Deck 14: Bivariate Statistical Analysis: Tests of Association

Question 1

If the value of r is +1.0, there is no relationship between the two variables under study.

Answer 1

False

Question 2

A Spearman's rank correlation can be used to test whether or not two ordinal variables are associated.

Answer 2

True

Question 3

If r = 0, it indicates that the two variables under study are interdependent.

Answer 3

False

Question 4

In correlation analysis, the alternative hypothesis is typically stated as ρ ≠ 1.

Question 5

The Pearson's correlation coefficient is a statistical measure of causality between two variables.

Question 6

In correlation analysis, the null hypothesis is typically stated as ρ = 0.

Question 7

In situations in which the data are ordinal, the Pearson correlation technique may be used.

Question 8

The Pearson's correlation coefficient is a standardised measure of effect size.

Question 9

Regression is a statistical technique for measuring the curvilinear association between a dependent and independent variable.

Question 10

Correlation and regression analysis can be used to test for simple associations between two nominal variables.

Question 11

The Pearson correlation analysis is a statistical procedure that tests for differences between two interval variables.

Question 12

A correlation analysis can be used to ascertain whether or not gender is related to brand awareness.

Question 13

The mathematical symbol Y is commonly used for the independent variable, and X typically denotes the dependent variable.

Question 14

In a regression equation, the slope of the line $\beta$ is the change in Y that occurs due to a corresponding change of one unit of X.

Question 15

Taking the square root of the correlation coefficient computes the coefficient of determination.

Question 16

The statistical significance of a correlation can be tested using the t-test.

Question 17

The Chi-square test is typically used to test for association between two interval or ratio variables.

Question 18

In correlation analysis, if associated values of the two variables differ from their means in the opposite direction, their covariance will be positive.

Question 19

If the value of r = 0, there is a perfect positive relationship between the two variables under study.

Question 20

In correlation analysis, if associated values of the two variables differ from their means in the same direction, their covariance will be negative.

Question 21

All of the following statements about the Pearson's correlation coefficient are true, except:

A) the Pearson's correlation coefficient, r, is a statistical measure of the covariation between two variables.
B) the Pearson's correlation coefficient, r, ranges from 0 to 1.
C) no correlation is indicated if the Pearson's correlation coefficient, r, equals 0.
D) a perfect positive linear relationship exists if the Pearson's correlation coefficient, r, equals 1.

Question 22

The least-squares regression line minimises the sum of the squared deviations of the actual values from the predicted values in the regression line.

Question 23

The appropriate statistical test to use to calculate the association between two nominal variables is:

A) Spearman's rank correlation
B) regression analysis.
C) Chi-square test.
D) correlation analysis.

Question 24

A researcher would like to predict sales volume against advertising dollar expenditure. Which of the following statistical tests would you suggest?

A) Spearman's rank correlation
B) Correlation analysis
C) Chi-square analysis
D) Regression analysis

Question 25

A Spearman's rank-order correlation coefficient examines the relationship between two ordinal variables.

Question 26

In regression analysis, the error of a predicted score is found by subtracting the predicted value of Y from the actual value of Y.

Question 27

To compute the Chi-square value for the contingency table, the researcher must first identify an expected distribution for that table.

Question 28

The Chi-square test tests the goodness of fit of the observed distribution with the expected distribution.

Question 29

An F-test can be applied to a regression to determine the residual error.

Question 30

When testing for association between two variables, it is possible that they can be statistically significant but not appear to be meaningfully associated.

Question 31

A researcher would like to test whether or not gender (that is, male or female) is related to brand awareness (that is, aware or unaware). Which of the following statistical tests would you suggest?

A) Spearman's rank correlation
B) Independent samples t-test
C) Chi-square test
D) Regression analysis

Question 32

The Chi-square test analyses the significance of the data in an R x C contingency table, in which R stands for row and C stands for column.

Question 33

Bivariate linear regression investigates the relationship between a dependent variable and two independent variables.

Question 34

To use the Chi-square test, both variables in a 2 x 2 contingency table must be measured on a ratio or interval scale.

Question 35

Which type of statistical test is appropriate for testing whether or not there is an association between two ordinal variables?

