Deck 13: Bivariate Statistical Analysis: Tests of Differences

Question 1

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.

Answer 1

False

Question 2

Given the limitation of group heterogeneity in experimental designs, researchers may wish to use some kind of pre-test posttest design.

Answer 2

True

Question 3

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.

Answer 3

False

Question 4

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

Question 5

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

Question 6

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 7

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

Question 8

An ANOVA is applied on one metric variable and one non-metric variable with two groups.

Question 9

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

Question 10

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

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

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 13

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

Question 14

T-tests are useful when more than four groups are analysed.

Question 15

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

Question 16

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

Question 17

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

Question 18

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 19

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

Question 20

A packaged-goods company wishes to know which of the three packaging types is most effective for consumers in control group vs uncontrolled group setting. This can be measured through paired samples t-test.

Question 21

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

Question 22

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 23

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 24

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 25

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 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

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 28

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 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

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 31

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 32

Which of the following test can be applied to see if the ranking differs between the two samples?

A) Non-parametric tests
B) Parametric tests
C) ANOVA test
D) Degree of freedom test.

Question 33

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 34

Which of the following sampling is dependent?

A) Independent sample
B) Paired sample
C) Stratified sample
D) Cluster sample

Question 35

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 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

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

Question 38

If dependent variable is a ranking data, then which of the following test is applied?

A) non parametric test
B) parametric test
C) F-ration test
D) Chi-square test.

Question 39

Suppose you used a 10-point rating scale to measure intention-to-buy (1 = definitely would not buy and 10 = definitely would buy). If a group of 40 males had a mean of 7 and a standard deviation of 2.5, while a group of 35 females had a mean of 5 and a standard deviation of 1.4, then the standard error of the difference between the means would be approximately:

A) 0.48.
B) 2.06.
C) 0.23.
D) 4.25.

Question 40

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

A) F-test
B) Z-test
C) X-test
D) Y-test

Question 41

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 42

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 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

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 45

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 46

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 47

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 48

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 49

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 50

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 51

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.