Deck 8: Confidence Intervals, Effect Size, and Statistical Power

Question 1

What falls within a 90 percent confidence interval?

A) all the means we would expect to obtain 10 percent of the time when repeatedly sampling from a population
B) all the means we would expect to obtain 90 percent of the time when repeatedly sampling from a population
C) the true population mean
D) the null hypothesis population mean

Answer 1

all the means we would expect to obtain 90 percent of the time when repeatedly sampling from a population

Question 2

Assume for a given study that the null hypothesis asserts the expected value of a phenomenon is 10.A research study results in a 95 percent confidence interval reported as [7.142, 9.865].What decision should be made based on this confidence interval?

A) Reject the null hypothesis.
B) Fail to reject the null hypothesis.
C) Retain the null hypothesis.
D) Perform a hypothesis test before making a decision.

Answer 2

Reject the null hypothesis.

Question 3

Recent research published by Frumin and colleagues (2011) in the journal Science addresses whether females' tears have an effect on males.Imagine that exposure to tears lowered self-rated sexual arousal by 1.27 points, with a margin of error of 0.32 points.The point estimate is _____, while the interval estimate is _____.

A) 0.32; [0.95, 1.59]
B) 1.27; [0.95, 1.59]
C) 0.32; [-0.95, 1.59]
D) 1.27; [-0.95, 1.59]

Answer 3

1.27; [0.95, 1.59]

Question 4

If the sample mean is 56.2, with an upper limit to the confidence interval of 62.74, what is the lower limit?

A) 6.54
B) 49.66
C) 52.46
D) 56.20

Question 5

When considering the results from an opinion poll, where several verbal expressions are rated for their level of annoyance, what is particularly useful about margins of error is that:

A) they tell us how accurate our data are.
B) they directly pinpoint a single value to estimate data.
C) the accuracy of the point estimate increases with the addition of the margin of error.
D) we can figure out more than one interval estimate for the same poll to see if they overlap.

Question 6

A confidence interval is a(n) _____ that includes the population mean after repeatedly sampling.

A) point estimate
B) interval estimate
C) probability
D) hypothesis

Question 7

As sample size increases, the:

A) population mean increases.
B) standard error increases.
C) size of the test statistic increases.
D) size of the test statistic decreases.

Question 8

Michelle is a cognitive psychologist studying reading times for stories that contain either consistent or inconsistent information.She runs 38 people through her study and concludes that reading times slow when coherence breaks occur in a story.Specifically, she concludes reading times slow by 6.9 milliseconds on average.Michelle's prediction is a(n):

A) interval estimate.
B) standard deviation.
C) point estimate.
D) sigma score.

Question 9

Recent research published by Frumin and colleagues (2011) in the journal Science addresses whether females' tears have an effect on males.Imagine that exposure to tears lowered self-rated sexual arousal by 1.27 points, with a margin of error of 0.32 points.The interval estimate is:

A) 1.27.
B) +/- 0.32.
C) [0.95, 1.59].
D) 0.32.

Question 10

Hypothesis testing tells:

A) what the size of an effect is.
B) which group differences are of practical importance.
C) whether two distributions overlap at all.
D) what results are significant, but no details regarding significant results.

Question 11

The range of raw scores contained in an 80 percent confidence interval will be _____ the range of raw scores contained in a 95 percent confidence interval.

A) larger than
B) smaller than
C) the same size as
D) smaller than or the same size as.

Question 12

Confidence in a point estimate _____, whereas confidence in an interval estimate _____.

A) is very high; is very low
B) is based on the alpha level used; is based on the margin of error calculated
C) cannot be articulated; is directly related to the size of the interval constructed
D) is very low; is very high

Question 13

An article in the journal Applied Nutritional Investigation reported the results of a comparison between a low-calorie soy-protein diet and a low-calorie traditional-protein diet (Liao, 2007).Twelve obese participants were randomly assigned to each diet.At the end of the diet period, those on the soy diet lost an average of 2.3 percent of their body fat (SD = 0.55), while those on the traditional diet lost an average of 1.22 percent of their body fat (SD = 0.50).If the sample size of this study is increased, the value of the test statistic would _____ and the effect size would _____.

