In-class activity 10: Correlation between teams rank and wins

For 2012 correlation

teamRank = c(1,2,3,3,4,4,4,4,5,5) # Create teh Vector teamRank
wins2012 = c(94,88,95,88,93,94,98,97,93,94) # Create the vector wins2012

Let us find the correlation between Team Rank and the number of winds.

cor(teamRank,wins2012)

[1] 0.3477129

We can see that there is a very low correlation between team rank and wins for the year 2012. This correlation is 0.34 which is fairly less than 50%.

Lets run some test statistics to see if the p value.

cor.test(teamRank,wins2012)

    Pearson's product-moment correlation

data:  teamRank and wins2012
t = 1.0489, df = 8, p-value = 0.3249
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 -0.3609319  0.8018015
sample estimates:
      cor 
0.3477129 

We can see the p value is not significant. So we can Not reject the null, that there is no correlation. So we must accept that there is no correlation.

For 2013 correlation

teamRank2 = c(1,2,3,3,4,4,4,4,5,5)
wins2013 = c(97,97,92,93,92,96,94,96,92,90)

cor(teamRank2,wins2013)

[1] -0.6556945

We can see that there is some negative correlation between a teams rank and wins. So apparantely the more you win your chance of lower rank increases, which is highly counter intuitive. Maybe this is due to exhaustion, maybe this indication would lead team management to only prioritize games that will influence their rank in the leauge.

Lets run some test statistics to inspect the p value.

cor.test(teamRank2,wins2013)

    Pearson's product-moment correlation

data:  teamRank2 and wins2013
t = -2.4563, df = 8, p-value = 0.03955
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 -0.90974104 -0.04439732
sample estimates:
       cor 
-0.6556945 

We can see that the p value is less than alpha so we can reject hO (that there is no correlation). So in rejecting hO we acccept the turth that there is a correlation, which we sae already to be: -0.65.