Assignment 9, Fall 2000

STATISTICS 403 - Assignment 9

We will go over in class Thursday, December 7, 2000

The data below were collected by W. F. Woodward, shortstop of the 1970 Cincinnati Reds National League baseball team. The question of interest was whether the way a runner rounded first base made a difference in the time it took to get to second base. The three methods were "round out", "narrow angle" and "wide angle".

                       Method

Player   Round out   Narrow angle   Wide angle
-----------------------------------------------
   1        5.40         5.50          5.55
   2        5.85         5.70          5.75
   3        5.20         5.60          5.50
   4        5.55         5.50          5.40
   5        5.90         5.85          5.70
   6        5.45         5.55          5.60
   7        5.40         5.40          5.35
   8        5.45         5.50          5.35
   9        5.25         5.15          5.00
  10        5.85         5.80          5.70
  11        5.25         5.20          5.10
  12        5.65         5.55          5.45
  13        5.60         5.35          5.45
  14        5.05         5.00          4.95
  15        5.50         5.50          5.40
  16        5.45         5.55          5.50
  17        5.55         5.55          5.35
  18        5.45         5.50          5.55
  19        5.50         5.45          5.25
  20        5.65         5.60          5.40
  21        5.70         5.65          5.55
  22        6.30         6.30          6.25
--------------------------------------------------

(a) Why is it beneficial to have a block design for this study?

(b) Analysis of Variance can be used to test to see if there are significant differences among the methods in terms of average times to reach second base. Below is Minitab output for such an analysis.


     Analysis of Variance for Time

     Source   df   Sum of Squares   Mean Square     F       P
     --------------------------------------------------------
     Method    2       0.09371        0.04686    6.29   0.004
     Player   21       4.21864        0.20089   26.96   0.000
     Error    42       0.31295        0.00745                
     --------------------------------------------------------
     Total    65       4.62530

Interpret the output and indicate what, if any, methods are significantly different.

(c) Test the hypothesis that there is no difference in average times for the three methods using Friedman's test statistic. What does this test tell you?
(d) Use the multiple comparison method associated with Friedman's test to see what, if any, methods are statistically different.