Deck 15: Power

Question 1

All other things being equal, one study will have more power than another study if

A) it has more subjects.
B) it controls error variance better.
C) it compares groups that are more extreme.
D) all of the above

Answer 1

all of the above

Question 2

The effect size can best be thought of as

A) the size of the largest mean.
B) the size of the difference between means in standard deviation units.
C) a mixture of the size of the difference and the sample size.
D) the largest difference we would hope to find.

Answer 2

the size of the difference between means in standard deviation units.

Question 3

When we are worrying about power we are most concerned with

A) a Type I error.
B) a Type II error.
C) the right answer to the wrong question.
D) none of the above

Answer 3

a Type II error.

Question 4

In general, power increases as

A) the difference between the means decreases.
B) the sample size increases.
C) the variance increases.
D) None of the above is correct.

Question 5

Sometimes different experimenters find different results because of

A) chance.
B) small sample sizes.
C) "the cruel hand of fate."
D) all of the above

Question 6

When we calculate the power for a number of different experimental designs, the calculations depend upon

A) a different approach to each kind of problem.
B) the way we use the tables.
C) the number of subjects we have.
D) the same basic steps, but with slightly different formulae.

Question 7

Power is most often conceived of as

A) a constant.
B) a variable.
C) a set of equations.
D) a probability.

Question 8

To increase power, the easiest variable to control in designing an experiment is usually

A) the difference between the population means.
B) the sample size.
C) the sample standard deviation.
D) the shape of the distribution.

Question 9

Which of the following represents Cohen's rough estimates of small, medium, and large effect sizes?

A) .20, .50, .80
B) .00, .50, 1.50
C) .80, .50, .20
D) .40, .50, .60

Question 10

The probability of a Type II error is usually denoted by

A) beta (β).
B) alpha (α).
C) power.
D) the effect size ( g ).

Question 11

A Type II error is the probability of

A) finding a difference that is really there.
B) finding a difference that is not really there.
C) not finding a difference that is really there.
D) not finding a difference that is not really there.

Question 12

If we have two experiments in which the groups are equally different, the one with the larger power will be the one that

A) had the larger sample size.
B) had the smaller level of α.
C) had the larger β.
D) assigned subjects randomly.

Question 13

The fact that the popular press can always find studies that failed to obtain the same findings as others suggests that

A) power is less than 1.00.
B) not all studies are equally clean.
C) there may be extraneous variables that are not being considered.
D) all of the above

Question 14

Which of the following is involved in the calculation of power?

A) alpha (α)
B) the standard deviation
C) the difference between the means
D) All of the above are involved.

Question 15

When people such as Cohen say that a medium size difference has an effect size of .50, they are saying that we want the power for

A) one mean being half as large as another.
B) one mean being half a point larger than another.
C) one mean being half a standard deviation larger than another.
D) one mean being based on half as many subjects as the other.

Question 16

The effect size is generally denoted by

A) beta (β).
B) alpha (α).
C) d-hat ( ).
D) delta (δ).

Question 17

When it comes to estimating the effect size we can use

A) prior research.
B) a statement of what we would expect to find.
C) special conventions that have been set by others.
D) all of the above

Question 18

The effect size (
) is

A) the size of the difference between the means.
B) the size of the samples you use.
C) the difference between the means scaled by the size of the standard deviation.
D) the width of the distribution.

Question 19

Knowledgeable and unbiased observers have generally noted, and studies have reliably shown, that psychotherapy is better than no treatment at all for a person who is seriously depressed. My study failed to find a difference. From this I can conclude that

A) psychotherapy really is not effective.
B) my study must have been poorly done.
C) my study may have lacked sufficient power to find a difference.
D) other psychologists don't know what they are talking about.

Question 20

In the text the author complained about being asked "how many subjects do I need." His point was that this is a more complex question than it seems because you need to consider

A) how many subjects you have available.
B) how many subjects it would be convenient to run.
C) how many subjects your animal welfare committee will accept.
D) what the treatment effect is.

Question 21

In calculating power we calculate a statistic called delta (δ). This statistic is

A) the effect size.
B) the sample size.
C) a combination of the effect size and the sample size.
D) the difference we are looking for.

Question 22

Which of the following is a reason why we may NOT find a significant difference between two groups?

A) The sample size was too small.
B) The true mean difference between the groups was too small.
C) The variability between the groups was too large.
D) all of the above

Question 23

Is it more meaningful to find a significant difference with a relatively small sample size or with a relatively large sample size?

A) It points to a more robust difference if you have a small sample size.
B) It points to a more substantial difference if you have a large sample size.
C) The two differences are equally substantial.
D) We can't tell anything about the size of the effect from what is given here.

