Statistics for psychology : Pearson new international edition

Aron, Arthur; Aron, Elaine; Coups, Elliot J

Chapter 6 Making Sense of Statistical Significance - all with Video Answers

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Chapter Questions

01:07

Problem 1

Define alpha and beta.

Ajay Singhal

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For each of the following studies, make a chart of the four possible correct and incorrect decisions, and explain what each would mean. Each chart should be laid out like Table 1, but put into the boxes the possible results, using the names of the variables involved in the study.
(a) A study of whether increasing the amount of recess time improves schoolchildren's in-class behavior.
(b) A study of whether color-blind individuals can distinguish gray shades better than the population at large.
(c) A study comparing individuals who have ever been in psychotherapy to the general public to see if they are more tolerant of other people's upsets than is the general population.

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Problem 3

In a completed study, there is a known population with a normal distribution, $\mu=25$, and $\sigma=12$. What is the estimated effect size if a sample given an expenmental procedure has a mean of (a) 19, (b) 22 , (c) 25 , (d) 30 , and (e) 35 ? For each part, also indicate whether the effect is approximately small, medium, or large.

Rashmi Sinha

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Problem 4

In a planned study, there is a known population with a normal distribution, $\mu=50$, and $\sigma=5$. What is the predicted effect size $(d)$ if the researchers predict that those given an experimental treatment have a mean of (a) 50 , (b) 52 , (c) 54 , (d) 56 , and (e) 47 ? For each part, also indicate whether the effect is approximately small, medium, or large.

Rashmi Sinha

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Problem 5

In a planned study, there is a known population with a normal distribution, $\mu=15$, and $\sigma=2$. What is the predicted mean if the researcher predicts (a) a small positive effect size, (b) a medium negative effect size, (c) a large positive effect size, (d) an effect size of $d=.35$, and (e) an effect size of $d=-1.50$ ?

Rashmi Sinha

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Problem 6

Here is information about several possible versions of a planned experiment. Figure effect size for each; sketch the distributions involved, showing the area for alpha, beta, and power. (Assume all populations have a normal distribution.) ADVANCED TOPIC: Figure the power for each version.
(table can't copy)

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Problem 7

You read a study in which the result is significant ( $p<.05$ ). You then look at the size of the sample. If the sample is very large (rather than very small), how should this affect your interpretation of (a) the probability that the null hypothesis is actually true and (b) the practical importance of the result? (c) Explain your answers to a person who understands hypothesis testing but has never learned about effect size or power.

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Problem 8

Aron and colleagues (1997) placed strangers in pairs and asked them to talk together following a series of instructions designed to help them become close. At the end of 45 minutes, individuals privately answered some questions about how close they now felt to their partners. (The researchers combined the answers into a "closeness composite.") One key question was whether closeness would be affected by either (a) matching strangers based on their attitude agreement or (b) leading participants to believe that they had been put together with someone who would like them. The result for both agreement and expecting to be liked was that "there was no significant differences on the closeness composite" (p. 367). The researchers went on to argue that the results suggested that there was little true effect of these variables on closeness:
There was about $90 \%$ power in this study of achieving significant effects . . . for the two manipulated variables if in fact there were a large effect of this kind $(d=8)$. Indeed, the power is about $90 \%$ for finding at least a nearsignificant $(p<.10)$ medium-sized effect $(d=.5)$. Thus, it seems unlikely that we would have obtained the present results if in fact there is more than a small effect. . . . (p.367)
Explain this result to a person who understands hypothesis testing but has never learned about power or effect size.

Rashmi Sinha

Numerade Educator

Problem 9

How does each of the following affect the power of a planned study?
(a) A larger predicted difference between the means of the populations.
(b) A larger population standard deviation.
(c) A larger sample size.
(d) Using a more extreme significance level (e.g., . 01 instead of .05 ).
(e) Using a two-tailed test instead of a one-tailed test.

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00:09

Problem 10

List two situations in which it is useful to consider power, indicating what the use is for each.

