> set.seed(1234)         # Set random number generator seed to reproduce samples
> (t <- max(opp_id))     # t = number of opponents ("treatments")
[1] 7
> (N <- length(runs))    # N = total number of games
[1] 78
> (ybar_all <- mean(runs))   # ybar_all = overall sample mean number of runs per game
[1] 6.358974


> teamrange
     [,1] [,2]
[1,]    1   12
[2,]   12   23
[3,]   23   34
[4,]   34   45
[5,]   45   56
[6,]   56   67
[7,]   67   78
> ybar
[1] 7.500000 5.416667 4.750000 8.000000 7.166667 6.416667 4.916667
> sumsq_obs
[1] 113.5855

         randgrp
 [1,]  1       9
 [2,]  2      48
 [3,]  3      47
 [4,]  4      76
 [5,]  5      64
 [6,]  6      75
 [7,]  7       1
 [8,]  8      17
 [9,]  9      73
[10,] 10      36
[11,] 11      77
[12,] 12      37
[13,] 13      19
[14,] 14      61
[15,] 15      66
[16,] 16      53
[17,] 17      18
[18,] 18      71
[19,] 19      12
[20,] 20      14
[21,] 21      74
[22,] 22      62
[23,] 23      78
[24,] 24       3
[25,] 25      60
[26,] 26      43
[27,] 27      28
[28,] 28      70
[29,] 29      42
[30,] 30      55
[31,] 31      22
[32,] 32      13
[33,] 33      15
[34,] 34      23
[35,] 35       8
[36,] 36      33
[37,] 37      56
[38,] 38      11
[39,] 39      40
[40,] 40      32
[41,] 41      68
[42,] 42      24
[43,] 43      54
[44,] 44      38
[45,] 45      69
[46,] 46      65
[47,] 47      35
[48,] 48      16
[49,] 49      44
[50,] 50      45
[51,] 51      49
[52,] 52      50
[53,] 53      58
[54,] 54      51
[55,] 55       4
[56,] 56      34
[57,] 57      41
[58,] 58      31
[59,] 59      67
[60,] 60      63
[61,] 61      21
[62,] 62      72
[63,] 63       6
[64,] 64      26
[65,] 65      20
[66,] 66      10
[67,] 67      59
[68,] 68      57
[69,] 69      46
[70,] 70      39
[71,] 71      25
[72,] 72       7
[73,] 73      30
[74,] 74      29
[75,] 75      27
[76,] 76       2
[77,] 77       5
[78,] 78      52
> 
> summary(sumsq_rand)   # Give the summary of the sum of squares
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
   1.14   48.47   73.53   80.99  105.50  415.60 
> 
> ### Compute the p-value for the observed sum of squares
> ### Count the number of permutation samples with sum of squares >= observed
> ### Add 1 to include the observed sample in numerator and denominator
> 
> (p_rand <- (sum(sumsq_rand >= sumsq_obs)+1)/(num_samp+1))
[1] 0.20502