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Statistics For The Behavioral And Social Sciences 5th Edition Arthur Aron Elliot Coups, Elaine N. Aron - Solutions
Make up two examples of studies (not in the book or from your lectures) that would be tested with a t test for independent means.
Gallagher-Thompson, Dal Canto, Jacob, and Thompson (2001) compared 27 wives who were caring for their husbands who had Alzheimer’s disease to 27 wives in which neither partner had Alzheimer’s disease. The two groups of wives were otherwise similar in terms of age, number of years married, and
Van Aken and Asendorpf (1997) studied 139 German 12-year-olds. All of the children completed a general self-worth questionnaire and were interviewed about the supportiveness they experienced from their mothers, fathers, and classmates. The researchers then compared the self-worth of those with high
What are the approximate numbers of participants needed for each of the following planned studies to have 80% power, assuming equal numbers in the two groups and all using the .05 significance level? (Be sure to give the total number of participants needed, not just the number needed for each
Figure the approximate power of each of the following planned studies, all using a t test for independent means at the .05 significance level, one-tailed, with a predicted small effect size: Study N N (a) 3 57 (b) 10 50 (c) 20 40 (d) 30 30
Figure the estimated effect size for problems (a) 4, (b) 5, and (c) 6. (d) Explain what you have done in part (a) to someone who understands the t test for independent means but knows nothing about effect size.
A developmental researcher compares 4-year-olds and 8-year-olds on their ability to understand the analogies used in stories. The scores for the five 4-year-olds tested were 7, 6, 2, 3, and 8. The scores for the three 8-year-olds tested were 9, 2, and 5. Using the .05 level, do older children do
A teacher was interested in whether using a student’s own name in a story affected children’s attention span while reading. Six children were randomly assigned to read a story under ordinary conditions (using names like Dick and Jane). Five other children read versions of the same story, but
A communication researcher randomly assigned 82 volunteers to one of two experimental groups. Sixty-one were instructed to get their news for a month only from television, and 21 were instructed to get their news for a month only from the Internet. (Why the researcher didn’t assign equal numbers
For each of the following experiments, decide whether the difference between conditions is statistically significant at the .05 level (two-tailed). Experimental Group Control Group Study N M N M S (a) 30 12.0 2.4 (b) 28 20 12.0 2.4. 40 30 12.0 2.2 30 88 30 11.1 2.8 11.1 2.8 11.1 3.0
Figure SDifference for each of the following studies: Study N S N S (a) 20 1 20 (b) 20 1 40 (c) 40 1 20 (d) 40 1 40 (e) 40 1 40 22224
For each of the following studies, say whether you would use a t test for dependent means or a t test for independent means.(a) An education researcher randomly assigns a group of 47 fourth-grade students to receive a new after-school math program and 48 other fourth-grade students to receive the
Explain how and why the scores from Steps ❸ and ❹ of the hypothesis-testing process are compared. Explain the meaning of the result of this comparison with regard to the specific research and null hypotheses being tested.
Describe why and how you figure the t score of the sample mean on the comparison distribution.
Describe the logic and process for determining the cutoff sample score(s) on the comparison distribution at which the null hypothesis should be rejected.
Explain why the shape of the comparison distribution that is used with a t test for independent means is a t distribution (as opposed to the normal curve).
Outline the logic of estimating the population variance and the variance of the two distributions of means. Describe how to figure the standard deviation of the distribution of differences between means.
Explain the entire complex logic of the comparison distribution that is used with a t test for independent means (the distribution of differences between means). Be sure to explain why you use 0 as its mean. (This and point 3 will be the longest part of your essay.)
Describe the core logic of hypothesis testing in this situation. Be sure to mention that the t test for independent means is used for hypothesis testing when you have scores from two entirely separate groups of people. Be sure to explain the meaning of the research hypothesis and the null
How many participants do you need in each group for 80% power in a planned study in which you predict a small effect size and will be using a t test for independent means, one-tailed, at the .05 significance level?
What is the approximate power of a study using a t test for independent means, with a two-tailed test at the .05 significance level, in which the researchers predict a large effect size, and there are 6 participants in one group and 34 participants in the other group?