Maxime Rossetti

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Problem 11

ADVANCED TOPIC: Based on a particular theory of creativity, a psychologist predicts that artists will be greater risk takers than the general population. The general population is normally distributed with a mean of 50 and a standard deviation of 12 on the risk-taking questionnaire this psychologist plans to use. The psychologist expects that artists will score, on the average, 55 on this questionnaire. The psychologist plans to study 36 artists and test the hypothesis at the .05 level. (a) What is the power of this study? (b) Sketch the distributions involved, showing the areas for alpha, beta, and power. (c) Explain your answer to someone who understands hypothesis testing with means of samples but has never learned about power.

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10:44

Problem 12

ADVANCED TOPIC: On a memory task in which words are learned in a random order, it is known that people can recall a mean of 11 words with a standard deviation of 4 and that the distribution follows a normal curve. A cognitive psychologist, to test a theory, modifies that task so that the words are presented in a way in which words that have a related meaning are presented together. The cognitive psychologist predicts that, under these conditions, people will recall so many more words that there will be a large effect size. She plans to test this with a sample of 20 people, using the .01 significance level, two-tailed. (a) What is the power of this study? (b) Sketch the distributions involved, showing the areas for alpha, beta, and power. (c) Explain your answer to someone who understands hypothesis testing involving means of samples but has never learned about effect size or power.

Ahmad Reda

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Problem 13

For each of the following studies, make a chart of the four possible correct and incorrect decisions, and explain what each would mean. (Each chart should be laid out like Table 1, but put into the boxes the possible results, using the names of the variables involved in the study.)
(a) A study of whether infants bom prematurely begin to recognize faces later than do infants in general.
(b) A study of whether high school students who receive an AIDS prevention program in their school are more likely to practice safe sex than are other high school students.
(c) A study of whether memory for abstract ideas is reduced if the information is presented in distracting colors.

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Problem 14

In a completed study, there is a known population with a normal distribution, $\mu=122$, and $\sigma=8$. What is the estimated effect size if a sample given an experimental procedure has a mean of (a) 100 , (b) 110 , (c) 120 , (d) 130 , and (e) 140 ? For each part, also indicate whether the effect is approximately small, medium, or large.

Rashmi Sinha

Numerade Educator

02:36

Problem 15

In a planned study, there is a known population with a normal distribution, $\mu=0$, and $\sigma=10$. What is the predicted effect size $(d)$ if the researchers predict that those given an experimental treatment have a mean of (a) -8 , (b) -5 . (c) -2 , (d) 0 , and (e) 10 ? For each part, also indicate whether the effect is approximately small, medium, or large.

James Kiss

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02:36

Problem 16

In a planned study, there is a known population with a normal distribution, $\mu=17.5$, and $\sigma=3.2$. What is the predicted mean if the researcher predicts (a) a small positive effect size, (b) a medium negative effect size, (c) an effect size of $d=40$, (d) an effect size of $d=-40$, (e) an effect size of $d=3$ ?

James Kiss

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01:50

Problem 17

Here is information about several possible versions of a planned experiment, each with a single sample. Figure effect size for each; then sketch the distributions involved, showing the areas for alpha, beta, and power. (Assume all populations have a normal distribution.) ADVANCED TOPIC: Figure the power for each version.
(table can't copy)

Manik Pulyani

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00:24

Problem 18

You read a study that just barely fails to be significant at the . 05 level. That is, the result is not significant. You then look at the size of the sample. If the sample is very large (rather than very small), how should this affect your interpretation of (a) the probability that the null hypothesis is actually true and (b) the probability that the null hypothesis is actually false? (c) Explain your answers to a person who understands hypothesis testing but has never learned about power.

