The most simple method to look into wave-based disparity in a golf tournament would be to look at the scoring averages for each wave. Here, I am comparing the scoring average for morning and afternoon waves at the Bubba Conlee Junior. I know these scores are high, but trust me when I say it was playing difficult. Don't worry, these are still some of the best junior golfers out there.
82.66
Morning Wave Scoring Average
58 Players
82.4
Afternoon Wave Scoring Average
40 Players
There is a noticeable difference here, but it does not seem like much. How would we know if this difference in average scores constituted an unfair form of competition?
We would have to take into consideration different statistics from both the morning and afternoon populations, such as:
Average Score(x̄)
Sample Size(n)
Sample Standard Deviation(s)
With this information, we could perform a significance test to determine whether the difference in scores is statistically significant or just from random variance. We can treat these tournament players as two samples from two different populations and draw a conclusion on how the overall junior golfer population would have performed in each weather condition
Morning Wave:
x̄1 = 82.65517241
n1 = 58
s1 = 5.599347469
Afternoon Wave:
x̄2 = 82.4
n2 = 40
s = 4.395802193
Based off these statistics and a Two Sample T-Test, we can conclude that the P-Value of the test is 0.4007143026, meaning that there is about a 40% chance of this difference in scores occurring from random variance. This number is rather large, as most significance tests require a P-Value of 0.05 or lower to be considered statistically significant.
As seen in the graphic, there is a lot of overlap in the possible range of scoring averages for both the morning and afternoon populations.
So, looking at only scoring averages did not lead us to a believe that there was an unfair nature between the morning and afternoon tee times. What else can we look at?