Handle tied ranks

1. The table below shows the number of televised tournaments won and the total number of tournaments won by the top 10 ranked darts players in 2020

Michael did not want to calculate Spearman's rank correlation coefficient between player's rank and the rank in televised tournaments won because there would be tied ranks.

1. Explain how Michael could have dealt with these tied ranks. Given that the largest number of total tournaments won is ranked number 1
2. calculate the value of Spearman's rank correlation coefficient between player's rank and the rank in total tournaments won.
3. Stating your hypotheses and critical value clearly, test at the \(5 \%\) level of significance, whether or not there is evidence of a positive correlation between player's rank and the rank in total tournaments won for these darts players. Michael does not believe that there is a positive correlation between player's rank and the rank in total number of tournaments won.
4. Find the largest level of significance, that is given in the tables provided, which could be used to support Michael's claim.
   You must state your critical value.

1. Anisa is investigating the relationship between marks on a History test and marks on a Geography test. She collects information from 7 students. She wants to calculate the Spearman's rank correlation coefficient for the 7 students so she ranks their performance on each test.

1. Write down the value of \(s\) and the value of \(t\) The full product moment correlation coefficient (pmcc) formula is used with the ranks to calculate the Spearman's rank correlation coefficient instead of \(r _ { s } = 1 - \frac { 6 \Sigma d ^ { 2 } } { n \left( n ^ { 2 } - 1 \right) }\) and the value obtained is 0.7106 to 4 significant figures.
2. Explain why the full pmcc formula is used to carry out the calculation.
3. Stating your hypotheses clearly, test whether or not there is evidence to suggest that the higher a student ranks in the History test, the higher the student ranks in the Geography test. Use a \(5 \%\) level of significance.

At the end of a season a league of eight ice hockey clubs produced the following table showing the position of each club in the league and the average attendances (in hundreds) at home matches.

1. Calculate the Spearman rank correlation coefficient between position in the league and average home attendance. [5]
2. Stating clearly your hypotheses and using a 5\% two-tailed test, interpret your rank correlation coefficient. [4]

Many sets of data include tied ranks.

1. Explain briefly how tied ranks can be dealt with. [2]

In a competition, a wine-enthusiast has to rank ten bottles of wine, \(A\) to \(J\), in order starting with the one he thinks is the most expensive. The table below shows his rankings and the actual order according to price.

1. Calculate Spearman's rank correlation coefficient for these data. [6]
2. Stating your hypotheses clearly, test at the 5% level of significance whether or not there is evidence of positive correlation. [4]
3. Explain briefly how you would have been able to carry out the test if bottles \(B\) and \(F\) had the same price. [2]