A) increase; remain the same
B) decrease; remain the same
C) decrease; increase
D) increase; decrease

Question 14

It is known that the population mean for the verbal section of the SAT is 500 with a standard deviation of 100.In 2006, a sample of 400 students whose family income was between $70,000 and $80,000 had an average verbal SAT score of 511.The point estimate of the mean for this group is _____ and the 95 percent confidence interval for this group is _____.

A) 500; [501.2, 520.8]
B) 500; [490.2, 509.8]
C) 511; [501.2, 520.8]
D) 511; [490.2, 509.8]

Question 15

Assume for a given study that the null hypothesis asserts the expected value of a phenomenon is 100.A research study results in a 95 percent confidence interval reported as [98.76, 105.24].What decision should be made based on this confidence interval?

A) Reject the null hypothesis.
B) Fail to reject the null hypothesis.
C) Retain the null hypothesis.
D) Perform a hypothesis test before making a decision.

Question 16

The statement "The findings based on a sample of 1000 participants were statistically significant, providing evidence for the hypothesis" would be strengthened by:

A) using convenience sampling.
B) hypothesis testing.
C) measuring effect sizes.
D) sampling university students.

Question 17

According to a "how to stop bullying" website, 15 percent of students report experiencing bullying one to three times within the most recent month.Assume the standard deviation is 4.5 percent of students.Joseph collects data from 175 students at a medium-sized school in Iowa and finds that only 12 percent reported this rate of bullying.What is his 95 percent confidence interval?

A) [7.5, 16.5]
B) [11.33, 12.67]
C) [11.94, 12.06]
D) [14.53, 15.67]

Question 18

The sample mean is _____ the confidence interval.

A) at the beginning of
B) at the end of
C) in the center of
D) excluded from

Question 19

What falls within the 95 percent confidence interval?

A) all the means we would expect to obtain 5 percent of the time when repeatedly sampling from a population
B) all the means we would expect to obtain 95 percent of the time when repeatedly sampling from a population
C) the true population mean
D) the null hypothesis population mean

Question 20

Recent research published by Frumin and colleagues (2011) in the journal Science addresses whether females' tears have an effect on males.Imagine that exposure to tears lowered self-rated sexual arousal by 1.27 points, with a margin of error of 0.32 points.The point estimate is:

A) 1.27.
B) 1.27 +/- 0.32.
C) [0.95, 1.59].
D) 0.32.

Question 21

Increasing sample size:

A) decreases the likelihood that we will reject the null hypothesis.
B) increases the likelihood that we will reject the null hypothesis.
C) has no effect on the likelihood that we will reject the null hypothesis.
D) makes it more likely that we will make a Type II error.

Question 22

According to Cohen's convention, a value of _____ is a medium effect size.

A) 0.2
B) 0.5
C) 0.8
D) 340

Question 23

It becomes progressively easier to declare statistical significance as the _____ increases.

A) standard error
B) value of the critical cutoff
C) sample size
D) number of items on the instrument

Question 24

Cohen's d is the:

A) method for calculating confidence intervals for the z test.
B) difference between the sample means divided by the standard error.
C) standardized difference between group means.
D) measure of statistical power.

Question 25

According to Cohen's convention, a value of _____ is a small effect size.

A) 0.2
B) 0.5
C) 0.8
D) 340

Question 26

According to Cohen's convention, a value of _____ is a large effect size.

A) 0.2
B) 0.5
C) 0.8
D) 340

Question 27

Mehl (2007) published a study in the journal Science reporting the results of an extensive study of 396 men and women comparing the number of words uttered per day by each sex.He found that on average women uttered 16,215 words a day and men uttered 15,669 words a day.The effect size calculated on the basis of his findings is Cohen's d = 0.07.This effect size indicates that the:

A) number of words uttered by the men and women significantly differed from one another.
B) women uttered a significantly greater number of words in a day than did the men.
C) means of the men and women overlap by only 7 percent.
D) means of the men and women are not even one-tenth of 1 standard deviation apart.

Question 28

Effect size assesses the degree to which two:

A) populations overlap.
B) populations do not overlap.
C) samples overlap.
D) samples do not overlap.

Question 29

The larger the effect size, the:

A) smaller is the test statistic.
B) smaller is the sample size.
C) more two distributions overlap.
D) less two distributions overlap.