Question 24

It is easy to forget whether the entry in the table at the back of the book represents power or 1 - power. (Different tables do it differently). We can easily figure it out, however. If the entry is power, we would expect

A) the values to decrease as we move down the table to larger sample sizes.
B) the values to decrease as we move across to higher levels of δ.
C) the values to increase as we move to the left to smaller α.
D) the values to increase as we move down the table to higher levels of δ.

Question 25

The formula
allows us to calculate

A) the power for a t test for two independent samples.
B) the power for a t test for one sample.
C) the power for a test on a correlation coefficient.
D) any kind of power we need.

Question 26

The text suggested that the highest value of power that we are likely to be able to afford, assuming that we don't have huge differences between our groups, is something like

A) .20
B) .50
C) .80
D) .95

Question 27

A harmonic mean can be used to calculate the mean sample size for unequal sample sizes. For _______ the values of k would equal _______.

A) related means t test; 3
B) related means t test; 2
C) independent samples t test; 3
D) independent samples t test; 2

Question 28

Power is controlled by

A) sample size.
B) variability.
C) true mean differences.
D) all of the above

Question 29

If we have two related samples, the power of our test will

A) increase as the correlation between the two samples increases.
B) increase as the correlation between the two samples decreases.
C) be at its maximum when the correlation is zero.
D) The correlation is irrelevant.

Question 30

If we have the possibility of different numbers of subjects in each of two groups, we will maximize our power if

A) we put most of the subjects in the group we care most about.
B) we put most of the subjects in the group we care least about.
C) we equalize the number of subjects in the two groups.
D) it doesn't make any difference so long as we maximize the total number of subjects overall.

Question 31

Which of the following reduces power?

A) large differences between the means
B) large levels of variability
C) large sample sizes
D) large alpha levels

Question 32

What is the power in an experiment with two independent groups when the null hypothesis is true?

A) .05
B) .95
C) .05/2
D) undefined

Question 33

If we use the standard approach to solve for the necessary sample size so that we have power = .75 in a two-sample t test, the value of N that we will obtain from the tables is

A) the number of subjects we will need in each group.
B) the number of subjects we will need overall.
C) the number of groups we will need to run.
D) the number of subjects that we actually have available.

Question 34

Do you have more power with a one-tailed test or a two-tailed test?

A) We have more power with a two-tailed test.
B) We have more power with a one-tailed test.
C) It depends on which alternative hypothesis is true.
D) Beats me!

Question 35

In calculating power we separate the effect size and the sample size. We do this so that

A) we can look up the sample size needed for a specific effect size and power.
B) we can calculate the effect size we need for a given power.
C) we can avoid ever having to deal with the sample size.
D) we can confuse everyone.

Question 36

When we use the notation " f(N)" we are denoting

A) some function of the sample size.
B) a fraction of N .
C) the number of observations in the full sample.
D) the symbol for power.

Question 37

Before running an experiment, we decide to calculate power. We find that the power equals .95. What conclusion can be made?

A) We should not run the experiment.
B) 95% of the time, we will not find a significant result.
C) We should run the experiment.
D) We need 95 subjects to find a significant result.

Question 38

It is important to think about power because

A) everyone uses it.
B) we don't want to run experiments that have little chance of finding something.
C) it is likely to guarantee successful studies.
D) none of the above

Question 39

Suppose a weak relationship exists between fetal alcohol syndrome and hyperactivity. We are more likely to find that the sample correlation is significant if

A) we have a small sample.
B) we have a very large sample.
C) it doesn't depend at all on sample size.
D) we choose people who have all experienced fetal alcohol syndrome.

Question 40

When we have two independent groups with different numbers of subjects in the two groups, and we want to calculate the power we have for a given set of values of μ and σ, the N that we will use in our calculations is

A) the number of subjects in the smaller group.
B) the number of subjects in the larger group.
C) the harmonic mean of the two sample sizes.
D) the total number of subjects in our experiment.

Question 41

Power is the probability of correctly rejecting the null hypothesis.

Question 42

Power is defined as the

A) probability of rejecting a true null hypothesis.
B) probability of accepting a false null hypothesis.
C) probability of rejecting a false null hypothesis.
D) Power is not related directly to the null hypothesis.

Question 43

According to statistical conventions, .80 is a small effect size.

Question 44

Power is higher when α is large than when α is small.

Question 45

The larger the true difference between two means, the smaller power is.

Question 46

Effect size is the difference between two population means divided by the sample size.

Question 47

The probability of rejecting a false null hypothesis is called

A) statistics.
B) power.
C) statistical significance.
D) prediction.

