Spearman's Rank Correlation Coefficient (rS)

The following practice questions are focused on checking, and developing, your understanding of the key ideas on this topic. You can print the page by choosing 'print this page' from the menu on the right OR you can use the onscreen version and check your answers as you go.

For the scatter graph below is Spearman's rank correlation coefficient or Pearson's product moment correlation coefficient the more appropriate measure of correlation and why:

For the scatter graph below is Spearman's rank correlation coefficient or Pearson's product moment correlation coefficient the more appropriate measure of correlation and why:

For the scatter graph below is Spearman's rank correlation coefficient or Pearson's product moment correlation coefficient the more appropriate measure of correlation and why:

Which of the following statements are true:

(A) Pearson's correlation coefficient gives the same value as Spearman's rank correlation coefficient for linear data

(B) Spearman's rank correlation coefficient can measure how well an exponential model fits the data

(C) Spearman's coefficient measures to what extent a set of data is constantly increasing or decreasing

(D) Pearson's correlation coefficient can be used to measure the goodness of fit for quadratic models

(E) Spearman's coefficient can be used as a measure of goodness of fit for cubic models.

(A) not true - Spearman's suggests a greater fit than Pearson's for the data below. Pearson's, in this case, is the more accurate measure since it does measure how well a linear model fits to data, whereas Spearman's measures the extent to which the data is constantly increasing or decreasing (monotonicity), without considering whether that relationship is linear, exponential, logistic etc.

(B) Not true - see graph below. The exponential model does not fit perfectly the data points, but Spearman's coefficient rS = 1 suggests it does.

A certain bacteria is believed to grow faster at higher temperatures (below 60°C).

(a) Rank the data below from largest (=1) to lowest (=8) temperature and volume (largest = 1, lowest = 8)

(b) Calculate Spearman's rank correlation coefficient for this data and Pearson's correlation coefficient.

(c) Which is the better measure of correlation for this data and why?

(a)

(b) Pearson's = 0.956 (3 s.f),  Spearman's = 1

(c) Spearman because it is not a linear relationship.

Total Score:

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