Deck 14: Using Inferential Statistics

Question 1

Statistics that assess the reliability of your findings are called _____ statistics.

A) descriptive
B) inferential
C) evaluative
D) reliability

Answer 1

inferential

Question 2

The distribution of a statistic that one would get by taking every possible sample of n scores from a population is the _____ of the mean.

A) sampling distribution
B) frequency distribution
C) skewed distribution
D) None of the answers is correct.

Answer 2

sampling distribution

Question 3

An estimate of the amount of variability in sample means expected across a series of samples is provided by the:

A) standard deviation of the mean.
B) standard error of the mean.
C) standardized variability around the mean.
D) error variance.

Answer 3

standard error of the mean.

Question 4

If you want the average of 10 scores to equal 100, you can choose any numbers you want for 9 of the scores, but the 10^th score will have to be whatever number will make the average of the scores equal 100. Thus, the _____ are 9.

A) dependent variables
B) degrees of variability
C) degrees of freedom
D) independent variables

Question 5

The main difference between parametric and nonparametric statistics is that a parametric statistic:

A) makes no assumptions about the population distribution underlying a sample distribution.
B) assumes that the underlying population distribution is skewed and makes allowances for the skewness.
C) cannot be used with dependent measures scaled on ratio and interval scales.
D) estimates the value of a population parameter from the characteristics of a sample.

Question 6

The _____ allows one to examine the relationship between experimentally manipulated variables while statistically controlling another variable that may be correlated with them.

A) analysis of covariance
B) Mann-Whitney U test
C) t test for independent samples
D) z test for proportions

Question 7

Means of samples drawn randomly from a single population differ only because of:

A) the central limit theorem.
B) poorly designed independent variables.
C) sampling error.
D) None of the answers is correct.

Question 8

The hypothesis that sample means are drawn from the same population is referred to as the _____ hypothesis.

A) alternative
B) equivalence
C) sampling error
D) null

Question 9

The hypothesis that sample means are drawn from different populations is called the _____ hypothesis.

A) alternative
B) nonequivalence
C) null
D) differential means

Question 10

A statistically significant difference between sample means leads us to:

A) accept that the observed differences between sample means were not due to chance.
B) conclude that the means represent a single underlying population.
C) accept that the observed differences were due mainly to chance fluctuations in the data.
D) None of the answers is correct.

Question 11

Which of the following is a Type I statistical error?

A) Saying that an independent variable had no effect when in fact it did
B) Saying that an independent variable had an effect when in fact it did not
C) Saying that an independent variable had a weak effect when in fact it had a strong effect
D) Identifying one independent variable as affecting the dependent variable when in fact a different independent variable had the effect

Question 12

A statistical test led Dr. Jones to incorrectly decide that his independent variable had no effect when in fact it did. Dr. Jones committed a(n):

A) Type I error.
B) Type II error.
C) Type III error.
D) alpha error.

Question 13

By setting a criterion probability for rejecting the null hypothesis, one can set the rate at which one will commit Type I errors. This criterion that is the probability of making a Type I error is known as the _____.

A) alpha level
B) beta level
C) effect size
D) F ratio

Question 14

In the context of inferential statistics, which of the following statements is true of the alpha level?

A) The minimum acceptable alpha traditionally has been set at .01.
B) The alpha value determines the probability of making a Type II error.
C) The particular level of alpha one adopts is called the effect size.
D) The probability of making a Type I error is less when the value of alpha is small.

Question 15

A one-tailed test is used:

A) in any situation where finding statistical significance is important.
B) when you want to minimize the possibility of making a Type II error.
C) if you are interested only in whether the obtained value of the statistic falls in one tail of the sampling distribution for that statistic.
D) if you are interested in bidirectional differences between means (for example, the experimental group mean is either higher or lower than the control group mean).

Question 16

At a given significance level, a one-tailed test:

A) is less likely to detect real differences between means than is a two-tailed test.
B) has a higher critical value than does a two-tailed test.
C) is less accurate than a two-tailed test.
D) is more likely to detect real differences between means than is a two-tailed test, given that the correct tail was selected for the test.

