor people c) The row means show that there is no difference between rich and poor in their average interest in religion d) There is a clear interaction effect in which poor people value religion more in urban areas, while rich people value it more in rural areas

On the average, religion is more important to rich people than to poor people.

In a two-way factorial design, there can be a) one interaction and one main effect b) one interaction and two main effects c) two interactions and one main effect d) two interactions and two main effects

One interaction and two main effects

A crucial feature of planned comparisons is that they are a) planned before the study is conducted b) planned after the study is conducted, but before the analysis of variance is conducted c) tests of power, conducted before the study is conducted d) only conducted if power is greater than .80

Planned before the study is conducted

Analysis of variance should be conducted only when a) sample sizes are greater than 30 per group b) sample sizes are smaller than 30 per group c) population variances can be assumed to be equal d) population sizes are approximately equal

Population variances can be assumed to be equal

[(S2Between)(dfBetween)]/[(S2Between)(dfBetween) + (S2Within)(dfWithin)] = a) R2 b) F c) f d) t

R2

[(S2Between)(dfBetween)] / [(S2Between)(dfBetween) + (S2Within)(dfWithin)] = a) R^2 b) F c) f d) t

R^2

The item below is based on the following scenarios.The scenarios below are possible results of a study in which participants completed a measure of how important religion was to them personally. Participants are either from a Rural or Urban area, and are either Poor or Rich.Which statement is true about Scenario B? a) There is a moderate interaction effect. b) Religion is consistently more important for rich people than for poor people, regardless of where they live. c) Religion is more important to people who live in the urban areas, regardless of their wealth. d) Religion is particularly important to people who are both poor and live in rural areas.

Religion is consistently more important for rich people than for poor people, regardless of where they live.

Advanced topic: In an analysis of variance table, which of the following can be used to refer to "within-groups"? a) treatment b) model c) group d) error

error

Most psychology research a) avoids anything more than a one-way analysis of variance b) concurrently examines four or five main variables c) is limited to two-way and occasionally three-way factorial designs d) concurrently examines at least 20 variables

is limited to two-way and occasionally three-way factorial designs

Advanced topic: One disadvantage of using the structural model to understand the analysis of variance (as opposed to the method which involves averaging the variances of each group) is that a) it provides less accurate results. b) it makes analyzing the results more difficult when group sizes are equal c) it is more structured, and therefore more rigid. d)it is not as intuitive or easy to grasp.

it is not as intuitive or easy to grasp.

In general, using the Bonferroni procedure as a post-hoc comparison procedure means that a) important interactions would be overlooked in fewer studies. b) the .05 alpha will be divided into such small parts that finding any significant comparisons will be a long shot. c) fewer subjects will be required per group to detect significant results. d) an overall .10 significance level will guarantee that each comparison can be conducted at the .05 level.

the .05 alpha will be divided into such small parts that finding any significant comparisons will be a long shot

The formula "Σ(M-GM)2/dfBetween" is used to compute a) the F ratio for a repeated measures design b) the between-groups sum of squared deviations c) the estimated variance of the distribution of means d) the between-groups estimate of the population variance

the between-groups estimate of the population variance

Advanced topic: In a two-way analysis of variance, the degrees of freedom for each main effect are a) the number of cells minus the number of variables b) the number of variables minus the total scores within the column or row. c) the number of levels of the variable minus 1. d) the total number of scores in that row or column minus 2.

the number of levels of the variable minus 1.