What is the power of a study using a t test for independent means, with a two-tailed test at the .05 significance level, in which the researchers predict a large effect size and there are 20 participants in each group?
What is the predicted effect size for a study in which the sample drawn from Population 1 has a mean of 17, Population 2’s sample mean is 25, and the pooled estimate of the population standard deviation is 20?
Why do you need to assume the populations have the same variance?
List two assumptions for the t test for independent means. For each, give the situations in which violations of these assumptions would be a serious problem.
Using the .05 significance level, two-tailed, figure a t test for independent means for an experiment in which scores in an experimental condition are predicted to be lower than scores in a control condition. For the experimental condition, with M = 8, S2 = 1226 participants, M = 5, S2 = 10; for
List the ways in which hypothesis testing for a t test for independent means is different from a t test for dependent means in terms of (a) Step ❷, (b) Step ❸, and (c) Step ❹.
For a particular study comparing means of two samples, the first sample has 21 participants and an estimated population variance of 100; the second sample has 31 participants and an estimated population variance of 200. (a) What is the standard deviation of the distribution of differences between
Explain (a) why a t test for independent means uses a single pooled estimate of the population variance, (b) why, and (c) how this estimate is “weighted.”
Write the formula for each of the following: (a) pooled estimate of the population variance, (b) variance of the distribution of means for the first population, (c) variance of the distribution of differences between means, and (d) t score in a t test for independent means. (e) Define all the
(a) In the context of the t test for independent means, explain the logic of going from scores in two samples to an estimate of the variance of this comparison distribution. (b) Illustrate your answer with sketches of the distributions involved.(c) Why is the mean of this distribution 0?
(a) What is the comparison distribution in a t test for independent means?(b) How is this different from the comparison distribution in a t test for dependent means?
(a) When would you carry out a t test for independent means? (b) How is this different from the situation in which you would carry out a t test for dependent means?
Table 13 (reproduced from Table 4 of Larson, Dworkin, & Verma, 2001) shows ratings of various aspects of work and home life of 100 middle-class men in India who were fathers. Pick three rows of interest to you and explain the results to someone who is familiar with the mean, variance, and Z
Baker and Moore (2008) surveyed 58 people when they first started using MySpace(the researchers called this “Time 0”) and again 2 months later (referred to as “Time 1” by the researchers). At both time points, the participants completed a measure of social integration. Also, at Time 1, the
A study compared union activity of employees in 10 plants during two different decades. The researchers reported “a significant increase in union activity, t(9) = 3.28, p 6 .01” Explain this result to a person who has never had a course in statistics. Be sure to use sketches of the
About how many participants are needed for 80% power in each of the following planned studies that will use a t test for dependent means with p 6 .05? Study Predicted Effect Size Tails (a) Small Two (b) Medium One (c) Large Two
What is the power of each of the following studies, using a t test for dependent means (based on the .05 significance level)? Study Effect Size N Tails (a) Small 50 Two (b) Medium 50 Two (c) Large 50 Two (d) Small 10 Two (e) Small 40 Two (f) Small 100 Two (g) Small 100 One
Figure the estimated effect size and indicate whether it is approximately small, medium, or large, for each of the following studies: Study Mean Change S (a) 8 30 (b) 8 10 (c) 16 30 (d) 16 10
Five sophomores were given an English achievement test before and after receiving instruction in basic grammar. Their scores are shown below.Is it reasonable to conclude that future students would show higher scores after instruction?Use the .05 significance level. (a) Use the steps of hypothesis
Five people who were convicted of speeding were ordered by the court to attend a workshop. A special device put into their cars kept records of their speeds for 2 weeks before and after the workshop. The maximum speeds for each person during the 2 weeks before and the 2 weeks after the workshop
Four individuals with high levels of cholesterol went on a special diet, avoiding high-cholesterol foods and taking special supplements. Their total cholesterol levels before and after the diet were as follows:Using the .05 level of significance, was there a significant change in cholesterol level?
