Hypothesis testing and analysis of Madden running back data:
I thought my results for the Madden cover running back data were pretty interesting so I decided to test the hypothesis that running backs who were on the cover of Madden performed worse the year after making the cover.
Null hypothesis: a null hypothesis is a claim that you revert back to when the data you've collected fails to make a compelling case to the contrary. In our case, the null hypothesis represents the claim that there is actually no difference in the performance of running backs that make the cover of Madden vs running backs who don't, with respect to the year they make the cover.
Alternative hypothesis: This is the claim we default to when the null hypothesis has been rejected. In our case, the alternative hypothesis is the claim that there actually IS a difference in performance.
Choosing which statistics to use: I decided to look for which year running backs made the cover of Madden in their career, and average those values to come up with a base line value to collect data against. The value I came to was 6.25 years into a running backs career is when the average Madden running back will make the cover. I then gathered 22 other running backs data. I took their 6th season and 7th season total yard stat and then took the difference. There is in fact a downward trend between a running backs 6th and 7th season, with an average loss of roughly 140 yards (no where near the average Madden cover running back loss of ~910 yards!).
Complicated mumbo-jumbo: The value above (t) is the 'critical t value' on the x-axis of a t-curve. We take that value, with another calculated value (degrees of freedom) and look up in a table what the probability is that the data we're testing differs by "pure chance." What does this mean? Long story short, it means that the probability that there is no difference in the population mean values is essentially 0% given the t value we calculated. 4.1 is very high.
Take Away: There is a very small chance (with the data gathered) that the difference between the mean values is zero, with a P-Value = 0.004 (there is a 0.4% chance that the difference is pure chance). Madden cover running backs perform worse.