Question 30

Measures of effect size:

A) are unaffected by sample size.
B) increase as sample size increases.
C) decrease as the difference between population means increases.
D) do not rely on sample means.

Question 31

The formula for Cohen's d substitutes the _____ symbol for the _____ symbol used in the denominator of the z statistic formula.

A) $\sigma$ _M; $\mu$
B) $\sigma$ ; $\sigma$ _M
C) $\mu$ _M; $\mu$
D) $\mu$ ; $\sigma$ _M

Question 32

Effect sizes are affected by _____ and _____.

A) large standard deviations; large standard errors
B) standard deviations; variability of population distributions
C) standard errors; variability of population distributions
D) mean differences; variability of population distributions

Question 33

Effect sizes rely on comparison of a distribution of _____ rather than on a distribution of _____ and are therefore unaffected by sample size.

A) means; scores
B) scores; means
C) errors; residuals
D) residuals; errors

Question 34

To remove the adjustment for the influence of sample size, Cohen's d uses the _____ rather than the _____ as part of its formula.

A) standard error; standard deviation
B) standard deviation; standard error
C) raw scores; standard scores
D) variance; raw scores

Question 35

As sample size increases, the:

A) standard error decreases.
B) test statistic decreases.
C) standard error increases.
D) standard deviation increases.

Question 36

Imagine that a study of memory and aging finds that younger participants correctly recall 55 percent of studied words, older participants correctly recall 42 percent of studied words, and the size of this effect is Cohen's d = 0.49.This effect size indicates that the memory performance of:

A) older participants is approximately half a standard deviation above that of younger participants.
B) older participants is approximately half a standard deviation below that of younger participants.
C) younger participants is approximately half a standard deviation below that of older participants.
D) younger participants is significantly lower than that of older participants.

Question 37

As sample size increases, the test statistic increases because the:

A) difference between the means increases.
B) overlap between distributions increases.
C) distance between distributions decreases.
D) standard error decreases.

Question 38

Why are effect sizes rather than test statistics used when comparing study results?

A) Effect sizes, unlike test statistics, are not affected by sample size and thus ensure a fair comparison.
B) It is easier to average effect size than it is to average test statistics.
C) Effect sizes are based on standard error, while test statistics are based on standard deviation.
D) Effect sizes, unlike test statistics, account for sample size, thus ensuring an accurate comparison.

Question 39

Cohen's d is one measure of:

A) statistical significance.
B) effect size.
C) clinical significance.
D) sample characteristics.

Question 40

Mehl (2007) published a study in the journal Science reporting the results of an extensive study of 396 men and women comparing the number of words uttered per day by each sex.He found that on average women uttered 16,215 words a day and men uttered 15,669 words a day.The effect size calculated on the basis of his findings is Cohen's d = 0.07.According to Cohen's conventions for interpreting d, this effect is:

A) small.
B) medium.
C) large.
D) so small as to be considered virtually no effect.

Question 41

If an effect is significant but the effect size for the difference between the two means is medium (according to Cohen's conventions), about how much overlap will there be between the two distributions?

A) 99 percent
B) 85 percent
C) 67 percent
D) 53 percent

Question 42

If a researcher performs a meta-analysis and finds that the mean d = 0.45, and the 95 percent confidence interval around this mean is (0.34, 0.56), what can the researcher conclude?

A) All future studies of this effect will find effect sizes somewhere between 0.34 and 0.56.
B) Averaging across all of the literature, there really is no effect.
C) There is a medium effect, but it is unclear what the direction of the effect is.
D) Averaging across all of the literature, there is a medium effect, and this effect is statistically significant.

Question 43

A high degree of overlap between two distributions of approximately 95 percent is likely to result in a(n) _____ effect size.

A) small
B) medium
C) large
D) unconventional

Question 44

An overlap between two distributions of approximately 39 percent is likely to result in a(n) _____ effect size.

A) small
B) medium
C) large
D) unconventional

Question 45

Meta-analysis involves:

A) finding all studies published on a topic, contacting the authors of the studies to request their original data, and then analyzing all the obtained data in one large analysis of variance.
B) finding all studies published on a topic, calculating the effect size for each of those studies, and averaging the effect sizes together to find the average size of the effect across all studies.
C) averaging all the test statistics from every possible study on a given topic.
D) attempting to recreate the experimental conditions of every published study on a given topic.

