The rxc table
the_rxc_table(n, alpha = 0.05, nboot = 10000)NULL. This function should be called for its printed output.
set.seed(8047)
# Unordered tables
## Treatment for ear infection (van Balen et al., 2003)
the_rxc_table(table_7.3, nboot = 200)
#>
#> Method Statistic P-value
#> -------------------------------------------------------------------
#> Unordered rxc tables
#> Pearson chi-square 17.562 (df=2) 0.000154
#> Likelihood ratio 16.700 (df=2) 0.000236
#> Fisher-Freeman-Halton asymptotic 16.260 (df=2) 0.000295
#> Fisher-Freeman-Halton exact conditional 0.000271
#> Fisher-Freeman-Halton mid-P 0.000267
#> Pearson exact conditional 0.000155
#> Pearson mid-P 0.000151
#> Likelihood ratio exact conditional 0.000303
#> Likelihood ratio mid-P 0.000299
#> -------------------------------------------------------------------
#> Pearson residuals:
#> [,1] [,2]
#> [1,] -1.5753727 3.045850
#> [2,] 0.8467851 -1.637187
#> [3,] 0.7124830 -1.377526
#>
#> Standardized Pearson residuals:
#> [,1] [,2]
#> [1,] -4.178875 4.178875
#> [2,] 2.213411 -2.213411
#> [3,] 1.949026 -1.949026
#>
#> The Scheffe-type simultaneous intervals
#> pi_1|1 - pi_1|2: estimate = -0.2699 (-0.4482 to -0.0916)
#> pi_1|1 - pi_1|3: estimate = -0.2476 (-0.4252 to -0.0701)
#> pi_1|2 - pi_1|3: estimate = 0.0222 (-0.1181 to 0.1625)
#>
#> The Bonferroni-type simultaneous intervals
#> pi_1|1 - pi_1|2: estimate = -0.2699 (-0.4443 to -0.0955)
#> pi_1|1 - pi_1|3: estimate = -0.2476 (-0.4213 to -0.0740)
#> pi_1|2 - pi_1|3: estimate = 0.0222 (-0.1150 to 0.1594)
#> pi_1|3 - pi_1|3: estimate = 0.0000 (-0.1362 to 0.1362)
#>
#> Method Statistic P-value
#> ------------------------------------------------------------------
#> Singly ordered rxc tables
#> Kruskal-Wallis asymptotic 17.473 (df=2) 0.000161
#> Kruskal-Wallis exact conditional 0.000155
#> Kruskal-Wallis mid-P 0.000151
#>
#>
#> Method Statistic P-value
#> ---------------------------------------------------------------
#> Doubly ordered rxc tables
#> Linear-by-linear -3.477 0.000508
#> