Deck 11: Power

Question 1

Maximizing the power of an experiment _________.

A) minimizes alpha
B) minimizes beta
C) increases the probability of rejecting H ₀ when H ₀ is true
D) increases the probability of making a Type II error

Answer 1

minimizes beta

Question 2

With other factors held constant, as the effect of the independent variable decreases, power will _________ and the probability of a Type II error will _________.

A) decrease, increase
B) decrease, decrease
C) increase, decrease
D) increase, increase

Answer 2

decrease, increase

Question 3

Which of the following values of P represents the largest effect?

A) P _real = 0.20
B) P _real = 0.70
C) P _real = 0.75
D) P _null = 0.50

Answer 3

P _real = 0.20

Question 4

If the null hypothesis is false, the probability of making a correct decision is given by _________.

A) alpha
B) beta
C) 1 - alpha
D) power

Question 5

You can only compute power when ________.

A) alpha > 0.05
B) H ₁ is given
C) Beta > 0.05
D) 1 - power = 0.05

Question 6

If N = 4, P _real = 0.80 in the direction predicted, and a = 0.05_{1 tail}, using the sign test, the power is _________.

A) 0.9375
B) 0.0000
C) 1.0000
D) 0.0625

Question 7

If H ₀ is true, then the probability of rejecting H ₀ is limited by _________.

A) Power
B) 1 - power
C) alpha
D) beta

Question 8

If the power of an experiment is 0.7496, the probability of making a Type II error is _________.

A) 0.2498
B) 0.05
C) 0.2504
D) cannot tell without more information

Question 9

With alpha and N held constant, as the effect of the independent variable increases _________.

A) the probability of rejecting H ₀ increases
B) power increases
C) the probability of rejecting H ₀ remains the same
D) the probability of making a Type II error decreases
E) a, b, and d

Question 10

The advantage of a powerful experiment is that _________.

A) the probability of a Type I error is reduced.
B) you are more likely to detect the real effects of the independent variable, if there are any.
C) as power increases, alpha increases.
D) as power increases, N increases

Question 11

You are considering testing a new drug that is supposed to facilitate learning in mentally retarded children. Because there is relatively little known about the drug, you plan to use a nondirectional alternative hypothesis. Since your resources are limited, you can test only 15 subjects. The subjects will be run in a repeated measures design and the data will be analyzed with the sign test, using a = 0.05_{2 tail}. If the drug has a medium effect on learning such that P _real = 0.70, what is the probability you will detect the effect when doing your experiment.

A) 0.2968
B) 0.0176
C) 0.2969
D) 0.0352

Question 12

With alpha and the effect of the independent variable held constant, as N increases _________.

A) power increases
B) the probability of a Type I error increases
C) the probability of a Type II error increases
D) power decreases

Question 13

In an experiment in which H ₁ is nondirectional, and the state of reality is such that the probability of a plus = 0.50, the probability of making a Type II error is _________.

A) 1 - alpha
B) 0
C) 1
D) need more information

Question 14

With the effect of the independent variable and N held constant, as a gets more stringent _________.

A) power increases
B) power stays the same
C) power decreases
D) beta decreases

Question 15

Power equals _________

A) alpha + beta
B) 1 - beta
C) 1 - alpha
D) alpha - beta

Question 16

If H ₀ is in reality false and it is legitimate to use a directional H ₁, which of the following will yield a more powerful test?

A) one-tailed alternative hypothesis
B) two-tailed alternative hypothesis
C) one-tailed or two-tailed alternative hypothesis will yield the same power
D) type of alternative hypothesis has no effect on power

Question 17

The power of an experiment is affected by _________.

A) the alpha level
B) the sample size
C) the size of effect of the independent variable
D) all of these

Question 18

If H ₀ is true and the probability of making a Type I error is 0.05, then the probability of making a correct decision is _________.

A) power
B) 0.05
C) 0.95
D) need more information

Question 19

If H ₁ is nondirectional and the size of the effect of the independent variable decreases, the probability of making a Type I error _________.

A) decreases
B) increases
C) equals zero
D) need more information

Question 20

You are considering testing a new drug that is supposed to facilitate learning in mentally retarded children. Because there is relatively little known about the drug, you plan to use a nondirectional alternative hypothesis. Since your resources are limited, you can test only 15 subjects. The subjects will be run in a repeated measures design and the data will be analyzed with the sign test, using a = 0.05_{2 tail}. What is the probability of a Type II error?

