Correlations

Question 1

What does covariance measure?

1) The variability of a single variable
2) The average deviation of a variable from its mean
3) How two variables change together
4) The relationship between categorical variables

Answer 1

How two variables change together

Question 2

What does a positive covariance indicate?

1) As one variable increases, the other decreases
2) As one variable increases, the other also increases
3) No relationship between the variables
4) A perfect linear relationship

Answer 2

As one variable increases, the other also increases

Question 3

Why is standardisation necessary in correlation analysis?

1) To simplify the calculations of covariance
2) To remove the influence of scale and variance differences between variables
3) To ensure the variables are normally distributed
4) To convert categorical variables into continuous data

Answer 3

To remove the influence of scale and variance differences between variables

Question 4

What does Pearson’s correlation coefficient measure?

1) The variance within a single sample
2) The direction and strength of the linear relationship between two variables
3) The difference between two sample means
4) The proportion of shared variance between two samples

Answer 4

The direction and strength of the linear relationship between two variables

Question 5

What range of values does Pearson’s correlation coefficient return?

1) 0 to +1
2) -2 to +2
3) -1 to +1
4) 0 to infinity

Answer 5

-1 to +1

Question 6

What is Spearman’s Rho used for?

1) Testing differences between two sample means
2) Measuring the relationship between ordinal or non-normally distributed data
3) Identifying causal relationships between variables
4) Assessing variance within a single variable

Answer 6

Measuring the relationship between ordinal or non-normally distributed data

Question 7

What is the main difference between Pearson’s correlation and Spearman’s Rho?

1) Pearson’s is for non-parametric data, while Spearman’s is for parametric data
2) Pearson’s requires data to be normally distributed, while Spearman’s does not
3) Spearman’s provides a more accurate measure of linear relationships
4) Pearson’s is only for categorical data

Answer 7

Pearson’s requires data to be normally distributed, while Spearman’s does not

Question 8

What does a Pearson’s correlation coefficient of 0 indicate?

1) A weak linear relationship between the variables
2) No linear relationship between the variables
3) A strong non-linear relationship between the variables
4) A significant difference between the variables

Answer 8

No linear relationship between the variables

Question 9

What is the null hypothesis in a correlation analysis?

1) The two variables are perfectly correlated
2) The correlation coefficient is significantly different from zero
3) The correlation coefficient is equal to zero
4) There is a causal relationship between the variables

Answer 9

The correlation coefficient is equal to zero

Question 10

What does the square of the correlation coefficient (r²) represent?

1) The significance level of the correlation
2) The proportion of variance in one variable explained by the other
3) The standard error of the covariance
4) The reliability of the dataset

Answer 10

The proportion of variance in one variable explained by the other

Question 11

What is the primary limitation of correlation analysis?

1) It cannot measure the strength of relationships
2) It assumes all relationships are non-linear
3) It cannot establish causation between variables
4) It is only applicable to normally distributed data

Answer 11

It cannot establish causation between variables

Question 12

What does a negative correlation coefficient indicate?

1) Both variables increase together
2) As one variable increases, the other decreases
3) No relationship between the variables
4) A perfect non-linear relationship

Answer 12

As one variable increases, the other decreases

Question 13

What is the first step in conducting a correlation analysis?

1) Calculate the covariance
2) Perform a visual inspection and check assumptions
3) Calculate the correlation coefficient
4) Square the r-value

Answer 13

Perform a visual inspection and check assumptions

Question 14

What does r = -.56 suggest in a Spearman’s correlation analysis?

1) A weak negative relationship
2) A moderate negative relationship
3) A strong negative relationship
4) No relationship

Answer 14

A strong negative relationship

Question 15

How should correlation results be reported?

1) With exact p-values, r-values, and sample sizes
2) By stating the null hypothesis was rejected
3) By including confidence intervals and standard errors only
4) By specifying the covariance value only

Answer 15

With exact p-values, r-values, and sample sizes

Question 16

What type of data is suitable for Spearman’s Rho?

1) Interval data with normal distribution
2) Ordinal data or data that violates parametric assumptions
3) Nominal data
4) Data with unequal variances

Answer 16

Ordinal data or data that violates parametric assumptions

Question 17

Why is “correlation does not equal causation” an important reminder?

1) Correlation coefficients are often inaccurate
2) Correlation analysis assumes a bidirectional relationship
3) Correlation cannot determine which variable influences the other or if a third variable is involved
4) Correlation is a weaker form of statistical analysis

Answer 17

Correlation cannot determine which variable influences the other or if a third variable is involved

Question 18

What does a significant positive correlation imply?

1) Variable X predicts Variable Y perfectly
2) As Variable X increases, Variable Y tends to increase
3) As Variable X increases, Variable Y tends to decrease
4) The variables are not related

Answer 18

As Variable X increases, Variable Y tends to increase

Question 19

In the example provided, what was the relationship between hours of driving and driving anxiety?

1) A positive correlation
2) A negative correlation
3) No correlation
4) A causal relationship

Answer 19

A negative correlation

Question 20

If r² = 0.18 in a correlation analysis, what does this indicate?

1) 18% of the variance in one variable is explained by the other
2) The correlation coefficient is 0.18
3) The p-value is below 0.05
4) There is no significant relationship between the variables

Answer 20

18% of the variance in one variable is explained by the other