Question 17

According to the text, a two-tailed test should be used:

A) unless there is a compelling a priori reason not to.
B) if you are sure that the difference between your means is sufficiently large to ensure statistical significance.
C) when you are interested in controlling Type II errors but less interested in controlling Type I errors.
D) None of the answers is correct.

Question 18

Which of the following is not one of the assumptions that underlie parametric inferential tests?

A) The scores have been sampled randomly from a population.
B) The sampling distribution of the mean is normal.
C) The sample sizes are large.
D) The within-groups variances are homogeneous.

Question 19

Serious violations of one or more of the assumptions underlying parametric inferential tests:

A) have little effect on the validity of a statistic.
B) will lead one to commit a Type I error either more or less often than the stated alpha probability.
C) affect Type I error rates but not Type II error rates.
D) affect Type II error rates but not Type I error rates.

Question 20

The _____ is used when there is data from two groups of participants who were assigned at random to the two groups.

A) analysis of variance (ANOVA)
B) t test for independent samples
C) Bayesian approach
D) t test for correlated samples

Question 21

You have just completed an experiment in which different subjects were randomly assigned to an experimental and a control group. Your dependent variable was the number of errors made on a memory test. The most appropriate parametric statistic for your data is the:

A) t test for independent samples.
B) t test for correlated samples.
C) z test for proportions.
D) All of the answers are correct.

Question 22

Which of the following statements would be true of the pooled version of the t test for independent samples?

A) It should not be used when you have unequal sample sizes.
B) Sample size has no effect on the value of the t statistic calculated.
C) It can be used unless there are large differences in sample sizes and standard errors.
D) Calculating the t test when more than four groups are included in an experiment becomes difficult.

Question 23

If your dependent variable were a dichotomous yes/no response, you could compare the proportion of subjects saying yes in the experimental group to the proportion saying yes in the control group by using the:

A) z test for the difference between two proportions.
B) t test for correlated samples.
C) t test for independent samples.
D) t test for proportions.

Question 24

For an experiment that includes four levels of a single independent variable, the most appropriate statistical test is the:

A) z test for multiple groups.
B) t test for multiple groups.
C) chi-square test.
D) analysis of variance.

Question 25

The value of any particular score obtained in a between-subjects experiment is determined by:

A) characteristics of the subject at the time the score was measured.
B) measurement or recording errors.
C) the value of the independent variable.
D) All of the answers are correct.

Question 26

When an experiment includes more than two groups, the statistical test of choice is the:

A) z test for the difference between proportions.
B) analysis of variance (ANOVA).
C) t test for correlated samples.
D) linear regression analysis.

Question 27

For analysis of variance (ANOVA), variability is partitioned into two sources. These are:

A) experimental error and subject error.
B) random variability and systematic variability.
C) between-groups variability and within-groups variability.
D) experimental variability and control variability.

Question 28

The statistic used in the analysis of variance (ANOVA) to determine statistical significance is the:

A) F ratio.
B) z test.
C) t test.
D) p value.

Question 29

After doing analysis of variance (ANOVA), you want to see which of your means differed significantly. Before you began your experiment, you specifically hypothesized that certain means would differ. Consequently, you would perform:

A) unplanned comparisons.
B) planned comparisons.
C) multistage comparisons.
D) systematic comparisons.

Question 30

Because of _____, you should not conduct many post hoc comparisons, even if you predicted particular differences between means.

A) inflated beta
B) probability inflation
C) orthogonal inflation
D) probability pyramiding

Question 31

The two types of errors that must be considered when making many unplanned comparisons are:

A) Type I and Type II errors.
B) beta and theta errors.
C) per-comparison and family wise errors.
D) systematic and random errors.

Question 32

If one ends up with unequal sample sizes for reasons unrelated to the effects of one's treatments, one could use a(n) _____ that involves a minor correction to the analysis of variance (ANOVA).

