Exam 3: The Phoenix of Statistics

A sports nutritionist undertook a study to examine the impact of a reduction in protein intake and team performance, which showed a statistical significance between reduced protein intake and increased team performance. How can she explain to her manager that this does not mean she should start removing protein from the team's diet?

A manager of an inclusive sports programme in schools was concerned about the lack of girls being recruited on to the programme. There were thirty places on the programme and fifty children had applied, of which only ten were girls. Theoretically, all the children in the participating schools have an equal probability of being recruited as they all match the selection criteria, i.e. they are children at a participating school. However, the manager has data that suggests that boys are more likely to join school based sports programmes than girls based on data from across the school sports programme nationally and from within her own programme historically. However the manager has heavily promoted this initiative, specifically targeting girls and therefore wants to determine the probability that still fewer girls than boys will join. What formula could she use to determine this probability?

Your sports and exercise lecturer has devoted the past ten weeks to teaching you the Bayesian approach and is now asking that you offer a critique of it. What key criticism could you raise?

A customer services strategy manager for a national wellbeing and fitness company is interested in assessing customer usage of their gyms across 20 sites nationally. Different gym managers have collected and analysed data from each of the sites but the resultant twenty reports showed differing p-values, some sites found a statistical significance between increased opening hours of gyms and usage and others did not. Which of the following would it be useful for her to review?

You have just joined the performance modelling team for a national elite sports programme. Your boss has decided that from now on the team will adopt a Bayesian approach. However, not all staff understand what this is; your boss asks you to present a training session. How would you explain a Bayesian approach in your session introduction?

A sports researcher wanted to assess the likelihood that girls score more goals than boys do in five a-side soccer. She conducted one study where the probability of making a Type I error was 0.05 and a Type II error was 0.2. Does her research have empirical probability?

You lead a product-testing unit for a large sports nutrition company. Your team has conducted forty trials of a new energy supplement but you are not sure if the results are conclusive enough to urge the company to start producing it. A new data analyst has joined your team suggesting that meta-analysis might be a good idea, do you agree?

A sports student conducted a Bayesian analysis of time spent watching sports and improved academic performance. He calculated a Bayes factor of 1. Should he use time spent watching sports as a predictor of academic performance?

A new member of a basketball coaching staff, whose team is at the bottom of the league, has just completed a study into factors that affect player performance levels. However, he finds only one statistically significant factor, which he includes in his report but deliberately, omits the other six non-significant findings. What is the term for what the coach has done?

You are the CEO of a sports performance forecasting company. You have decided to adopt a Bayesian approach to data analysis and modelling. When you announce this new policy, your staff are unhappy and unconvinced, as they are used to a NHST approach. You stress that the Bayesian approach has several key advantages, including which of the following.

You work for a performance sports clothing company. Your CEO has just read a book on criticisms of the NHST and worries that all company data analysis is now flawed and will lead to huge financial losses. How might you reassure her?

Which of the following is not a factor in data analysts' over-use of p-values and NHST in sports and exercise research?

In our previous example, the human resources manager had already calculated the probability of no girls joining her programme based on sector wide data. In the Bayesian approach, what sort of probability is this?

Your CEO has followed your advice and now wants you to measure effect sizes. You report a Pearson's r of 0.50 for the impact of Power Nylon shorts on athletic performance times. Your CEO wants to know if this is bad, as she remembers that a p-value of 0.30 is not good. What do you tell her?

A researcher working in a sports performance lab was interested in gender and perception of pain during extreme sports and so conducted a t-test. The mean for males was 66.25 and the mean for females was 78.24, with both groups having a standard deviation of 7. What is the effect size using Cohen's d?

A swim coach is assessing swimmers' satisfaction with a new training regime. He had a sample size of 22 and a p-value of 0.3. Does the coach recommend that the swimmers stop using the new training regime?