For each of the following studies using difference scores, test the significance using a t test for dependent means. Number of Difference Scores Mean of Difference Scores Estimated Population Variance of Difference Study in Sample in Sample Scores Tails Significance Level (a) 10 3.8 50 1 (high
In a particular country, it is known that college seniors report falling in love an average of 2.20 times during their college years. A sample of five seniors, originally from that country but who have spent their entire college career in the United States, were asked how many times they had fallen
Evolutionary theories often emphasize that humans have adapted to their physical environment. One such theory hypothesizes that people should spontaneously follow a 24-hour cycle of sleeping and waking—even if they are not exposed to the usual pattern of sunlight. To test this notion, eight paid
In each of the following studies, a single sample’s mean is being compared to a population with a known mean but an unknown variance. For each study, decide whether the result is significant. Estimated Population Study Sample Size (M) Population Standard Mean Deviation (S) Sample Mean (M) Tails
A researcher conducts a study of perceptual illusions under two different lighting conditions.Twenty participants were each tested under both of the two different conditions.The experimenter reported: “The mean number of effective illusions was 6.72 under the bright conditions and 6.85 under the
Weller and Weller (1997) conducted a study of the tendency for the menstrual cycles of women who live together (such as sisters) to become synchronized. For their statistical analysis, they compared scores on a measure of synchronization of pairs of sisters living together versus the degree of
About how many participants are needed for 80% power in each of the following planned studies that will use a t test for dependent means with p 6 .05? Study Predicted Effect Size Tails (a) Medium Two (b) Large One (c) Small One
What is the power of each of the following studies, using a t test for dependent means (based on the .05 significance level)? Study Effect Size N Tails (a) Small 20 One (b) Medium 20 One (c) Medium 30 One (d) Medium 30 Two (e) Large 30 Two
Figure the estimated effect size and indicate whether it is approximately small, medium, or large, for each of the following studies: Study Mean Change S (a) 20 (b) 5 (c) .1 (d) 100 28 32 10 .4 500
A researcher assesses the level of a particular hormone in the blood in five patients before and after they begin taking a hormone treatment program. Results for the five are as follows:Using the .05 level of significance, was there a significant change in the level of this hormone? (a) Use the
A program to decrease littering was carried out in four cities in California’s Central Valley starting in August 2009. The amount of litter in the streets (average pounds of litter collected per block per day) was measured during the July before the program was started and then the next July,
For each of the following studies using difference scores, test the significance using a t test for dependent means. Also, figure the estimated effect size for each study. Number of Difference Scores Mean of Difference Scores Estimated Population Variance of Difference Study in Sample in Sample
A researcher tests five individuals who have seen paid political ads about a particular issue. These individuals take a multiple-choice test about the issue in which people in general (who know nothing about the issue) usually get 40 questions correct. The number correct for these five individuals
Suppose a candidate running for sheriff claims that she will reduce the average speed of emergency response to less than 30 minutes, which is thought to be the average response time with the current sheriff. There are no past records, so the actual standard deviation of such response times cannot
In each of the following studies, a single sample’s mean is being compared to a population with a known mean but an unknown variance. For each study, decide whether the result is significant. (Be sure to show all of your calculations.) Estimated Sample Population Study Size (M) Mean Population
Explain how and why the scores from Steps and of the hypothesis-testing process are compared. Explain the meaning of the result of this comparison with regard to the specific research and null hypotheses being tested.
Describe why and how you figure the t score of the sample mean on the comparison distribution.
Describe the logic and process for determining the cutoff sample score(s) on the comparison distribution at which the null hypothesis should be rejected.
Describe the comparison distribution (the t distribution) that is used with a t test for dependent means. Explain why a t distribution (as opposed to the normal curve) is used as the comparison distribution.
Outline the logic of estimating the population variance of difference scores from the sample scores. Explain the idea of biased and unbiased estimates of the population variance, and describe the formula for estimating the population variance. Describe how to figure the standard deviation of the
Explain why you use 0 as the mean for the comparison distribution.
Describe the core logic of hypothesis testing in this situation. Be sure to mention that the t test for dependent means is used for hypothesis testing when you have two scores from each person in your sample. Be sure to explain the meaning of the research hypothesis and the null hypothesis in this
Explain how and why the scores from Steps and of the hypothesis-testing process are compared. Explain the meaning of the result of this comparison with regard to the specific research and null hypotheses being tested.
Describe why and how you figure the t score of the sample mean on the comparison distribution.