Maxime Rossetti

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Problem 19

In the Decision Errors, Effect Size, and Power in Research Articles section earlier in this chapter, you read about a review study conducted by Huey and Polo (2008) that examined psychological treatments for clinical problems among ethnic minority youth. As part of their review, the researchers identified twentyfive studies that compared the effect of a psychotherapy treatment versus a control treatment on youths' clinical problems. They conducted a meta-analysis of the twenty-five studies and reported the results as follows:
[T]he mean effect size was $d=.44$. Because coefficients of . 20 or lower represent" "small" effects, coefficients around .50 "medium" effects, and coefficients of 80 or higher "large effects", the overall $d$ reported here falls somewhat below the standard for a "medium" effect (Cohen, 1988). (p. 282)
Explain the purpose and results of this meta-analysis to someone who is familiar with effect size but has never heard of meta-analysis.

Rashmi Sinha

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Problem 20

Caspi and colleagues (1997) analyzed results from a large-scale longitudinal study of a sample of children born around 1972 in Dunedin, New Zealand. As one part of their study, the researchers compared the 94 in their sample who were, at age 21, alcohol dependent (clearly alcoholic) versus the 863 who were not alcohol dependent. The researchers compared these two groups in terms of personality test scores from when they were 18 years old. After noting that all results were significant, they reported the following results:
Young adults who were alcohol dependent at age 21 scored lower at age 18 on Traditionalism $(d=.49)$. Harm Avoidance $(d=.44)$. Control $(d=.64)$. and Social Closeness $(d=40)$, and higher on Aggression $(d=.86)$, Alienation ( $d=.66$ ) and Stress Reaction $(d=.50$ ).
Explain these results, including why it was especially important for the researchers in this study to give effect sizes, to a person who understands hypothesis testing but has never learned about effect size or power.

Rashmi Sinha

Numerade Educator

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Problem 21

Tsang and colleagues (2009) conducted a review to examine the statistical power of studies that had compared patients' experiences of serious adverse events (such as a life-threatening medical event) during randomized controlled trials of medical treatments. They identified six studies that reported the results of statistical analyses to test whether the number of adverse effects experienced by patients receiving one medical treatment differed from the number experienced by those receiving a different treatment. Tsang et al. summarized their results as follows: Three of the six studies included in this analysis reported non-statistically significant differences in serious adverse event rates, and concluded that there was no difference in risk despite [having power] of less than 0.37 to detect the reported differences" (p. 610). They also noted that: "A high probability of type II error may lead to erroneous clinical inference resulting in harm. The statistical power for nonsignificant tests should be considered in the interpretation of results" (p. 609). Explain the results of this review to a person who understands hypothesis testing and decision errors but has never learned about effect size or power.

Rashmi Sinha

Numerade Educator

01:20

Problem 22

You are planning a study that you compute as having quite low power. Name six things that you might do to increase power.

John Wells

Numerade Educator

02:45

Problem 23

ADVANCED TOPIC: A psychologist is planning a study on the effect of motivation on performance on an attention task. In this task, participants try to identify target letters in a stream of letters passing by at a rapid rate. The researcher knows from long experience that, under ordinary experimental conditions, the population of students who participate in this task identify a mean of 71 of the key letters, that the standard deviation is 10 , and that the distribution is approximately normal. The psychologist predicts that, if the participant is paid a dollar for each letter identified correctly, the number correctly identified will increase to 74 . The psychologist plans to test 20 participants under these conditions, using the . 05 level. (a) What is the power of this study? (b) Sketch the distributions involved, showing the areas for alpha, beta, and power. (c) Explain your answer to someone who understands hypothesis testing involving means of samples but has never learned about power.

Jameson Kuper

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04:18

Problem 24

ADVANCED TOPIC: An organizational psychologist predicts that assembly workers will have a somewhat higher level of job satisfaction if they are given a new kind of incentive program (that is, he predicts a medium effect size). On a standard job satisfaction scale, for assembly workers in this company overall. the distribution is normal, with $\mu=82$ and $\sigma=7$. The psychologist plans to provide the new incentive program to 25 randomly selected assembly workers. (a) What is the power of this study (using $p<.01$ )? (b) Sketch the distributions involved, showing the areas for alpha, beta, and power. (c) Explain your answer to someone who understands hypothesis testing involving means of samples but has never learned about effect size or power.

Sheryl Ezze

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