Question 48

Which of the following determines how the power of an experiment varies with sample size?

A) delta ( d )
B)
C) m ₁ - m ₂
D) Σ

Question 49

If δ = 2.80, and α = .05, then power = .80.

Question 50

As sample size increases, so does power.

Question 51

We are trying to evaluate the efficacy of a treatment for claustrophobia. We have a control group that receives no treatment and an experimental group that receives our new treatment. We ask each participant to enter a very small room and stay there are long as they can. The mean of the control group is 10 seconds, with a standard deviation of 4 seconds. The mean of the experimental group is 18 seconds with a standard deviation of 8 seconds. Our best estimate of effect size is

A) 2.0
B) 1.33
C) 1.0
D) 1.75

Question 52

Suppose that in the previous question the 95% confidence interval on the difference between group means was computed to be 2.63 ≤  µ1 -  µ2  ≤ 13.37. What can we conclude about the null hypothesis of no treatment effect?

A) The difference is significant.
B) The difference is not significant.
C) The treatment doesn't work.
D) Confidence intervals are totally unsuited to this question.

Question 53

What is the easiest way to increase power?

A) redesign the study
B) decrease the error variance
C) use different statistical tests
D) increase the sample size

Question 54

When we have two independent samples, the best measure of effect size

A) will use a pooled standard deviation.
B) might be based on the standard deviation of a control group.
C) both a and b
D) is best based on the standard deviation of the treatment group.

Question 55

If power = .75, there is a 25% chance of correctly rejecting the null hypothesis.

Question 56

When effect size is small, a small sample is typically sufficient to identify important differences.

Question 57

When we have two independent samples, a confidence limit is generally used to

A) say something about the difference between population means.
B) say something about the difference between sample means.
C) specify the location of a single sample mean.
D) refine the estimate of the variance.

Question 58

In computing effect sizes for a comparison of independent samples, our measure may be less than ideal if

A) we have heterogeneous variances and no control group.
B) the data are decidedly nonnormal.
C) we choose the wrong statistic for our denominator.
D) all of the above

Question 59

When comparing independent means, power is greater when sample sizes differ substantially.

Question 60

You are on an Institutional Animal Care and Use Committee (IACUC) at your school. You receive a request to run an animal study where the power will be .40. Do you approve the study?

A) Yes; this indicates the study has a 60% chance of obtaining a significant result
B) No; this indicates the study has only a 40% chance of obtaining a significant result.
C) Yes; this indicates the results will be incorrect only 40% of the time.
D) No; this indicates the study has a 40% chance of missing the significant result.

Question 61

Given the following values for δ, what is power assuming α = .05?
a. δ = 1.55
b. δ = 3.60
c. δ = 2.65

Question 62

A clinician is interested in examining the effectiveness of a new treatment approach for depression. Currently, 20 people are in the control group and 20 people are in the intervention group. In similar research, clinicians have reported post-treatment depression scores of 30 and 26 for the control groups and intervention groups respectively, and a standard deviation of 4.5. What is a reasonable estimate of power if α = .05?

Question 63

In a related samples t-test, husbands and wives scores are correlated such that r = .55, and the typical standard deviation on the measure of marital satisfaction is 5. Assuming the true mean difference in marital satisfaction is 5 points, the sample consists of 10 couples, and α = .05:
a. What is
?
b. What is δ?
c. What is power?

Question 64

A student preparing to use a one-sample t-test indicated that power = .80 with a sample of 30. What was the effect size assuming α = .05?

Question 65

The effect size for a one-sample t-test is .45. How many subjects would be necessary for the following levels of power if α = .05?
a. .40
b. .80
c. .95

Question 66

A pediatrician is interested in determining if cognitive development scores are lower for low-birthweight infants than normal infants. She has 49 active cases involving low-birthweight infants from who she could collect data to compare to the national average. What would power be assuming the following effect sizes and α = .05?
a.
=.20
b.
=.50
c.
=.80

Question 67

Calculate effect size given the following information:
a. μ ₁ =30,  μ ₂ = 35, σ = 3
b. μ ₁ =40,  μ ₂ = 30, σ =10
c. μ ₁=100,  μ ₂ = 98, σ = 5

Question 68

The effect size for an independent samples t-test is .90. How many subjects would be necessary for the following levels of power if α = .05?
a. .50
b. .77
c. .91

Question 69

An English teacher believes his method of teaching grammar, usage, and mechanics is superior to most other approaches. He plans to compare his students' average score on a standardized test to the national average. Assuming a medium effect size, 20 students in his class, and α = .05, what is power?

Question 70

Identify and explain three factors that affect power.