Deck 13: Bivariate Statistical Analysis: Tests of Differences

Question 1

The independent samples t-test is used to test for mean differences among three of more groups.

Answer 1

False

Question 2

The independent samples t-test is used to test for significance between the sample mean and the hypothesised mean.

Answer 2

False

Question 3

When the sample size is large, the Z-test is a close approximation to the t-test.

Answer 3

False

Question 4

In an analysis of variance, the variation of scores within the groups is due to the characteristics of the independent variable.

Question 5

In an analysis of variance, the systematic variation of scores between the groups is due to individual differences.

Question 6

If the F-value is large, the results are likely to be insignificant.

Question 7

The analysis of variance is used to compare the mean between two related samples.

Question 8

In the independent samples t-test, the variances are assumed to be equal for the two samples when the significant value of the 'Levene's test for equality of variances' is significant.

Question 9

The F-test partitions the total variance into within-group variance and between-group variance.

Question 10

To test differences in means between two or more groups, we need to ensure that the variable we are taking the mean of is ordinal-scaled.

Question 11

A t-test is used when the sample size in both groups is relatively large and the population standard deviation is known.

Question 12

One of the most frequently tested hypotheses states that two groups differ with respect to some behaviour, characteristic or attitude.

Question 13

The null hypothesis for an analysis of variance (ANOVA) test comparing the means of three groups is stated as: $\mu$ 1 ≠ $\mu$ 2 ≠ $\mu$ 3.

Question 14

In an ANOVA test, variances between three or more groups are compared.

Question 15

The variance between groups is divided by the variance within groups to obtain the F-statistic (or F-ratio).

Question 16

In an ANOVA test, if the grouping variable is not responsible for differences in the dependent variable, then the variation between the groups will be comparatively larger than the variation in responses within the groups.

Question 17

The paired-samples t-test is used to compare the means of two independent groups to see if they are significantly different from one another.

Question 18

The null hypothesis is not rejected when the calculated absolute value of t is greater than the critical t value.

Question 19

In the independent samples t-test, if the null hypothesis is true, then there will be no difference in the two population means.

Question 20

In an ANOVA test, if the grouping variable is responsible for differences in the dependent variable, then the variation between the groups will be comparatively smaller than the variation in responses within the groups.

Question 21

A one-way ANOVA is a multivariate statistical analysis technique.

Question 22

In an analysis of variance, the variability of the group means about a grand mean is calculated by:

A) squaring the sum of the within-group variance and between-group variance.
B) squaring the deviation of each score from its group mean and summing these scores.
C) squaring the deviation of each score from the grand mean and summing these squares.
D) squaring the deviation of each group mean from the grand mean, multiplying by the number of items in the group, and summing these scores.

Question 23

In the independent samples t-test, the t-value is calculated by taking:

A) the squared ratio between the standard deviation and the standard error.
B) the ratio between the standard deviation and the standard error.
C) the ratio of the difference between the two sample means and the standard error.
D) the ratio of the difference between the two sample means and the standard deviation.

Question 24

If I want to test for a difference in the sample means between two metric variables from the same sample group, I could use a paired samples t-test.

Question 25

In comparing the difference of the means between two groups, the null hypothesis can be stated as:

A) $\mu$ 1 - $\mu$ 2 = 0.
B) $\mu$ 1 + $\mu$ 2 = 0.
C) $\mu$ 1 x $\mu$ 2 = 0.
D) $\mu$ 1 / $\mu$ 2 = 0.

Question 26

The independent samples t-test requires that the test variable(s) be measured on a ________ scale and the grouping variable be measured on a ________ scale.

A) nonmetric; nonmetric
B) metric; metric
C) metric; nonmetric
D) nonmetric; metric

Question 27

A brand manager would like to determine if males are more frequent purchasers of the company's product than females. Which of the following statistical tests is appropriate?

A) Independent samples t-test
B) Paired-samples t-test
C) ANOVA
D) One-sample t-test

Question 28

The t-test is used when the number of observations (sample size) in one or both groups is ___________ and the population standard deviation is ___________.

A) small; known
B) small; unknown
C) large; known
D) large; unknown

Question 29

The Z-test is used when the number of observations (sample size) is ___________ and the population standard deviation is ___________.

A) small; known
B) small; unknown
C) large; known
D) large; unknown

Question 30

To examine changes in attitudes among an experimental group in a pretest-post-test design, an independent samples t-test would be appropriate.

Question 31

Suppose you used a 9-point rating scale to compare men who had an annual income over $50 000 (Group 1) with men who had an annual income less than or equal to $50 000 (Group 2) on their liking of a new product. If you studied 40 men in Group 1 and they had a mean of 7 and a standard deviation of 2.5, while the 35 men in Group 2 had a mean of 5 and a standard deviation of 1.4, what is the approximate value of using the t-test?

A) 8.78
B) 4.19
C) 0.97
D) 0.47

Question 32

To compare the prices charged by the same retailers in their shops and on their websites, which of the following statistical tests is appropriate?

A) Independent samples t-test
B) Paired-samples t-test
C) ANOVA
D) One-sample t-test

Question 33

In an analysis of variance, squaring the deviation of each score from the grand mean and summing these squares computes the:

A) total sum of squares.
B) between group sum of squares.
C) within group sum of squares.
D) mean square within groups.

Question 34

In the independent samples t-test, to determine if the variances of the two samples are equal:

A) the significance value for Levene's statistics is consulted.
B) the significance value for the t-test for equality of means is consulted.
C) the standard deviations of both samples must be relatively equal.
D) the standard error of both sample means must be relatively equal.

Question 35

An estimate of the standard error for a t-test of independent means that assumes that the variances of both groups are equal is called the:

A) mean squared standard error estimate.
B) pooled estimate of the standard error.
C) significance error estimate.
D) between-group standard error.

