Deck 8: Issues in Inferential Statistics

Question 1

If a researcher used an independent t-test but should have used a dependent t-test, which errors are most likely?

A) SE of the mean is too small, Type II
B) SE of the mean is too large, Type I
C) SE of the mean is too small, Type I
D) SE of the mean is too large, Type II

Answer 1

D

Question 2

Which of the following would a researcher be LEAST likely to use to examine the practical difference between two sample means?

A) The population mean
B) Effect size
C) Omega squared
D) Percent improvement

Answer 2

A

Question 3

If a researcher retains the null hypothesis, but it is false, what error has been committed, and what is its probability? (α = .05)

A) Type I, 5%
B) Type II, 5%
C) Type I, cannot determine from information given
D) Type II, cannot determine from information given

Answer 3

D

Question 4

Which of the following correctly indicates that a one-tailed test will be used?

A) H₀:μ₁- μ₂= 0
B) H₁:μ₁- μ₂≠0
C) H₁:μ₁<μ₂
D) H₀:μ₁>μ₂

Question 5

Which of the following is NOT a definition of statistical power?

A) The condition of avoiding making a Type II error
B) 1 -β
C) Not making a Type I error
D) The ability to reject a false null hypothesis correctly

Question 6

How can statistical power be increased?

A) Increase the population variance
B) Increase the sample size
C) Increase Type I error protection (e.g., change α from .10 to .05)
D) Increase the value of the standard error

Question 7

If α = .05 and β = .90, what is the power?

A) .05
B) .10
C) .90
D) .95

Question 8

Why is a dependent t-test usually more powerful than an independent t-test?

A) The denominator is smaller
B) The denominator is larger
C) The numerator is smaller
D) The numerator is larger

Question 9

A researcher concluded that the null hypothesis was tenable (could be defended). What error has possibly been committed, and what is the probability of committing it?

A) Type I, alpha level
B) Type II, alpha level
C) Type I, cannot determine
D) Type II, cannot determine

Question 10

A decrease in which of the following will generally increase power?

A) The alpha level
B) Sample size
C) The difference between the sample mean and the actual mean
D) The reliability of the measurement used

Question 11

If α = .05, β = .15, N =100, and S = 25, what is the power?

A) .95
B) .85
C) .75
D) .05

Question 12

The simplest experimental design has how many independent variables, with how many levels, and how many dependent variables?

Question 13

What name is given to the condition in an experimental design where the same subjects are in every group?

A) Between groups
B) Repeated measures
C) Mixed
D) Cross-sectional

Question 14

A 2 x 5 between-groups experimental design has how many different treatment conditions?

A) 1
B) 2
C) 5
D) 10

Question 15

How many total subjects are needed in a 2 x 2 mixed-model group design with 20 subjects in each treatment group?

A) 10
B) 20
C) 40
D) 80

Question 16

In a 2 x 4 between-groups design, how many total subjects are needed if 10 subjects are required for each group?

A) 10
B) 40
C) 80
D) 120

Question 17

How many independent variables exist in a 2 x 3 x 4 experimental design?

A) 1
B) 3
C) 9
D) 24

Question 18

How many total subjects are needed in a 2 x 2 repeated-measures design with 10 subjects in each treatment condition?

A) 10
B) 20
C) 40
D) 80

Question 19

Which of the following describes a mixed-model design?

A) One between-groups factor and one repeated-measures factor
B) Two between-groups factors and no repeated-measures factor
C) One between-groups factor measured on an interval scale and another independent factor measured on a nominal scale
D) One independent variable is normally distributed and another one is not

Question 20

What do statistically significant results imply?

A) The results are important.
B) The results are not very important.
C) The results are likely to be attributable to chance differences among groups.
D) The results are likely to be attributable to real differences between groups.

Question 21

For which significance level (or alpha) would the chance of making a Type I error be the greatest when H₀ is rejected?

A) 0.25
B) 0.10
C) 0.01
D) 0.001

Question 22

If the alpha is changed from 0.10 to 0.05, what happens to the chances of a Type I and a Type II error, respectively?

A) Increases, decreases
B) Decreases, decreases
C) Increases, increases
D) Decreases, increases

Question 23

Researchers set alpha at a relatively small level to avoid which of the following errors?

A) Rejecting the null hypothesis when it is false
B) Retaining the null hypothesis when it is false
C) Rejecting the null hypothesis when it is true
D) Retaining the null hypothesis when it is true

Question 24

What has happened when a researcher rejects H₀ when H₀ is false?

A) The researcher made a correct decision.
B) The researcher made a Type I error.
C) The researcher made a Type II error.
D) The researcher made an incorrect decision.

Question 25

When a researcher fails to reject H₀ when it is false, what has occurred?

A) He made a correct decision
B) He made a Type I error
C) He made a Type II error
D) None of the above

Question 26

If a researcher accepts a false null hypothesis, what has occurred?

A) Committed a Type I error
B) Committed a Type II error
C) Committed both a Type I and Type II error
D) Committed no error

Question 27

What does the significance level (alpha level) protect against doing incorrectly?

A) Rejecting the alternative hypothesis
B) Rejecting the null hypothesis
C) Failing to reject the null hypothesis
D) Either rejecting or failing to reject the null hypothesis

Question 28

What does p < .05 indicate?