Question 46

The minimum acceptable level of estimated power for a study is:

A) 0.95.
B) 0.80.
C) 0.45.
D) 0.10.

Question 47

Statistical power is calculated as 0.93.This means that if the null hypothesis is _____, there is a _____ percent chance of rejecting the null hypothesis.

A) false; 93
B) false; 7
C) true; 93
D) true; 7

Question 48

One of the roles of the researcher performing a meta-analysis is to:

A) determine how many studies were never published and find those studies.
B) throw out statistical outliers from the analysis.
C) decide on the criteria for the inclusion of studies in the analysis.
D) convince the reader of the existence of the effect of interest.

Question 49

If a researcher performs a meta-analysis and finds that the mean d = 0.11, and that the 95 percent confidence interval around this mean is (-0.04, 0.26), what could the researcher conclude?

A) All future studies of this effect will find effect sizes somewhere between 0.34 and 0.56.
B) Averaging across all of the literature, there really is no effect.
C) There is a strong effect, but it is unclear what the direction of the effect is.
D) Averaging across all of the literature, there is a strong effect, and this effect is statistically significant.

Question 50

When Cohen's d is large (based on Cohen's conventions), the amount of overlap between the two distributions being compared is _____ percent.

A) 75
B) 53
C) 15
D) 0

Question 51

Imagine that a study of memory and aging finds that younger participants correctly recall 55 percent of studied words, older participants correctly recall 42 percent of studied words, and the size of this effect is Cohen's d = 0.49.According to Cohen's conventions for interpreting d, this effect is:

A) small.
B) medium.
C) large.
D) so small as to be considered virtually no effect.

Question 52

Following a meta-analysis, the researcher might decide to perform a(n) _____ to determine the number of null results that would have to exist to overturn any statistically significant effect found in the meta-analysis.

A) power analysis
B) file drawer analysis
C) effect-size analysis
D) hypothesis test

Question 53

If there is less than a(n) _____ percent chance of rejecting the null hypothesis when it is false, there is insufficient power.

A) 50
B) 60
C) 80
D) 90

Question 54

An overlap between two distributions of approximately 99 percent is likely to result in a(n) _____ effect size.

A) small
B) medium
C) large
D) unconventional

Question 55

Statistical power is a measure of the ability to reject the null hypothesis when:

A) it is true.
B) it is false.
C) there are no significant differences.
D) the sample size cannot be increased.

Question 56

An overlap between two distributions of approximately 55 percent is likely to result in a(n) _____ effect size.

A) small
B) medium
C) large
D) unconventional

Question 57

The ability to reject the null hypothesis given that the null hypothesis is false is:

A) a Type II error.
B) statistical power.
C) a false alarm.
D) a Type I error.

Question 58

A degree of overlap between two distributions of approximately 50 percent is likely to result in a(n) _____ effect size.

A) small
B) medium
C) large
D) unconventional

Question 59

If an effect is significant but the effect size for the difference between the two means is small (according to Cohen's conventions), about how much overlap will there be between the two distributions?

A) 99 percent
B) 85 percent
C) 50 percent
D) 15 percent

Question 60

The statistical convention for the minimal acceptable power is:

A) 0.95.
B) 0.90.
C) 0.80.
D) 0.75.

Question 61

Which of the following does NOT increase statistical power?

A) increasing alpha
B) using a one-tailed hypothesis
C) increasing sample size
D) reducing differences between levels of the independent variable

Question 62

Before hypothesis testing and at the beginning of a study, a researcher is advised to conduct _____ because it _____.

A) a power analysis; tells the researcher the number of participants needed for trustworthy results
B) an effect size estimate; tells the researcher the number of participants needed for trustworthy results
C) a statistical significance; determines how meaningful the study results will be
D) alpha testing; determines how meaningful the study results will be

Question 63

Statistical power is:

A) the strength of the research study.
B) the ability to find important results.
C) a combination of the distance between group means and distribution variability.
D) the percent of the comparison distribution that falls beyond the critical cutoff.