A) Chi-square test
B) Spearman's rank correlation
C) Regression analysis
D) Paired-samples t-test

Question 36

If there is no relationship between two variables, then the Pearson's correlation coefficient between them will be:

A) +1.0.
B) -1.0.
C) +0.50.
D) 0.

Question 37

A correlation matrix can quickly give the researcher an overview of the direction, strength and statistical significance of each paired relationship.

Question 38

One of the simplest techniques for describing sets of relationships between two interval variables is the cross-tabulation.

Question 39

All of the following statistical tests can be used to test for associations between variables, except:

A) Spearman's rank correlation.
B) regression analysis.
C) Chi-square test.
D) ANOVA.

Question 40

To calculate the expected frequencies for the cells in a cross tabulation, the actual observed numbers of respondents in each individual cell is required.

Question 41

If the correlation coefficient is +0.63, then the coefficient of determination is approximately:

A) +0.63.
B) +0.40.
C) +1.26.
D) +0.79.

Question 42

If the correlation between X and Y is -0.42, approximately what percentage of the variance in Y can be explained by X?

A) 18 per cent
B) 42 per cent
C) 21 per cent
D) 84 per cent

Question 43

In regression analysis, the deviation not explained by the regression is known as the:

A) sampling error.
B) residual error.
C) total error.
D) standardised error.

Question 44

When the correlation between two variables is +0.52 and its associated significance level (p-value) is 0.153, it is implied that:

A) there is no relationship between the variables.
B) there is a weak positive relationship between the variables.
C) there is a moderate positive relationship between the variables.
D) there is a strong positive relationship between the variables.

Question 45

The formula below is the formula for _______________________. $$r _ { w y } = r _ { y w } = \frac { \Sigma \left( X _ { i } - \bar { X } \right) \left( Y _ { i } - \bar { Y } \right) } { \sqrt { \Sigma \left( X _ { i } - \bar { X } \right) ^ { 2 } \Sigma \left( Y _ { i } - \bar { Y } \right) ^ { 2 } } }$$

A) the standard error of the estimate
B) the standard error of the mean
C) the coefficient of determination
D) the Pearson's correlation coefficient

Question 46

To determine the proportion of variance in the dependent variable that is explained by the independent variable, which of the following needs to be derived?

A) The Pearson's correlation coefficient
B) The regression coefficient
C) The residual error
D) The coefficient of determination

Question 47

The coefficient of determination, r², ranges from:

A) zero to +1.0.
B) -1.0 to zero.
C) -1.0 to +1.0.
D) -2.0 to +2.0.

Question 48

When analysing regression results, model fit is determined by consulting the:

A) R-square value in the model summary table.
B) significance value in the ANOVA output table.
C) calculated t-values in the coefficients output table.
D) Beta value in the coefficients output table.

Question 49

If the relationship between two variables is such that both variables are caused by a third variable, then the original relationship between the first two variables is said to be:

A) strong.
B) weak.
C) neutral.
D) spurious.

Question 50

In correlation analysis, the strength of the association between the variables under investigation is determined by:

A) how close the coefficient is to zero.
B) how close the significance value is to 1.
C) how close the coefficient is to ±1.
D) whether the coefficient is positive or negative.

Question 51

Which of the following statements is true?

A) Causation always exists when there is a high correlation between the variables.
B) Variables can be statistically related even if they are not causally related.
C) Regression can be used to measure the linear association between two nominal variables.
D) When the correlation between two variables is 0, it implies a perfect positive association.

Question 52

When the correlation between two variables is -0.32 and its associated significance level (p-value) is 0.0352, it is implied that:

A) there is no relationship between the variables.
B) there is a weak inverse relationship between the variables.
C) there is a moderate inverse relationship between the variables.
D) there is a strong inverse relationship between the variables.

Question 53

In the regression equation, is the symbol for the: $$Y = \alpha + \beta X , \alpha$$

A) residual error.
B) y-intercept.
C) regression coefficient.
D) standard error of the estimate.