A) 0.7032
B) 0.7031
C) 0.9824
D) 0.9648

Question 21

In an experiment with N = 14 and P _real = 0.10, what is the power using a = .01_{2 tail}?

A) 0.0500
B) 1.0000
C) 0.5847
D) 0.9868

Question 22

In an experiment with N = 6 and P _real = 0.15, what is the power using a = 0.01_{2 tail}?

A) 1.0000
B) 0.5000
C) 0.0000
D) 0.3771

Question 23

An experiment with N = 18 is more powerful than an experiment with N = 17, all other things being the same.

Question 24

In an experiment, if the effect of the independent variable and alpha remain the same and N increases, _________.

A) power increases
B) power decreases
C) power remains the same
D) cannot be determined

Question 25

Truth demands that scientists set _________.

A) alpha equal to 0.05
B) alpha equal to 0.01
C) a or b
D) not necessarily a = 0.01 or 0.05, but use their best judgment

Question 26

In a two-tailed test, which of the following would yield the same power as a size of effect represented by P _real = 0.90?

A) P _real = 1.00
B) P _real = 0.10
C) P _real = 0.80
D) none of these

Question 27

Which of the following may be false ?

A) alpha + beta = 1
B) power + beta = 1
C) 1 - power = beta
D) 1 - beta = power

Question 28

If H ₀ is false, the probability of making a correct decision is _________.

A) alpha
B) 1 - alpha
C) power
D) 1 - power

Question 29

You are considering testing a new drug that is supposed to facilitate learning in mentally retarded children. Because there is relatively little known about the drug, you plan to use a nondirectional alternative hypothesis. Since your resources are limited, you can test only 20 subjects. The subjects will be run in a repeated measures design and the data will be analyzed with the sign test, using a = 0.05_{2 tail}. What is the power this time?

A) 0.4163
B) 0.2969
C) 0.6161
D) 0.2458

Question 30

If the independent variable has a real effect, the probability of rejecting H ₀ is _________.

A) power
B) 1 - power
C) alpha
D) beta

Question 31

Which of the following P values represents the strongest effect?

A) P _null = 0.50
B) P _real = 0.70
C) P _real = 0.80
D) P _real = 0.

Question 32

Which of the following represents the null hypothesis condition for a nondirectional H ₁?

A) P _real = 0.49
B) P _null = 0.50
C) P _real = 0.51
D) all of these

Question 33

Assume that you have conducted an experiment and the tail probability for the results you obtained was 0.0900 and a = 0.05. You can conclude _________.

A) the independent variable has no effect
B) the independent variable has a small effect
C) you were unable to detect an effect of the independent variable with your experiment
D) the null hypothesis is false

Question 34

If the power of an experiment is 0.3400, the probability of retaining H ₀ when H ₀ is false is _________.

A) 0.6600
B) 0.3400
C) 0.5000
D) 1.0000

Question 35

In the case of N = 3, P _real = 0.90, a = 0.05_{1 tail}, using the sign test, the power is _________.

A) 1.0000
B) 0.1250
C) 0.8750
D) 0.0000

Question 36

In an experiment with N = 14 and P _real = 0.10, what is the power using a = 0.05_{2 tail}?

A) 0.8417
B) 0.0132
C) 0.0000
D) 0.0500

Question 37

If beta = 0.7500, what is the power of the experiment?

A) 0.7500
B) 0.5000
C) 0.2500
D) 1.0000

Question 38

Power is defined as ______.

A) the probability of rejecting H ₀ if H ₀ is false
B) the probability of accepting H ₁ if H ₁ is true
C) the probability of rejecting H ₀ if H ₀ is false and the probability of accepting H ₁ if H ₁ is true
D) the probability of rejecting H ₀ if H ₀ is true

Question 39

In the sign test, if H ₀ is false, then P _real _________.

A) equals 0.05
B) equals 0.50
C) equals 1 - 0.05
D) does not equal 0.50

Question 40

One can increase power by _________.

A) increasing N
B) making alpha more stringent
C) increasing the effect of independent variable
D) increasing N and the effect of independent variable

Question 41

P _null _________.

A) always equals 1 - P _real
B) never equals 0.50
C) always equals 0.50
D) equals 0.50, ?5= 0.50, or ?4= 0.50, depending on H ₁

Question 42

Increasing N affects the magnitude of the effect of the independent variable.

Question 43

It is impossible to ever prove that H ₀ is true because _________.

A) the power to detect very weak but real effects of the independent variable is always low
B) chance is a vague concept
C) very strong real effects of the independent variable swamp out chance
D) power decreases as N decreases

Question 44

Other factors held constant, a one-tailed test is more powerful than a two-tailed test.

Question 45

"Nonsignificant results" means _________.

A) H ₀ was unable to be rejected
B) the power of the experiment was too low
C) H ₁ was wrong
D) H ₀ was unable to be rejected and the power of the experiment was too low

Question 46

"State of Reality" means _________.

A) true state of affairs regarding the alpha level
B) true state of affairs regarding H ₁
C) true state of affairs regarding H ₀
D) true state of affairs regarding H ₁ and true state of affairs regarding H ₀

Question 47

Increasing N increases the probability of a Type II error.

Question 48

High power is desirable in an experiment.

Question 49

If H ₀ is false, as the power of the experiment increases, the probability of rejecting H ₀ increases.

Question 50

"Correct Decision" is defined as _________.

A) retaining H ₀ when it is true
B) rejecting H ₀ when it is false
C) rejecting H ₁ when it is false
D) accepting H ₁ when it is true
E) all of these

Question 51

The higher the power, _________.

A) the larger is P _real
B) the larger the N of the experiment
C) the more the experiment allows H ₀ to be rejected if it is false
D) the more likely H ₀ is to be rejected whether H ₀ is true or false
E) the larger is P _real and the larger the N of the experiment

Question 52

Power and beta are inversely related.

Question 53

In general, the sum of alpha and beta should equal 1.

Question 54

A real effect of the independent variable is defined as _________.

A) all possible effects including no change in the dependent variable
B) any effect that produces a change in the dependent variable
C) an effect that produces an increase in the value of the dependent variable
D) an effect showing no change in the dependent variable

Question 55

Power is a measure of the sensitivity of an experiment to detect the real effects of the independent variable, if there are any.

Question 56

Power is the probability of rejecting H ₀ if it is false.

Question 57

P _null is defined as _________.

A) the probability of getting a plus with any subject in the sample of the experiment when the independent variable has no effect in the direction predicted by a directional H ₁
B) the probability of getting a plus with any subject in the sample of the experiment when the independent variable has a real effect
C) the probability of getting a plus with any subject in the sample of the experiment when the independent variable has an effect in the direction predicted by a directional H ₁
D) the probability of getting a plus with any subject in the sample of the experiment when the independent variable has no effect.

Question 58

P _real is defined as _________.

A) the probability of getting a plus with any subject in the sample of the experiment when the independent variable has a real effect
B) the probability of getting a plus with any subject in the sample of the experiment when the independent variable has no effect
C) the probability of getting a plus with any subject in the sample of the experiment when chance alone is at work
D) the probability of getting a plus with any subject in the sample of the experiment when the independent variable has a real effect in the direction predicted by the directional H ₁

Question 59

Using sample data, it is impossible to prove with certainty that H ₀ is true.

Question 60

If H ₀ is true, as the power of the experiment increases, the probability of rejecting H ₀ increases.

Question 61

Alpha + beta = 1.

Question 62

An experiment where P _real = 0.10 is less likely to allow rejection of H ₀ if H ₀ is false than one where P _real = 0.80.

Question 63

A good experiment is one where both a and b are low.

Question 64

Power is the probability of making a correct decision when H ₀ is true.

Question 65

Beta is the probability of retaining H ₀ when H ₀ is false.

Question 66

Power varies from - 1 to +1.

Question 67

The greater the sample size the greater the power.

Question 68

A power analysis is useful when the results of an experiment fail to reach significance.

Question 69

H ₀ states that the independent variable has no effect. H ₁ is nondirectional.

Question 70

Power = 1 ?2- b

Question 71

b = 1 ?2- a .

Question 72

It is impossible for an experiment to have power equal to zero.

Question 73

Decreasing beta will generally cause a to increase.

Question 74

An experiment with a = 0.05 is more powerful than one where a = 0.01, other factors held constant.

Question 75

If one conducts an experiment and ends up retaining H ₀ , it is probably because the experiment was not powerful enough.

Question 76

The concept of statistical power applies only to the sign test.

Question 77

If H ₀ is true, power is the probability of not making a Type II error.

Question 78

In an experiment where we retain H ₀ , one cannot be certain if it was because H ₀ was true or that the experiment was not powerful enough to detect an effect by the independent variable.

Question 79

If the independent variable is more powerful in experiment A than in experiment B, there is a higher probability of rejecting H ₀ in A than in B if, in fact, H ₀ is false.

Question 80

If in reality H ₀ is true, then designing a very powerful experiment (without changing alpha) will allow us to reject H ₀ more readily.