A) unweighted means analysis
B) t test for independent samples
C) z test for the difference between proportions
D) alternate inferential statistic

Question 33

Dr. Harris conducts an experiment in which rats are first subjected to various levels of environmental pollutants and then tested on a memory task. He finds that all subjects survived in the low- and moderate-exposure groups, whereas 7 of 20 rats died in the high-exposure group. Dr. Harris wants to conduct an analysis of variance on his data. What would be the most appropriate thing to do?

A) Eliminate the high-exposure group from the experiment.
B) Perform an unweighted means analysis.
C) Perform a weighted means analysis.
D) Go ahead and conduct the analysis of variance without worrying about the unequal sample sizes.

Question 34

The Latin square analysis of variance is used to:

A) correct for otherwise uncorrectable biases due to uneven subject loss.
B) counterbalance the order in which subjects receive treatments in within-subjects experiments.
C) control family wise error in multiple comparisons.
D) None of the answers is correct.

Question 35

Which of the following statements is true of the two-factor between-subjects analysis of variance (ANOVA)?

A) In this design, a single independent variable is assigned randomly to different subjects.
B) It is less complicated than a one-factor analysis of variance.
C) When one interprets a main effect, one suggests that the independent variable has no effect on the dependent variable.
D) Certain kinds of interactions between two factors cancel out the main effects.

Question 36

When an interaction is present, _____.

A) main effects are still interpreted
B) main effects are still the focus of attention because they are usually interesting
C) main effects should be carefully interpreted as neither of the independent variables has a simple, independent effect
D) it should be statistically controlled so that main effects can be clearly examined

Question 37

In a mixed design, _____.

A) there are both between-subjects and within-subjects components
B) interactions are not normally analyzed
C) experimental and correlational variables are mixed
D) analysis of variance cannot be used to analyze the data

Question 38

In a study of reaction time, Dr. Mills experimentally manipulates two independent variables and obtains a continuous correlational measure. The most appropriate analysis for her data would be a(n):

A) split-plot analysis of variance.
B) analysis of covariance.
C) Latin square analysis of variance.
D) five-factor between-subjects analysis of variance.

Question 39

When your dependent variable is a dichotomous decision, the most appropriate nonparametric test is _____.

A) a t test
B) the Mann-Whitney U test
C) the Wald-Wolfowitz runs test
D) a chi-square test

Question 40

The Mann-Whitney U test is used:

A) to analyze unequal sample sizes when the inequality was planned or reflects actual differences in a population.
B) when subjects are treated as a factor along with one's manipulated independent variables.
C) when the dependent variable is a dichotomous decision.
D) to evaluate the significance of a difference between two independent groups when the dependent variable is scaled on at least an ordinal scale.

Question 41

You conduct a single-factor, matched-pairs experiment, but your data require a nonparametric statistical analysis. A good choice for analysis here is the:

A) Mann-Whitney U test.
B) Wilcoxon signed ranks test.
C) t-test for correlated samples.
D) analysis of variance (ANOVA).

Question 42

Which of the following statements is true of nonparametric statistics?

A) They are more powerful than parametric statistics.
B) Complex designs can be more easily handled with nonparametric statistics than with parametric statistics.
C) They are less powerful than parametric statistics.
D) They do not require any form of computation.

Question 43

Which of the following statements would not be true of nonparametric statistics?

A) They are more powerful than parametric statistics.
B) Complex designs cannot be easily analyzed with nonparametric statistics.
C) They are less powerful than parametric statistics.
D) They are useful when data do not meet the restrictive assumptions of parametric statistics.

Question 44

The power of a statistical test is its ability to:

A) correct for flaws in your data.
B) detect real differences between population means.
C) withstand violations of assumptions.
D) None of the answers is correct.

Question 45

The power of a statistical test is affected by:

A) the alpha level selected.
B) the sample size.
C) whether a one-tailed or a two-tailed test is used.
D) All of the answers are correct.

Question 46

To estimate the sample sizes required to obtain a desired amount of power, one needs to state the:

A) amount of power required.
B) magnitude of the difference you expect to find in your experiment.
C) expected error variance.
D) All of the answers are correct.

Question 47

The probability that a difference between means at least as large as the one observed would have occurred by chance alone refers to _____ significance.