A) It depends on what the research hypothesis is
B) The null hypothesis (H₀) is tenable
C) The null (H₀) hypothesis should be rejected
D) A Type I error has occurred
E) None of the above

Question 29

You reported a relationship that really does not exist. What did you do?

A) Impossible to determine without knowing what the variables are
B) Generalized from a sample to a population
C) Committed a Type II error
D) Committed a Type I error
E) More than one of the above

Question 30

Given the following information, would you reject the null hypothesis? $\begin{array}{cccc}t & \text { df } & \text { Sig (2-tailed) } & \text { Mean Diff } \\2.65 & 123 & .03 & 4.8\end{array}$

A) No, but you might make a Type I error.
B) No, but you might make a Type II error.
C) Yes, but you might make a Type I error.
D) Yes, but you cannot not make a Type I error.
E) Impossible to determine from this limited information

Question 31

Use the following information to answer the question: The purpose of the research was to determine whether cholesterol level is related to lifestyle behaviors. The lifestyle behaviors of interest were physical activity, dietary fat intake, smoking status, and self-reported life satisfaction. The researchers rejected the null hypothesis. What was the primary independent variable in this study?

A) Smoking status
B) Physical activity
C) Risk for elevated cholesterol
D) Gender
E) Lifestyle behaviors

Question 32

Use the following information to answer the question: The purpose of the research was to determine whether cholesterol level is related to lifestyle behaviors. The lifestyle behaviors of interest were physical activity, dietary fat intake, smoking status, and self-reported life satisfaction. The researchers rejected the null hypothesis. What was the primary dependent variable in this study?

A) Lifestyle behaviors
B) Gender
C) Cholesterol level
D) Physical activity
E) None of the above

Question 33

Use the following information to answer the question: The purpose of the research was to determine whether cholesterol level is related to lifestyle behaviors. The lifestyle behaviors of interest were physical activity, dietary fat intake, smoking status, and self-reported life satisfaction. The researchers rejected the null hypothesis. Assume that the researchers are interested in differences between genders. They conclude p < .001 for genders. What does this mean?

A) The genders differ.
B) The genders do not differ.
C) There might be a Type II error.
D) More than one of the above

Question 34

In a particular study, a directional hypothesis was stated. (The researchers hypothesized that Group A would score significantly higher than Group B.) When the data were analyzed, the mean scores for Group A and Group B were 37 and 40, respectively. What should the researcher do now?

A) State that the hypothesis is not tenable.
B) Test to see whether 40 is significantly different from 37.
C) Reject the null hypothesis.
D) Assume that a Type II error has been made.

Question 35

Which procedure would reduce the power of a statistical test?

A) Using a one-tailed test instead of a two-tailed test
B) Reducing the variability of the scores
C) Changing the alpha level from .10 to .05
D) Decreasing the sample size

Question 36

An experimenter using the .05 alpha level determined that two means were not significantly different. In actual fact, the null hypothesis is false. What error has been committed, and what were the chances of its occurrence?

A) Type II error, cannot determine probability
B) Type II error, 1 chance in 20
C) Type I error, cannot determine probability
D) Type I error, 1 chance in 20

Question 37

When is it impossible to commit a Type I error?

A) When the null hypothesis is actually false
B) When N is very large
C) When the experimenter rejects the null hypothesis
D) It is always possible.

Question 38

A study was completed to determine whether a particular teaching method improved students' gymnastics abilities. The researcher was NOT interested in detecting whether the method decreased gymnastics ability. What is the smallest t-ratio that would allow rejection of the null hypothesis? (Assume 60 degrees of freedom, and use α = .05.)

A) 1.671
B) 2.000
C) 2.390
D) 2.660

Question 39

The t-ratio required for significance for a one-tailed test at the .05 level is the same as for a two-tailed test at what level?

A) .01
B) .05
C) .10
D) .20

Question 40

If σ₁² = 10 and σ₂² = 5, when will the robustness of the assumptions underlying the t-test be in jeopardy? (Consider Type I error only.)

A) When mean₁/mean₂= 2
B) When N₁/N₂= 3
C) When mean₂/mean₁= 2
D) When N₂/N₁= 3

Question 41

In a study of IQ scores, if the mean score and standard deviation for the control group are 100 and 15, respectively, and the researcher has decided not to do an experiment unless an effect size of at least 1.00 can be achieved, what minimum IQ score would the treatment group need to reach?

A) 85
B) 100
C) 115
D) Depends on alpha level

Question 42

What percentage of change of the treatment group over the control group is suggested by an effect size of 1.2?

A) 11.3%
B) 38.5%
C) 40.3%
D) 88.5%

Question 43

What is an effect size?

A) A z-score
B) A value to help interpret meaningfulness
C) The difference between two means expressed in standard deviation units
D) All of the above

Question 44

Which of the following statements correctly indicates the relationship between statistical significance and practical significance?

A) If findings are statistically significant, they are also practically significant.
B) If findings are statistically significant, they indicate a possibility of practical significance.
C) If findings are statistically significant, they are not of practical significance.
D) If a difference is of practical significance, it will be statistically significant.