statistics chapters 12 & 13

Researchers performed a study on the effects of a nonsteroidal anti-inflammatory drug (NSAID) given before and after arthroscopic knee surgery. A sample of 67 patients undergoing elective knee arthroscopy was randomly divided into three treatment groups. Researchers compared the mean pain scores of the patients in the three treatment groups one day after surgery, and the F value obtained was 4.79. The probability that the researchers would have seen differences among the mean pain scores more extreme than what they witnessed is _____. (Answer using three decimal places.)

0.012

Caleb conducts a study comparing the performance of the same nine individuals on the first quiz taken in each of three classes. The scores, out of 100, are provided for each class. Class 1: 87, 78, 87, 85, 93, 98, 83, 82, 73 Class 2: 87, 86, 92, 90, 90, 91, 89, 78, 73 Class 3: 87, 78, 92, 85, 90, 98, 89, 82, 76 For this study, R2 is _____. (Answer using two decimal places.)

0.05

Linus conducts a study comparing the performance of biology majors, psychology majors, and English majors taking the same Introductory Psychology quiz. The scores, out of 100, are provided for individuals in each group. Biology majors: 87, 78, 77, 85, 93, 98, 83 Psychology majors: 87, 96, 92, 90, 90, 98 English majors: 87, 96, 77, 90, 93, 91, 83 R2 is: 0.16. 0.84. 5.23. 6.23.

0.16

Consider a study comparing the effects of three different drugs on memory for words in a recall memory test. The scores, which measure the number of words remembered, are provided for 18 individuals tested after taking one of the three drugs. Red Drug: 7, 9, 8, 9, 7, 8 White Drug: 5, 7, 6, 8, 9, 7 Blue Drug: 7, 4, 5, 5, 5, 6 R2 is: 1.89. 0.89. 0.47. 0.53.

0.53

Xavier conducts a study comparing the performance of the same nine individuals on the first quiz taken in each of three classes. The scores, out of 100, are provided for each class. Class 1: 87, 78, 87, 85, 93, 98, 80, 82, 73 Class 2: 87, 86, 92, 90, 90, 91, 89, 78, 76 Class 3: 87, 78, 92, 85, 90, 98, 89, 82, 76 The value of F is: 8.445. 0.80. 3.63. 10.528.

0.80

Consider a study comparing the effects of three different drugs on memory for words in a recall memory test. The scores, which measure the number of words remembered, are provided for six individuals tested after taking each of the three drugs (but in different orders). Red Drug: 7, 9, 8, 9, 7, 8 White Drug: 5, 7, 6, 8, 9, 7 Blue Drug: 7, 7, 5, 5, 5, 6 Given this partial source table for a one-way within-groups ANOVA, the value of MSwithin, needed to complete the one-way within-groups ANOVA, is: Source of variation: SS Between: 14.111 Subjects: 4.278 Within: 14.555 Total: 32.944 0.687. 1.456. 0.442. 1.031.

1.456

Consider a study comparing the effects of three different drugs on memory for words in a recall memory test. The scores, which measure the number of words remembered, are provided for six individuals tested after taking each of the three drugs (but in different orders). Red Drug: 7, 9, 8, 9, 7, 8 White Drug: 5, 7, 6, 8, 9, 7 Blue Drug: 7, 7, 5, 5, 5, 6 The value of MSwithin, needed to complete the one-way within-groups ANOVA, is: 1.031. 1.456. 0.687. 0.442.

1.456

Consider a study comparing the effects of three different drugs on memory for words in a recall memory test. The scores, which measure the number of words remembered, are provided for six individuals tested after taking each of the three drugs (but in different orders). Red Drug: 7, 9, 8, 9, 7, 8 White Drug: 5, 7, 6, 8, 9, 7 Blue Drug: 7, 7, 5, 5, 5, 6 The value of SSbetween, needed to complete the one-way within-groups ANOVA, is: 14.555. 14.111. 4.278. 32.944.

14.111

Alexis conducts a Tukey HSD test based on the SAT scores of his students. He finds that the within-groups mean square is 520 and the sample size is 50. Calculate the standard error. 3.26 3.22 10.4 0.31

3.22

Which item demonstrates an appropriate set of null hypotheses for the analysis of variance (ANOVA) approach for comparing four means? Please choose the correct answer from the following choices, and then select the submit answer button. A. µ1 = µ2 = µ3 = µ4 B. µ1 = µ2, µ1 = µ3, µ1 = µ4, µ2 = µ3, µ2 = µ4, and µ3 = µ4 C. µ1 - µ2 = 0 and µ3 - µ4 = 0 D. µ1 - µ2 = 0, µ1 - µ3 = 0, µ1 - µ4 = 0, µ2 - µ3 = 0, µ2 - µ4 = 0, and µ3 - µ4 = 0

A

Consider a study using a one-way within-groups design with between-groups df = 4 and within-groups df = 28. Given an alpha level of 0.01, the researcher should: fail to reject the null hypothesis if F < 4.08. reject the null hypothesis if F < 2.72. reject the null hypothesis if F > 2.72. reject the null hypothesis if F < 4.08.

A. fail to reject the null hypothesis if F < 4.08.

Which statement is true regarding the condition for ANOVA inference that all populations must have the same variance? Please choose the correct answer from the following choices, and then select the submit answer button. A. If the variances are unequal but the sample sizes are fairly large, the condition is still satisfied. B.If the largest sample variance is no more than twice as large as the smallest one, the condition is considered to be satisfied. C. If the variances are unequal but the sample sizes are equal, the condition is still satisfied. D. The values of the sample variances must be exactly equal for the ANOVA to be valid.

B

Linus conducts a study comparing the performance of biology majors, psychology majors, and English majors taking the same Introductory Psychology quiz. The scores, out of 100, are provided for individuals in each group. Biology majors: 87, 78, 77, 85, 93, 98, 83 Psychology majors: 87, 96, 92, 90, 90, 98 English majors: 87, 96, 77, 90, 93, 91, 83 R2 is: A.5.23. B. 0.16. C. 6.23. D. 0.84.

B. 0.16

If it is not possible for participants to complete all conditions, matched-groups designs allow the researcher to retain which advantage of a within-groups study? A. Matched-groups designs use the same random assignment scheme as within-groups studies. B. Matched groups retain the statistical power of a within-groups design. C. Matched-groups designs also require the researcher to recruit fewer participants. D. Matched-groups designs require less time and resources than between-groups designs.

B. Matched groups retain the statistical power of a within-groups design

Consider a study comparing the effects of three different drugs on memory for words in a recall memory test. The scores, which measure the number of words remembered, are provided for 18 individuals each tested after taking one of the drugs. Red Drug: 7, 9, 8, 9, 7, 8 White Drug: 5, 7, 6, 8, 9, 7 Blue Drug: 7, 7, 5, 5, 5, 6 The researcher is likely to: A. reject the null hypothesis if the difference between means found for the three drugs is much smaller than the difference between means expected just by chance. B. reject the null hypothesis if the difference between means found for the three drugs is much larger than the difference between means expected just by chance. C. fail to reject the null hypothesis if the difference between means found for the three drugs is much larger than the difference between means expected just by chance. D. fail to reject the null hypothesis if the difference between means expected just by chance is much smaller than the difference between means found for the three drugs.

B. reject the null hypothesis if the difference between means found for the three drugs is much larger than the difference between means expected just by chance.

Consider a study comparing the effects of three different drugs on memory for words in a recall memory test. The scores, which measure the number of words remembered, are provided for six individuals tested after taking each of the three drugs (but in different orders). Red Drug: 7, 9, 8, 9, 7, 8 White Drug: 5, 7, 6, 8, 9, 7 Blue Drug: 7, 7, 5, 5, 5, 6 The appropriate hypothesis test is the: A. matched-samples t test because the number of participants taking each drug is matched. B. within-groups ANOVA because there are more than two levels of the independent variable and the same participants are in each sample. C. between-groups ANOVA because there are more than two levels of the independent variable and there are different individuals in each sample. D. independent-samples t test because the three drugs are given independently.

B. within-groups ANOVA because there are more than two levels of the independent variable and the same participants are in each sample.

Which statement is true? A. A post hoc test allows us to make multiple comparisons among several variances. B. A post hoc test is a statistical procedure frequently carried out after the null hypothesis has failed to be rejected in an analysis of variance. C. A post hoc test will let us know which specific pairs of means are different from one another. D. A post hoc test is a statistical procedure frequently carried out after the alternative hypothesis has been rejected in an analysis of variance.

C. A post hoc test will let us know which specific pairs of means are different from one another.

Consider a study using a between-groups design with 45 participants—three groups of 15. Given an alpha level of 0.01, the researcher should: A. reject the null hypothesis if F < 3.23. B. fail to reject the null hypothesis if F > 5.18. C. reject the null hypothesis if F > 5.18. D. reject the null hypothesis if F > 3.

C. reject the null hypothesis if F > 5.18

An eager graduate student has just completed a within-groups ANOVA that had three levels of the independent variable and 15 participants. He used an alpha level of 0.05 and calculated a between-groups F statistic of 4.06. Based on this result, which of the following is a reasonable next step? As the results do not show a significant effect, no additional work should be done. Calculate paired-samples t tests to see where the differences lie. Confirm that none of the assumptions of the test has been violated. Calculate Tukey HSD values for each pairwise comparison to see where the differences lie.

Calculate Tukey HSD values for each pairwise comparison to see where the differences lie.

In regard to deciding whether to use a z, t, or F distribution, which statement is false? A. A t distribution can be used with two samples without knowing either the population's mean or its variance. B. A t distribution can be used with one sample if the sample mean is known but the population variance is not. C. For three or more samples, an F distribution is required. D. A z distribution can be used with one sample without knowing either the population's mean or its variance.

D. A z distribution can be used with one sample without knowing either the population's mean or its variance.

Gerald wants to know if some video games increase spatial attention more than others do. He tests 10 participants on spatial attention after they play each of 3 video games. The average score after game 1 is 11, the average score after game 2 is 18, and the average score after game 3 is 25. The mean square within is 4.99, and the within-groups degrees of freedom is 7. Using a Tukey HSD post hoc test, is the comparison between game 1 and game 3 significant at a level of 0.01? Please choose the correct answer from the following choices, and then select the submit answer button. A. It is not significant. The calculated value of 19.82 does not exceed the critical value. B. It is not significant. The calculated value of 28.06 does not exceed the critical value. C. It is significant. The calculated value of 28.06 exceeds the critical value. D. It is significant. The calculated value of 19.82 exceeds the critical value.

D. It is significant. The calculated value of 19.82 exceeds the critical value.

The formula for calculating SSwithin, necessary for conducting a one-way within-groups ANOVA, is: ∑(X - GM)2. ∑(M - GM)2. ∑(Mparticipant - GM)2. SStotal - SSbetween - SSsubjects.

D. SStotal - SSbetween - SSsubjects

What is the defining difference between one-way ANOVA and two-way ANOVA? A. the number of levels of the independent variable B. the number of independent variables C. the number of populations D. the number of samples

D. number of independent variables

____ is a hypothesis test used with nominal or ordinal independent variables that have at least three levels and a scale dependent variable.

analysis of variance

In a matched-groups study, participants are matched so that they: are similar on the variables that need to be controlled. are different on the variables that need to be controlled. have similar outcomes on the dependent variable. have different outcomes on the dependent variable.

are similar on the variables that need to be controlled

The one-way within-groups ANOVA requires an additional assumption compared to the one-way between-groups ANOVA, which is that we must be careful to: avoid order effects. include order effects. avoid ordinal variables. avoid random selection.

avoid order effects

The one-way within-groups ANOVA differs from the one-way between-groups ANOVA in that it requires the researcher to calculate: dfwithin. dfsubjects. dftotal. dfbetween.

df subjects

The Tukey HSD test is a widely used post hoc test following one-way between-groups ANOVA that determines the differences between means in terms of standard _____

error

___ equal to one

f statistic

Populations are described as _____ if the populations do not have approximately the same variance. normal homoscedastic Bonferronic heteroscedastic

heteroscedastic

Larry conducts a study comparing the performance of biology majors, psychology majors, and English majors taking the same Introductory Psychology quiz. The scores, out of 100, are provided for individuals in each group. Biology majors: 87, 78, 77, 85, 93, 98, 83 Psychology majors: 87, 96, 92, 90, 90, 91 English majors: 87, 96, 77, 90, 93, 91, 83 Given this partial source table, according to conventions for R2, the effect size for this study is: Source of Variation: SS Between: 85.486 Within: 641.714 Total: 727.200 nonexistent. small. large. medium.

large

A one-way within-groups ANOVA differs from a one-way between-groups ANOVA in that, all else being equal, the one-way within-groups ANOVA will have a: lower MSwithin and thus a larger denominator for the F statistic. lower MSwithin and thus a smaller denominator for the F statistic. lower MSwithin and thus a larger denominator for the F statistic. higher MSwithin and thus a smaller denominator for the F statistic.

lower MSwithin and thus a smaller denominator for the F statistic.

Stella is calculating R2 for her study. The sum of squares between is 100, and the sum of squares total is 1500. Her effect size would be considered:

medium

Because one-way between-groups ANOVA tells us only that there is a difference between at least two of the means in the study, _____ are used to determine which pairs of means are statistically significantly different from each other.

post hoc tests

After conducting a one-way within-groups ANOVA, if the F test statistic is greater than the cutoff, the researcher should _____ the null hypothesis.

reject

Consider a study using a one-way within-groups design with 3 participants exposed to each of 4 conditions. Given an alpha level of 0.05, the researcher should _____ the null hypothesis if F > 4.76.

reject

Consider a study using a within-groups design with between-groups df = 3 and within-groups df = 51. Given an alpha level of 0.05, the researcher should: reject the null hypothesis if F < 2.79. fail to reject the null hypothesis if F > 2.79. reject the null hypothesis if F > 2.77. reject the null hypothesis if F > 2.79.

reject the null hypothesis if F > 2.79

Within-groups ANOVA is also called _____ ANOVA. multivariate repeated-measures two-way between-groups

repeated-measures