Question 64

If the mean difference between levels of the independent variable are exaggerated, statistical power:

A) increases.
B) decreases.
C) stays the same.
D) gets closer to 0.

Question 65

A point estimate offers an advantage over an interval estimate because it estimates the population parameter using a range of values rather than a single number.

Question 66

According to the textbook, a(n) _____ test has more statistical power; however, a(n) _____ is more conservative.

A) one-tailed; two-tailed
B) two-tailed; one-tailed
C) one-tailed; effect-size
D) effect-size; hypothesis

Question 67

Using a one-tailed test allows us to increase statistical power over a two-tailed test because it:

A) divides the alpha into two tails but only focuses on one of those tails.
B) divides the alpha into two tails, which reduces the size of each.
C) puts the entire alpha into one tail, increasing the chances of rejecting the null hypothesis.
D) puts the entire alpha into one tail, decreasing the chances of rejecting the null hypothesis.

Question 68

Before conducting a power analysis, a researcher should know the desired:

A) alpha level.
B) gender distribution.
C) standard error.
D) variance.

Question 69

The practical use of statistical power is that it informs researchers:

A) whether they will find significant results.
B) how many participants are needed to conduct a study with findings they can trust.
C) whether they will find important results.
D) what effect size they can expect to find in conducting their study.

Question 70

A behavioral neuroscientist is testing the effects of adrenaline on memory using a group of 12 rats.The researcher is unsure about how much adrenaline might produce an effect on memory.One group of rats will be injected with placebo saline (0 micrograms of adrenaline).The other group will be injected with a dose of adrenaline.When deciding between a 2-microgram dose or an 8-microgram dose (both of which are safe), the researcher opts to use the 8-microgram dose.The researcher has:

A) made a Type II error.
B) exaggerated the difference between the levels of the independent variable, thereby increasing statistical power.
C) exaggerated the difference between the levels of the independent variable, thereby decreasing statistical power.
D) given the rats an overdose of adrenaline.

Question 71

An interval estimate is based on a sample statistic and provides a range of plausible values for the population parameter.

Question 72

Increasing sample size does NOT:

A) increase statistical power.
B) decrease standard error.
C) increase the magnitude of the test statistic.
D) decrease statistical power.

Question 73

Which of the following does NOT increase statistical power?

A) increasing alpha
B) using a one-tailed hypothesis
C) decreasing sample size
D) exaggerating differences between levels of the independent variable

Question 74

Alpha refers to:

A) statistical power.
B) the probability of making a Type II error.
C) the probability of making a Type I error.
D) effect size.

Question 75

When alpha increases, both _____ and _____ increase.

A) standard error; power
B) power; probability of a Type I error
C) power; probability of a Type II error
D) probability of a Type I error; probability of a Type II error

Question 76

If the expected direction of an effect is correct, then using a one-tailed hypothesis test instead of a two-tailed hypothesis test:

A) increases power.
B) decreases power.
C) makes power 1.0.
D) makes power 0.

Question 77

A statistically significant difference between two groups indicates that all or most participants in one group are different from all or most of the participants in the other group.

Question 78

Which of the following does NOT increase statistical power?

A) decreasing alpha
B) using a one-tailed hypothesis
C) increasing sample size
D) exaggerating differences between levels of the independent variable

Question 79

A researcher interested in the effects of humor on memory randomly assigns 16 participants to either the humor group or the no-humor group.The humor group reads humorous sentences and the no-humor group reads non-humorous sentences.On a later memory test, the researcher finds that in terms of the direction of the means, the humor group had better memory than the no-humor group, but this effect was not significant (p = 0.06).What should this researcher do?

A) She can attempt to increase her statistical power by using a two-tailed hypothesis test rather than a one-tailed hypothesis test.
B) She can abandon the study of humor on memory because given her results it is obvious that humor has no effect on memory.
C) Because the effect looks as though it is barely missing significance, she can just treat it as though the effect exists and communicate this exciting effect to her colleagues.
D) Because the effect looks as though it is barely missing significance and her sample size is fairly small, she can increase her sample size to increase her statistical power to detect the effect.

Question 80

Which of the following does NOT increase statistical power?

A) increasing alpha
B) using a two-tailed hypothesis
C) increasing sample size
D) exaggerating differences between levels of the independent variable