Question 54

The correlations table below indicates that: Correlations
$\begin{array}{|l|l|r|r|}\hline & & {\text { Sales }} & \begin{array}{r}\text { Advertising } \\\text { expenditure }\end{array} \\\hline \begin{array}{l}\text { Productivity } \\\text { (average } \\\text { salesper } \\\text { month) }\end{array} & \text { Pearson correlation } &1 &0.354\left({ }^{* *}\right) \\\hline & \text { Sig. (two-tailed) } & & 0.103 \\\hline & N & 100 & 100 \\\hline \begin{array}{l}\text { Months } \\\text { employed }\end{array} & \text { Pearson correlation } & 0.843\left({ }^{* *}\right) & 1 \\\hline & \text { Sig. (two-tailed) } & 0.000 & \\\hline & N & 100 & 100 \\\hline\end{array}$
** Correlation is significant at the 0.01 level (two-tailed).

A) about 35 per cent of variance in productivity can be explained by the variance in months employed.
B) about 71 per cent of the variance in productivity can be explained by the variance in months employed.
C) about 13 per cent of the variance in productivity can be explained by the variance in months employed.
D) there is no association between productivity and months employed.

Question 55

In the regression equation, $\beta$ is the: $$Y = \alpha + \beta X$$

A) residual error.
B) independent variable.
C) regression coefficient.
D) standardised coefficient.

Question 56

If the correlation coefficient is -0.36, then the coefficient of determination is approximately:

A) +0.13.
B) -0.72.
C) -0.13.
D) +0.72.

Question 57

In a regression equation, if the average value of X is 4.6, the average value of Y is 2.3, and the slope is -1.2, then the y-intercept is approximately:

A) 5.70.
B) 0.42.
C) 7.82.
D) 3.22.

Question 58

The correlations table below indicates that: Correlations
$$\begin{array} { | l | l | r | r | } \hline & & { \text { Sales } } & \begin{array} { r } \text { Advertising } \\\text { expenditure }\end{array} \\\hline \text { Sales } & \text { Pearson correlation } & 1 & 0.753 \left( { } ^ { * * } \right) \\\hline & \text { Sig. (two-tailed) } & & 0.005 \\\hline & N & 100 & 100 \\\hline \begin{array} { l } \text { Adverting } \\\text { expenditure }\end{array} & \text { Pearson correlation } & 0.753 \left( { } ^ { * * } \right) & 1 \\\hline & \text { Sig. (two-tailed) } & 0.000 & \\\hline & N & 100 & 100 \\\hline\end{array}$$ ** Correlation is significant at the 0.01 level (two-tailed).

A) about 75 per cent of variance in sales can be explained by the variance in advertising expenditure.
B) about 57 per cent of the variance in advertising expenditure can be explained by the variance in sales.
C) about 57 per cent of the variance in sales can be explained by the variance in advertising expenditure.
D) about 75 per cent of the variance in advertising expenditure can be explained by the variance in sales.

Question 59

Suppose that two groups of consumers (for example, males and females) are asked to rank, in order of preference, the brands of a product class (for example, microwave meals). Which statistical test would be appropriate to determine the agreement between the two groups?

A) Correlation analysis
B) Chi-square analysis
C) Spearman's correlation
D) Independent samples t-test

Question 60

When examining regression results, how well the model fits the data is determined by consulting the:

A) R-square.
B) F statistic.
C) standardised coefficient.
D) calculated t-value.

Question 61

The Pearson's correlation coefficient is actually a standardised measure of __________.

Question 62

The square of the correlation coefficient is called the ___________ of _____________.

Question 63

Two groups of students - those looking to study science degrees and those looking to study business degrees - are asked to rank, in order of preference, the universities they are applying for. The researcher then wants to determine the correlation between the two groups. Which statistical test is most appropriate?

A) Pearson's correlation coefficient
B) Chi-square test
C) Spearman's rank-order correlation coefficient
D) Independent samples t-test

Question 64

In a regression equation, if the average value of Y is 15.6, the average value of X is 5.3, and the y-intercept is 8.5, then the slope is approximately:

A) 1.13.
B) 1.21.
C) 4.55.
D) 1.34.

Question 65

If the correlation between two variables is -0.64, then the coefficient of determination is approximately ____.