A) practical
B) internal
C) statistical
D) external

Question 48

The importance of a research finding refers to its _____ significance.

A) practical
B) statistical
C) internal
D) external

Question 49

By convention, an alpha level of _____ has been established as the minimum criterion for statistical significance.

A) .5
B) .1
C) .05
D) .01

Question 50

A linear data transformation changes:

A) the underlying scale of measurement of a dependent variable but not the magnitude of the numbers representing your data.
B) the magnitude of the numbers representing your data but not the underlying scale of measurement.
C) both the magnitude of the numbers representing your data and the underlying scale of measurement.
D) neither the magnitude of the numbers representing your data nor the underlying scale of measurement.

Question 51

Data transformations are used to:

A) adjust data to meet assumptions of statistical tests.
B) adjust nonsignificant data to make them significant.
C) adjust for the effects of unequal sample sizes.
D) All of the answers are correct.

Question 52

The use of _____ has been proposed by some researchers as an alternative to inferential statistics to test the reliability of data.

A) descriptive statistics
B) noninferential statistics
C) replication
D) data management

Question 53

Identify a true statement about replication as an alternative to inferential statistics.

A) It requires that an experimenter limits himself or herself to the replication of their own findings.
B) It necessitates one to conduct exactly the same experiment each time.
C) It is limited to situations in which violations of assumptions occur.
D) It leads to a similar pattern of results for all experiments if data are reliable.

Question 54

The degrees of freedom associated with a single sample distribution are (n - 1).

Question 55

Degrees of freedom are useful in descriptive statistics but have little use in inferential statistics.

Question 56

In the context of inferential statistics, a parameter is a characteristic of a sample, whereas a statistic is a characteristic of a population.

Question 57

Inferential statistics assess the probability that the means of two samples would differ by an observed amount or more if they had been drawn from the same population of scores.

Question 58

Incorrectly rejecting the null hypothesis is known as a Type I error.

Question 59

Steps taken to control the probability of making a Type I error increase the probability of making a Type II error.

Question 60

In the context of inferential statistics, the larger the value of alpha, the less likely it is to make a Type I error.

Question 61

In inferential statistics, p-value is the estimated probability of obtaining an apparent treatment effect at least as large as the one actually found, given that the null hypothesis is true.

Question 62

A two-tailed test is more powerful than a one-tailed test performed on the same data.

Question 63

A one-tailed test should be used only if you can specify the direction of an effect before conducting your experiment.

Question 64

Serious violations of the assumptions underlying parametric statistics do not significantly bias a statistical test.

Question 65

F = between-groups variability/within-groups variability.

Question 66

Latin square designs are used to counterbalance the order in which subjects receive treatments in within-subjects experiments.

Question 67

There are (a + 1) orthogonal comparisons in any set of means (where a = the number of groups).

Question 68

Probability pyramiding is not a problem when planned comparisons are used.

Question 69

The within-subjects analysis of variance treats subjects as a factor in the analysis.

Question 70

An interaction can be found when a one-factor analysis of variance is used to analyze data.

Question 71

If any of the expected cell frequencies in a chi-square test is less than 5, the value of chi-square may be artificially inflated.

Question 72

Changing the significance level of a statistical test from .05 to .01 makes the test more powerful.

Question 73

Increasing the sample size increases the power of a statistical test.

Question 74

A finding of significance at p < .01 is more statistically significant than one at p < .05.

Question 75

A statistically significant effect always has practical significance.

Question 76

In statistical terms, the power of a statistical test is the probability that it will reject the null hypothesis when the null hypothesis is false and is one minus the probability of a Type II error.

Question 77

Compare and contrast parametric and nonparametric statistics. What are the defining qualities of each, and when would each be applied to data?

Question 78

Draw a graph showing an interaction between two variables in a two-factor design. Would you still be interested in interpreting the main effects? Why or why not?

Question 79

What is the power of a statistical test? What factors affect it and how?

Question 80

Describe the data transformations that can be applied to data. Are data transformations a good idea? Why or why not?