Spearman’s rank correlation coefficient

Some researchers wanted to find out how much agreement there was between experts in their rating of drinks.

They asked 11 experts to rate the different drinks and they calculated the Spearman’s rank correlation coefficient between the ratings for each pair.

The table gives the Spearman’s rank correlation coefficients for each pair of experts.

Which expert has the least agreement with expert 6?

Which two experts have the greatest agreement in their ratings? Give a reason for your answer.

Researchers wanted to know what kind of reduced‑fat cheese that customers liked best.

They asked customers to rate 10 different cheeses and calculated an average score for ‘Overall liking’.

The table gives information about some of their data.

Calculate Spearman’s rank correlation coefficient between the ‘customer overall liking’ scores and the ‘yellowness of cheese’ scores.

The researchers calculated Spearman’s rank correlation coefficients between ‘customer overall liking’ scores and other characteristics of the cheeses.

In each case rank 1 represented the highest level of that quality.

The table gives some of their results.

Interpret in context the correlation for the characteristic that is most closely related to ‘customer overall liking’ scores.

The rankings for the characteristics ‘pleasantness of mouth feel’ and ‘customer overall liking’ were in perfect agreement.

Write down the Spearman’s rank correlation coefficient for the correlation between ‘pleasantness of mouth feel’ and ‘customer overall liking’.

Timur is investigating the heights and weights of rugby players. He collected data from the internet about the heights and weights of players from the Wales rugby squad.

The players from the Wales rugby squad are classed as Forwards or Backs. Timur draws a scatter diagram for the heights and weights of some of the Backs from the Wales rugby squad.

Explain why a scatter diagram is appropriate for the type of data Timur collected.

The data for three of the players was not plotted on the scatter diagram. The height and weight of each of these players is given in the table below.

Complete the scatter diagram by plotting the points for players A, B and C.

Describe and interpret the type of correlation shown by the scatter diagram.

The double mean point for the heights and weights of all of the Backs is (184, 92).

Draw a line of best fit through the double mean point.

Timur also collected the heights and weights of players from the England rugby squad. He found the Spearman’s rank correlation coefficient for the heights and weights of the Forwards from the England rugby squad.

The correlation coefficient was 0.00

Interpret this correlation coefficient in context.

Timur used statistical software to find the following information about the heights (x cm) and weights (y kg) of the Backs from the Wales rugby squad and the Backs from the England rugby squad.

Compare the Spearman’s rank correlation coefficients and interpret this comparison in the context of the question.

Timur uses the information in the table to conclude that the weight of the England rugby squad Backs increases faster than the weight of the Wales rugby squad Backs as their height increases.

Assess the validity of Timur’s conclusion with reference to the statistical results.

Researchers investigated the effect of changing land usage on the amount of surface runoff water for areas of land around Brandywine Creek.

They recorded the change in forest cover area (km²) from 1992 to 2000 They also recorded the change in the amount of surface runoff (mm water) from 1992 to 2000

The table gives information about their data.

Calculate Spearman’s rank correlation coefficient for this data. Interpret this correlation in the context of the question.

Elizabeth wants to investigate possible drainage solutions that reduce surface runoff. She wants to establish whether a particular drainage solution reduces surface runoff.

Elizabeth plans to measure surface runoff in 10 areas for a year without the drainage solution. She will then install the drainage solution in these 10 areas and measure the surface runoff for a year.

Explain how Elizabeth’s plan to collect data controls some extraneous variables. You should include in your answer an example of an extraneous variable that is likely to be controlled in this investigation.

Elizabeth would like to reduce the time that she is collecting data to one year overall.

Describe how she could do this using a matched pairs approach.

Gaby is researching the final position of a football team in the English Premier League and the mean value of all the players in the team.

Suggest a diagram that Gaby could draw to see if there is an association between the final position and the mean value.

The table gives information about the data for the 2018–2019 season that Gaby used.

(Source: www.transfermarket.com)

Calculate Spearman’s rank correlation coefficient for the information in the table. You may complete the d column and d² column of the table to help you.

Interpret your answer to part (b) in the context of Gaby’s research. You should refer to the effects of any anomalous data.

Amelia suggests that Pearson’s product moment correlation coefficient should be used instead of Spearman’s rank correlation coefficient to measure the correlation between the data Gaby is researching.

Discuss whether or not Amelia’s suggestion is appropriate.

In a town music competition, 6 groups competed against each other.

The table shows the marks awarded to each group by the invited independent judge.

The table also shows what the Mayor thought the rank order of the groups should be. (Best group is given rank 1)

Using suitable calculations, investigate how much agreement there is between the judge and the Mayor.

You may use the blank columns in the table for your working.