Question 66

If sales of baby strollers are associated with the number of babies born during the few months prior to the sales period, then the sales volume of baby strollers is the _________ variable and the number of babies born is the ___________ variable.

Question 67

When examining the correlation matrix, the p-value indicates the ___________ ____________ of the association.

Question 68

The Chi-square test involves comparing ________ frequencies with the ________ frequencies.

A) observed; actual
B) expected; predicted
C) expected; forecast
D) observed; expected

Question 69

The regression outputs for sales and number of salespeople are shown below. Model summary
$$\begin{array} { | l | l | r | r | r | } \hline \text { Model } & \boldsymbol { R } & \boldsymbol { R } \text {-square } & \begin{array} { c } \text { Adjusted } \\\boldsymbol { R } \text {-square }\end{array} & \begin{array} { r } \text { Std. error of } \\\text { the estimate }\end{array} \\\hline 1 & .201 \text { (a) } & .04 & .342 & 56.823 \\\hline\end{array}$$ a Predictors: (Constant), number of salespeople
ANOVA(b)
$$\begin{array} { | l | l | c | r | r | r | r | } \hline \text { Model } & & \begin{array} { c } \text { Sum of } \\\text { squares }\end{array} &\text{ df} & \text { Mean square } & \boldsymbol { F } & { \text { Sig. } } \\\hline 1 & \text { Regression } & 77152.238 & 1 & 77152.238 & 35.117 & .057 ( \mathrm { a } ) \\\hline & \text { Residual } & 61516.962 & 28 & 2197.034 & & \\\hline & \text { Total } & 138669.200 & 29 & & & \\\hline\end{array}$$ a Predictors: (Constant), number of salespeople
B Dependent variable: Sales (A$'000)
Coefficients(a)
$$\begin{array} { | l | l | c | r | r | r | r| } \hline \text { Model } & &{ \begin{array} { c } \text { Unstandardised } \\\text { coefficients }\end{array} } & \begin{array} { c } \text { Standardised } \\\text { coefficients }\end{array} & { \boldsymbol { t } } & { \text { Sig. } } \\\hline & & \boldsymbol { B } & \text { Std. Error } & \text { Beta } & & \\\hline 1 & \text { (Constant) } & 72.612 & 9.203 & & 2.565 & .013 \\\hline & \text { Number of salespeople } & 35.623 & 3.296 & .201 & 5.926 & .064 \\\hline\end{array}$$ a Dependent variable: Sales (A$'000)
The above shows that:

A) for every one-unit increase in number of salespeople, average sales will increase by approximately 73 units
B) the regression results suggested a good model fit
C) the observed results occurred as a result of sampling error
D) the regression coefficient is significant

Question 70

A __________ test is typically used to test for association between two nominal variables.

Question 71

The regression output for sales and number of salespeople are shown below. Model summary
$$\begin{array} { | l | c | r | r | r | } \hline \text { Model } & \boldsymbol { R } & \boldsymbol { R } \text {-square } & \begin{array} { c } \text { Adjusted } \\\boldsymbol { R } \text {-square }\end{array} & \begin{array} { r } \text { Std. error of } \\\text { the estimate }\end{array} \\\hline 1 & .746 ( \mathrm { a } ) & .556 & .541 & 46.873 \\\hline\end{array}$$ a Predictors: (Constant), number of salespeople
ANOVA(b)
$$\begin{array} { | l | l | r | r | r | r | r | } \hline \text { Model } & & \begin{array} { c } \text { Sum of } \\\text { Squares }\end{array} & { \boldsymbol { df } } & \text { Mean square } & \boldsymbol { F } & { \text { Sig. } } \\\hline 1 & \text { Regression } & 77152.238 & 1 & 77152.238 & 35.117 & .000 ( \mathrm { a } ) \\\hline & \text { Residual } & 61516.962 & 28 & 2197.034 & & \\\hline & \text { Total } & 138669.200 & 29 & & & \\\hline\end{array}$$ a Predictors: (Constant), number of salespeople
B Dependent Variable: Sales (A$'000)
Coefficients(a)
$$\begin{array} { | l | l | c | r | r | r | r| } \hline \text { Model } & &{ \begin{array} { c } \text { Unstandardised } \\\text { coefficients }\end{array} } & \begin{array} { c } \text { Standardised } \\\text { coefficients }\end{array} & { \boldsymbol { t } } & { \text { Sig. } } \\\hline & & \boldsymbol { B } & \text { Std. Error } & \text { Beta } & & \\\hline 1 & \text { (Constant) } & 72.612 & 9.203 & & 2.565 & .013 \\\hline & \text { Number of salespeople } & 35.623 & 3.296 & .746 & 5.926 & .000\\\hline\end{array}$$ a Dependent variable: Sales (A$'000)
The above shows that for every one-unit increase in number of salespeople, average sales will increase by approximately:

A) 36 units.
B) 73 units.
C) 75 units.
D) 108 units.

Question 72

A __________ ____ correlation coefficient is typically used to test for association between two ordinal variables.

Question 73

The ___________ coefficient, r, ranges from +1 to -1.

Question 74

It is a requirement in correlation analysis that both variables to be tested are ________ or _____ in nature.

Question 75

A research hypothesis states that male university students are more likely to study STEM courses than female university students. Thus, the researcher would like test to see if an association exists between gender and area of study. Which statistical test is most appropriate?

A) Pearson's correlation coefficient
B) Chi-square test
C) Spearman's rank-order correlation coefficient
D) Independent samples t-test

Question 76

'Tests of ___________' is a general term which refers to a number of bivariate statistical techniques used to test the nature of the relationship between the variables.

Question 77

A Spearman's rank-order correlation coefficient is a technique used when determining the correlation between two _______ scaled variables.

A) nominal
B) interval
C) ordinal
D) ratio

Question 78

If the relationship between two variables is such that both variables are caused by a third variable, then the original relationship between the first two variables is said to be __________ _______.

Question 79

A correlation coefficient indicates both the _________ of the relationship between two variables and the _________ of this relationship.

Question 80

The regression output for sales and advertising spend is shown below. Model summary
$$\begin{array} { | l | l | r | r | r | } \hline \text { Model } & \boldsymbol { R } & \boldsymbol { R } \text {-square } & \begin{array} { c } \text { Adjusted } \\\boldsymbol { R } \text {-square }\end{array} & \begin{array} { r } \text { Std. error of } \\\text { the estimate }\end{array} \\\hline 1 & .445 \text { (a) } & .198 & .169 & 1229.780 \\\hline\end{array}$$ a Predictors: (Constant), advertising spend
ANOVA(b)
$$\begin{array} { | l | l | r | r | r | r | c | } \hline \text { Model } & & \begin{array} { c } \text { Sum of } \\\text { squares }\end{array} & \text { df } & \text { Mean square } & { \boldsymbol { F } } & \text { Sig. } \\\hline 1 & \text { Regression } & 10448599.647 & 1 & 10448599.647 & 6.909 & .014 ( \mathrm { a } ) \\\hline & \text { Residual } & 42346067.019 & 28 & 1512359.536 & & \\\hline & \text { Total } & 52794666.667 & 29 & & & \\\hline\end{array}$$ a Predictors: (Constant), advertising spend
B Dependent variable: Sales (A$'000)
Coefficients(a)
$$\begin{array} { | l | l | c | r | r | r | r| } \hline \text { Model } & &{ \begin{array} { c } \text { Unstandardised } \\\text { coefficients }\end{array} } & \begin{array} { c } \text { Standardised } \\\text { coefficients }\end{array} & { \boldsymbol { t } } & { \text { Sig. } } \\\hline & & \boldsymbol { B } & \text { Std. Error } & \text { Beta } & & \\\hline 1 & \text { (Constant) } & 2993.298&706.247&&4.238&.000 \\\hline & \text { Number of salespeople } & 42.928&16.332&.445&2.628&.014\\\hline\end{array}$$ a Dependent variable: Sales (A$'000)
The above shows that:

A) approximately 45 per cent of the variance in sales can be explained by advertising spend.
B) approximately 43 per cent of the variance in Sales can be explained by advertising spend.
C) approximately 14 per cent of the variance in sales can be explained by advertising spend.
D) approximately 20 per cent of the variance in sales can be explained by advertising spend.