NICA-Exploratory Data Analysis

This is a table of the average, median, and standard deviation for each division.

Histograms of the total time in seconds for each division.

The Division System Exploration

As you can see below, all D1 and D2 groups have very similar means, medians and standard deviations. If you look at the density plots below you can also see that there is little differecne between the two divisions after accounting for the number of individuals in each division.

Missing Previous Race

Here are the results of missing the previous race. On average after missing one race it isnt a very big deal. Individuals who missed the previous race on average change about 1 more position than individuals who didnt miss the previous race.

Missing Previous Two Races

Here are the results of missing the previous two races. Individuals who missed the previous two races on average change about 5 more position than individuals who didnt miss the previous race two. To me this seems to be a more serious problem.

Mean Change in Position by number of races attended, gender, and division.

GEE Modeling

Using GEE modeling we can look to see if the number of races attended has a significant effect on the change in position.

With a p-value of 0.86 we fail reject the null hypothesis. The number of races attended does not have a significant effect on change in position. The race number, division, gender, and starting position all have a significant affect on the change in position.

## 
## Call:
## geeglm(formula = diffsf ~ numracesattended + Division + totaltime + 
##     startorder + race + Place, data = geedata, id = interaction(race, 
##     Division), corstr = "ar1")
## 
##  Coefficients:
##                    Estimate    Std.err   Wald Pr(>|W|)    
## (Intercept)       5.6897966  1.7130532 11.032 0.000896 ***
## numracesattended -0.0499713  0.2465218  0.041 0.839365    
## Division7D2M      0.6060399  1.0805450  0.315 0.574890    
## Division7F       -0.9943370  0.6906058  2.073 0.149923    
## Division8D1M     -0.2753780  1.0590214  0.068 0.794840    
## Division8D2M      1.0447334  1.2243237  0.728 0.393485    
## Division8F       -1.5292316  0.6958381  4.830 0.027972 *  
## DivisionFD1M      4.2669811  1.3985644  9.308 0.002281 ** 
## DivisionFD2M      1.6792618  1.1517053  2.126 0.144822    
## DivisionFF        0.3594046  1.6390854  0.048 0.826439    
## DivisionJV2D1M    3.3885625  1.4084135  5.789 0.016131 *  
## DivisionJV2D2M    7.2538030  1.5501945 21.896 2.88e-06 ***
## DivisionJV2F      1.4952427  1.7351989  0.743 0.388846    
## DivisionJV2M      3.5025205  1.0905591 10.315 0.001320 ** 
## DivisionJV3F      0.6595845  2.2038087  0.090 0.764717    
## DivisionJV3M      1.1727374  2.2752962  0.266 0.606258    
## DivisionVF        0.0312107  2.9550718  0.000 0.991573    
## DivisionVM        0.1360948  2.2681296  0.004 0.952153    
## totaltime        -0.0003262  0.0007747  0.177 0.673705    
## startorder        0.1975407  0.0351524 31.579 1.91e-08 ***
## race2             0.0667098  1.1408504  0.003 0.953371    
## race3            -2.1001106  0.8879189  5.594 0.018020 *  
## race4            -3.1215438  0.8336035 14.022 0.000181 ***
## race5            -2.6398537  0.8776793  9.047 0.002632 ** 
## race6            -3.0965613  0.9367611 10.927 0.000948 ***
## race7            -6.8502317  1.1414288 36.017 1.96e-09 ***
## Place            -0.0462183  0.0320856  2.075 0.149735    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Estimated Scale Parameters:
##             Estimate Std.err
## (Intercept)    80.04   8.513
## 
## Correlation: Structure = ar1  Link = identity 
## 
## Estimated Correlation Parameters:
##       Estimate Std.err
## alpha  0.08135 0.02406
## Number of clusters:   105   Maximum cluster size: 118