Describe the logic and process for determining the cutoff sample score(s) on the comparison distribution at which the null hypothesis should be rejected.
Describe the comparison distribution (the t distribution) that is used with a t test for a single sample, noting how it is different from a normal curve and why.Explain why a t distribution (as opposed to the normal curve) is used as the comparison distribution.
Outline the logic of estimating the population variance from the sample scores.Explain the idea of biased and unbiased estimates of the population variance, and describe the formula for estimating the population variance and why it is different from the ordinary variance formula.
Describe the core logic of hypothesis testing in this situation. Be sure to mention that the t test for a single sample is used for hypothesis testing when you have scores for a sample of individuals and you want to compare the mean of this sample to a population for which the mean is known but the
(a) Why do repeated-measures designs have so much power? (b) What is the main disadvantage of the kind of repeated-measures study discussed in this chapter?
You are planning a study in which you predict an effect size of .50. You plan to test significance using a t test for dependent means, one-tailed, with an alpha of .05. (a) What is the power of this study if you carry it out with 20 participants?(b) How many participants would you need to have 80%
(a) Write the formula for estimated effect size in a t test for dependent means situation, and (b) describe each of its terms.
(a) What is an assumption in hypothesis testing? (b) Describe a specific assumption for a t test for dependent means. (c) What is the effect of violating this assumption? (d) When is the t test for dependent means likely to give a very distorted result?
What about the research situation makes the difference in whether you should carry out a t test for a single sample or a t test for dependent means?
What about the research situation makes the difference in whether you should carry out a Z test or a t test for a single sample?
Five individuals are tested before and after an experimental procedure; their scores are given in the following table. Test the hypothesis that there is no change, using the .05 significance level. (a) Use the steps of hypothesis testing and (b) sketch the distributions involved. Person Before
In a t test for dependent means, (a) what is usually considered to be the mean of the “known” population (Population 2). (b) Why?
When doing a t test for dependent means, what do you do with the two scores you have for each participant?
Describe the situation in which you would use a t test for dependent means.
A population has a mean of 23. A sample of four is given an experimental procedure and has scores of 20, 22, 22, and 20. Test the hypothesis that the procedure produces a lower score. Use the .05 significance level. (a) Use the steps of hypothesis testing and (b) make a sketch of the distributions
List three differences in how you do hypothesis testing for a t test for a single sample versus for the Z test.
(a) How does a t distribution differ from a normal curve? (b) How do degrees of freedom affect this? (c) What is the effect of the difference on hypothesis testing?
(a) What are degrees of freedom? (b) How do you figure the degrees of freedom in a t test for a single sample? (c) What do they have to do with estimating the population variance? (d) What do they have to do with the t distribution?
What is the difference between the usual formula for figuring the variance and the formula for estimating a population’s variance from the scores in a sample (that is, the formula for an unbiased estimate of the population variance)?
In what sense is a sample’s variance a biased estimate of the variance of the population from which the sample is taken? That is, in what way does a sample’s variance typically differ from the population’s?
You are planning a study that you determine from a power table as having quite low power. Name six things that you might do to increase power.
Tsang, Colley, and Lynd (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
Caspi et al. (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
You read a study that just barely fails to be significant at the .05 level. That is, the result is not statistically 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 judgment of (a) the probability that the null
What is meant by the statistical power of an experiment? (Write your answer for a layperson.)
In the “Effect Size and Power in Research Articles” section earlier in the 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 25
What is meant by effect size? (Write your answer for a layperson.)
Here is information about several possible versions of a planned study, each involving a single sample. Figure the predicted effect size for each study: Population 2 Predicted Study M SD Population 1 M (a) 90 (b) 90 90 (d) (e) 90 88888 90 21222 91 91 92 94 86
In a planned study, there is a known population with a normal distribution, Population and Population What is the predicted effect size if the researchers predict that those given an experimental treatment have a mean of (a) (b) (c) (d) 0, and (e) 10? For each part, also indicate whether the
In a completed study, there is a known population with a normal distribution, Population and Population 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
List two situations in which it is useful to consider power, indicating what the use is for each.
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., instead of )(e) Using a two-tailed test
Aron et al. (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
You read a study in which the result is 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 practical importance of the
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