Correlation - Statistics

Statistical Tests: Correlation Page 1/3

Welcome to the "Correlation" quiz. There are 5 questions to answer.

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Q1. Which of the following statements is true regarding correlation?

a)It assesses the direction and strength of a relationship between any two variables. ✔ ✗

b)It assesses the direction and strength of a relationship between two categorical variables. ✔ ✗

c)It assesses the direction and strength of a relationship between two continuous variables. ✔ ✗

d)It quantifies the relationship between two categorical variables ✔ ✗

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The correct answer is c). If we want to assess the relationship between other types of variables, then other statistical techniques must be used.

Q2. Which of the following pairs of variables should not be analysed using Correlation?

a)Age -. Body Mass Index (BMI) ✔ ✗

b)FEV1 - Gender ✔ ✗

c)Systolic Blood Pressure - Cholesterol level ✔ ✗

d)Alanine transaminase (ALT) - Alcohol Consumption (units per week) ✔ ✗

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The answer is b). We should not use categorical variables, e.g. Gender, when calculating a correlation coefficient, only continuous variables as in cases a), c) and d).

Q3. When would it be appropriate to calculate the Spearman Rank Correlation coefficient?

a)When both variables follow a normal distribution ✔ ✗

b)When one of the variables follows a normal distribution and the other follows a skewed distribution ✔ ✗

c)When both variables follow show a skewed distribution ✔ ✗

d)When the relationship between the variables is not linear ✔ ✗

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The answer is c). We calculate the Spearman rank correlation coefficient when both variables have a skewed distribution. We calculate the Pearson correlation coefficient when one or both of the variables are reasonably Normally distributed. We should not use correlation if the relationship is not linear.

Q4. Which of the correlation coefficient best describes the relationship between the X and Y variables?

a)0.01 ✔ ✗

b)0.40 ✔ ✗

c)-0.01 ✔ ✗

d)-0.40 ✔ ✗

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The answer is d). There is a trend from top left to bottom right so the correlation coefficient will be negative. If the data points were randomly organised with no trend then options a) or c) would have been possible.

Q5. Which of the correlation coefficient best describes the relationship between the X and Y variables?

a)0.91 ✔ ✗

b)0.51 ✔ ✗

c)0.02 ✔ ✗

d)0.51 ✔ ✗

e)-0.96 ✔ ✗

Feedback:

The answer is c). The correlation coefficient will be closes to zero which mean there is no linear association. However this illustrates an important point, always plot the data to see what it tells you. Then calculate the correlation coefficient if appropriate. There is no linear association here, but there is a mathematical relationship. The plot is a parabola where Y= (X-10)².

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