Question 36

A researcher measures brand awareness prior to and after an advertising campaign of a single panel of consumers. A paired samples t-test would be appropriate to test if there is a statistically significant change in brand awareness.

Question 37

In an analysis of variance, the F-ratio is calculated by:

A) multiplying the mean square between groups by the mean square within groups.
B) dividing the mean square between groups by the mean square within groups.
C) summing the mean square between groups with the mean square within groups.
D) subtracting the mean square between groups from the mean square within groups.

Question 38

In the F-test, if the F-value is large, then:

A) the results are likely to be statistically inconclusive.
B) the results are likely to be statistically insignificant.
C) the more likely the differences in means has occurred as a result of the grouping variable.
D) the less likely the differences in means has occurred as a result of the grouping variable.

Question 39

Suppose a researcher wished to determine whether sales had improved since a recent promotions campaign by comparing the sales averages before and after the campaign to evaluate its effectiveness. Which of the following statistical tests would you suggest?

A) One-sample t-test
B) Independent samples t-test
C) Paired-samples t-test
D) ANOVA

Question 40

Suppose a car insurance company is interested to know the average size of insurance claims for people living in secured apartment complexes, gated communities and stand-alone houses. Which of the following statistical tests would be appropriate?

A) One-sample t-test
B) Paired-samples t-test
C) Independent samples t-test
D) ANOVA

Question 41

________ of ________ is the appropriate test to use when comparing the means of three or more groups to see if they are significantly different from each other.

Question 42

When conducting an independent samples t-test in SPSS, the metric variable is set as the ____ variable and the nonmetric variable as the ________ variable.

Question 43

In an analysis of variance, squaring the deviation of each score from its group mean and summing these scores computes the:

A) between-group sum of squares.
B) within-group sum of squares.
C) total sum of squares.
D) mean square within groups.

Question 44

A researcher wishes to compare the average number of product sales between stores in Melbourne, Sydney and Brisbane. To examine this, an appropriate statistical test would be a(n):

A) one-way ANOVA.
B) paired samples t-test.
C) independent samples t-test.
D) n-way ANOVA.

Question 45

In an analysis of variance, summing the within-group variance and the between-group variance computes the _____ ________.

Question 46

If an ANOVA test between the means of three groups yields a value of 55 for MSbetween and a value of 20 for MSwithin , then the F-ratio is approximately:

A) 7.56.
B) 2.75.
C) 0.36.
D) 0.13.

Question 47

The independent samples t-test is used to compare the means of two ___________ groups (for example, gender attitudes towards an advertisement) to see if they are significantly different from one another.

Question 48

In situations where the data is nonmetric and not normally distributed, _____________ techniques can be used.

Question 49

A procedure used to determine whether there is more variability in the scores of one sample than in the scores of another is called the ______.

Question 50

The formula for the _______ is MSbetween / MSwithin.

Question 51

An investigation of a hypothesis to determine if two or more groups differ with respect to measures on a variable is known as a ____ of ___________.

Question 52

A new range of Fat Yak Ale is test marketed in three different pubs. One pub sells the ale at $9.00, the second pub sells it at $8.50 and the third pub sells it at $8.00. The researcher would like to test the extent to which sales differ between each of these price points. To examine this, an appropriate statistical test would be a(n):

A) n-way ANOVA.
B) one-way ANOVA.
C) regression analysis.
D) cluster analysis.

Question 53

The paired samples t-test is used to compare the means of two _______ groups (for example, sales performance before and after a training program) to see if they are significantly different from one another.

Question 54

When conducting an independent samples t-test in SPSS, ________ test for equality of variances is consulted to determine if the variances of the two samples are equal.

Question 55

A paired samples t-test requires that the test variable(s) be measured on a ______ scale and from a ______ sample.

A) nonmetric; paired
B) metric; dependent
C) metric; paired
D) nonmetric; dependent

Question 56

Nonparametric tests have each of the following advantages over parametric tests, except:

A) they avoid the error caused by assuming that a population is normally distributed when it is not.
B) the data required (for instance, nominal or ordinal data) may be easier to collect than ratio- or interval-scaled data.
C) the computations that need to be made are often simpler.
D) they are more reliable when sample sizes are small.

Question 57

A retailer would like to test the hypothesis that female consumers are more likely to buy products when they visit their physical stores than their online stores. To examine this hypothesis, an appropriate statistical test would be a(n):

A) Chi-square test.
B) paired samples t-test.
C) independent samples t-test.
D) one-way ANOVA.

Question 58

When conducting a(n) ___________ _______ t-test in SPSS, the t-test for equality of means is consulted to determine if there is any significant difference between the group means.

Question 59

Red Cross Blood Service hypothesise that men make, on average, a higher number of donor visits per year than women. To examine this hypothesis, an appropriate statistical test would be a(n):

A) independent samples t-test.
B) paired samples t-test.
C) Chi-square test.
D) one-way ANOVA.

Question 60

In an analysis of variance, variation of scores ______ groups is due to individual differences, and systematic variation of scores _______ groups is due to manipulation of the independent variable or characteristics of the independent variable.

Question 61

A researcher comparing the number of units sold for a particular product in their online store versus their retail store would use a ______ _______ t-test.

Question 62

An analysis of variance tests for ___________ among three or more groups.

Question 63

A paired samples t-test requires ___ ______ variables from paired samples.

Question 64

When interpreting statistical tests, the _______ is consulted to determine how likely it is that the observed results have occurred due to sampling error.

Question 65

In an independent samples t-test, when the significant value of Levene's test for equality of variances is ___________ the variances of the two samples are assumed to be unequal.

Question 66

When interpreting statistical output, how meaningful the difference in means is can be determined by the ______ ____.