Monday, March 14, 2011

Calculating a Z Score for Marion Jones' 100m Time, 2000 Olympic 100m Finals

Here, we are going to calculate a z score for Marion Jones' time in the finals of the 100m at the 2000 Olympic Games. Her z score will be calculated in comparison to her elite peers in that race. In the photo, below, you can see the large distance between Jones and her peers as she crosses the finish line. The athletes' times for the race are listed, below the picture:

2000 Olympic Games, Women's 100m Final:
  • Marion Jones: 10.75 seconds
  • Ekaterini Thanou: 11.12
  • Tanya Lawrence: 11.18
  • Merlene Ottey: 11.19
  • Zhanna Pintusevych: 11.20
  • Chandra Sturrup: 11.21
  • Sevaheda Fynes: 11.22
  • Debbie Ferguson: 11.29

Now in the video, below, we go through process of getting Jones' z score and then locating it within the standard normal table to check for statistical significance. In the video, we will see that Jones' time, relative to her peers is statistically significant at the threshold of 0.05. What about at 0.01? And what does this mean?

Now, there are more important social issues than sports, but this was a good way of illustrating the process of getting z scores and locating them within the standard normal table. You could do the same thing, examining for instance, "the number of times someone was a victim of violence" or "the number of times someone had used illicit substances" in a given timeframe.

If you surveyed a large number of people, then you could get z scores for individuals' responses and see where they are located in the standard normal table. This is where statistics is very useful for more socially important topics.

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