MSDS 6371 Analysis Question
The winter Olympics are in PyeongChang, South Korea and the world is watching! Surprisingly, the sport of Curling has been around since the first Winter Olympics in 1924 but wasn’t recognized as a medal sport until 2006. This year, controversy has struck Curling as the bronze medal winner, Aleksandr Krushelnitckii, has tested positive for a banned substance known as meldonium. This is the same substance that former world tennis number one Maria Sharapova tested positive for in 2016.
There has been great debate about any advantage athletes may gain when taking meldonium with world doping expert Don Catlin concluding, ““There’s really no evidence that there’s any performance enhancement from meldonium – Zero percent”
Use the Curling.csv data set to answer the questions below. You may assume that his curling scores come from normal distribution and that the standard deviation of his scores within tournaments are consistent. In addition, although this may be a questionable assumption, you may assume that the scores within and between tournaments are independent of one another. You may finally, assume that it was known that he did not test positive for meldonium in any of the non-Olympic tournaments.
- (50 pts) Conduct a test to test for any evidence of different mean curling scores between tournaments. Address the assumptions of the test and show all 6 steps. Be sure and provide your SAS or R code as well. Let’s test here with an alpha = .05 level of significance.
We will conduct an ANOVA to answer this question.
Assumptions:
- Normality: We are given in the problem that that scores are normally distributed within tournaments.
- Equal SD: We are also given that the standard deviations of the scores have equal standard deviations within the tournaments.
- Independent: Finally, we are given that we are to assume the scores are independent both between and within the tournaments.
The assumptions are met for the ANOVA and below is the R code and results from the ANOVA.
Ho: All tournament mean scores are equal.
Ha: At least one pair of tournament mean scores are different.
Critical value: F = 2.178
Test statistic: 2.371
Pvalue: .0338
Decision: Reject Ho
Conclusion: There is sufficient evidence to suggest that at least one pair of tournament mean scores are different (pvalue = .0338). This does not provide enough evidence to suggest that the Olympic tournament mean match scores are higher than the other tournaments. We will investigate that next.
- (50 pts) Is there any evidence that the mean or median curling scores from 6 randomly selected tournaments where Aleksandr tested negative for meldonium are less than his average curling score in PyeongChang? Your analysis should include a clear conclusion that explains your analysis and supports it with relevant statistics (confidence interval to quantify significant differences, pvalues, etc. ) Be sure and provide your SAS or R code as well. Let’s test here at the alpha = .05 level of significance and use two sided tests.
Since we rejected Ho in the ANOVA, it makes sense to investigate which tournaments have evidence that supports them being different. We will run every pairwise comparison and look at just the ones that involve the Olympics tournaments versus the other tournaments (the potential meldonium tournament versus the non-meldonium tournaments). The results are below:
It is clear that without a multiple correction adjustment, there is convincing evidence that that all and only the Winter Olympic tournament have a mean match score that is different from (greater than) the other 6 tournaments. However, we have conducted 6 planned tests and need to make an adjustment to the pvalues. A Bonferroni adjustment can easily be applied by simply multiplying each Winter Olympic pvalue by 6. This yields
Even after a correction there is still convincing evidence that there is a significant difference in the mean scores of the Winter Olympic matches and 5 of the other 6 randomly selected tournaments (at the alpha = .05 level of significance). In addition, this evidence suggests that the the mean score of the Winter Olympic matches is greater than that of 5 of the 6 other tournaments (even after a Bonferroni correction.)
Students may have used a Tukey adjustment or a Bonferroni adjustment with k =21. This will lead to evidence of the mean match score of the Winter Olympics only being greater than the RussiaQual5 tournament. It is very close to the correct solution thus only 5 points will be subtracted if a student got this far.
A student may have also not performed a correction at all. While the results are similar to the what we have above, this is a more serious infraction and will take 10 points off if no adjustment was made.