rugby - south africa and new zealand player weights comparison
This example will show you how to write a report when the box plots are really close together. We will learn that in this case, it is not possible to make a call that one country is heavier than the other. Just because the median value for New Zealand is indicating a higher average weight, we use a special formula to make the call in these cases where the boxes are very close together. It's called the 1/3 rule but more on that later.
Problem
I wonder if the median weights of New Zealand rugby players tend to be greater than the median weights of South African rugby players back in the population of players of both countries. From my own observations, New Zealand players are highly successful and are world champions. Being big strong and fast are often related to that level of performance. So maybe the NZ players tend to be heavier.
plan
I will take my random sample of players from NZGrapher. The sample size is 67 NZ players and 68 South African players. NZGrapher will generate a dot plot and a box and whisker graph with 5 number summaries so I can analyze and make a conclusion about which country has the heaviest players.
data
analysis
Central Tendency:
The median weight for NZ rugby players is 104 kg and the median weight for South African players 101.5 kg, a difference of 2.5 kg. This indicates that the average NZ rugby player could be heavier than the average South African rugby player back in the population of players from both countries (data base sample of NZGrapher).
The median weight for NZ rugby players is 104 kg and the median weight for South African players 101.5 kg, a difference of 2.5 kg. This indicates that the average NZ rugby player could be heavier than the average South African rugby player back in the population of players from both countries (data base sample of NZGrapher).
Spread:
The IQR (middle 50%) for NZ Rugby players weight is 20 kg whereas the IQR for South African rugby player weight is 19.5 kg. This indicates that there is more variation in the weights of NZ rugby players. Overall visually the NZ rugby players seem to be more spread out than the male kiwi.
Spread:
The IQR (middle 50%) for NZ Rugby players weight is 20 kg whereas the IQR for South African rugby player weight is 19.5 kg. This indicates that there is more variation in the weights of NZ rugby players. Overall visually the NZ rugby players seem to be more spread out than the male kiwi.
Conclusion
Based on looking at my sample I cannot make the call that back in the population of rugby players from NZ and South Africa that the median weight of NZ players tends to be heavier than the median weight of South African players.
The distance between the medians compared to the overall visible spread is less than one third. This means we can't make the call that NZ players are heavier than the South African players in our sample. This surprised me as I expected the NZ players to be on average heavier.
Because the sample sizes around 30 I have to use the DBM/OVS (Distance between medians) / Overall visual spread) rule. The DBM is about 4 and the OVS is about 38. The ratio is 4/38 = 0.1 If the DBM/OVS is > 1/3, I can make the call. However 0.1 is less than 1/3, therefore, I cannot make the call that NZ rugby players are on average heavier than South African players.
Because the sample sizes around 30 I have to use the DBM/OVS (Distance between medians) / Overall visual spread) rule. The DBM is about 4 and the OVS is about 38. The ratio is 4/38 = 0.1 If the DBM/OVS is > 1/3, I can make the call. However 0.1 is less than 1/3, therefore, I cannot make the call that NZ rugby players are on average heavier than South African players.