Computes a Kendall rank correlation S-statistic for permutations of censored data. Collectively these represent the variation in S expected when the null hypothesis is true. Called by censeaken. computeS is not expected to be of much use to users on its own.
computeS(x, y, ycen, seas = NULL, R = R)Column of the time variable, either a sequence of days or decimal times, etc. Time data for one season.
The column of y (response variable) values plus detection limits for one season.
The y-variable indicators, where 1 (or TRUE) indicates a detection limit in the y column, and 0 (or FALSE) indicates a detected value in y.
Name of a single season classification. Usually though not necessarily a text variable.
The number of repetitions in the permutation process. R is often between 999 and 9999 (+ the 1 observed test statistic produces 1000 to 10000 realizations).
An Rx1 matrix containing an S-value for each of the R data permutations.
Helsel, D.R., Hirsch, R.M., Ryberg, K.R., Archfield, S.A., Gilroy, E.J., 2020. Statistical Methods in Water Resources. U.S. Geological Survey Techniques and Methods, book 4, chapter A3, 458p., https://doi.org/10.3133/tm4a3.
data(Brumbaugh)
#Artifical time and season variables for demonstration purposes
Brumbaugh$time=1:nrow(Brumbaugh)
Brumbaugh$sea=as.factor(round(runif(nrow(Brumbaugh),1,4),0))
with(Brumbaugh,computeS(time,Hg,HgCen,sea,R=100))
#> [,1]
#> [1,] 974
#> [2,] 134
#> [3,] -272
#> [4,] -1938
#> [5,] -4
#> [6,] 114
#> [7,] 130
#> [8,] -816
#> [9,] -94
#> [10,] 266
#> [11,] -688
#> [12,] 272
#> [13,] 922
#> [14,] 280
#> [15,] -40
#> [16,] 418
#> [17,] -454
#> [18,] 80
#> [19,] 828
#> [20,] -92
#> [21,] 886
#> [22,] -174
#> [23,] 560
#> [24,] -1106
#> [25,] 562
#> [26,] 442
#> [27,] -658
#> [28,] -148
#> [29,] -520
#> [30,] -1080
#> [31,] 452
#> [32,] 110
#> [33,] -472
#> [34,] 648
#> [35,] 524
#> [36,] 10
#> [37,] 360
#> [38,] -428
#> [39,] -1438
#> [40,] -930
#> [41,] -588
#> [42,] 360
#> [43,] 110
#> [44,] 828
#> [45,] 336
#> [46,] 436
#> [47,] 698
#> [48,] 558
#> [49,] -144
#> [50,] 538
#> [51,] 284
#> [52,] -280
#> [53,] 486
#> [54,] -296
#> [55,] -436
#> [56,] -160
#> [57,] -246
#> [58,] -14
#> [59,] -18
#> [60,] -548
#> [61,] 206
#> [62,] -150
#> [63,] -876
#> [64,] 62
#> [65,] -188
#> [66,] 576
#> [67,] 926
#> [68,] 258
#> [69,] 156
#> [70,] 62
#> [71,] -706
#> [72,] 542
#> [73,] -328
#> [74,] 182
#> [75,] -600
#> [76,] 380
#> [77,] 246
#> [78,] -422
#> [79,] 324
#> [80,] -218
#> [81,] -258
#> [82,] 290
#> [83,] -558
#> [84,] 1226
#> [85,] 1432
#> [86,] 410
#> [87,] 306
#> [88,] 60
#> [89,] -440
#> [90,] 1328
#> [91,] 248
#> [92,] -122
#> [93,] 120
#> [94,] -318
#> [95,] 176
#> [96,] -284
#> [97,] 208
#> [98,] -150
#> [99,] 866
#> [100,] 64