Topic 5: Women’s heptathlon

The women’s heptathlon is a combined sports contest comprising seven events: 100-metre hurdles, high jump, shot put, 200 metres, long jump, javelin throw and 800 metres. It is one of the toughest Olympic events for athletes.

You can input the data into RStudio from the following table or download/upload the .csv file from the zip folder (provided in the Downloads section in Step 2.13) that shows the results of two heptathlon disciplines, 200 metres (in seconds) and javelin throw (in metres), for 31 athletes competing at the 2016 Summer Olympics in Rio de Janeiro, Brazil. For full details, including the results in other heptathlon disciplines and the overall ranking, see Wikipedia in the ‘See also’ section in Step 2.13. The data is repeated in this table if you would find it easier to input into RSTudio compared to the .csv file already given in the hyperlink.

How can the performance in these two events be compared and combined to determine the overall winner? The trouble is that the results in these events are measured on different scales: ‘smallest’ is best for running, but ‘largest’ is best for throwing.

To put the measurements on equal footing, we can standardise them by using z-scores. We can then combine the standardised scores to come up with an overall ranking of the athletes.

Answer the following questions:

• Calculate the sample mean and standard deviation in each of the two disciplines.
• Calculate individual z-scores for each athlete in each discipline.
• Combine the two z-scores for each athlete to work out their overall performance index. Would just taking the sum of the two z-scores be reasonable? If not, how could you do it differently?

Comment: In the real Olympic games, a more complicated scoring system is used which awards proportionally more points for the more outstanding results. The system also ensures that the distribution of scores is consistent from one Olympics to the next.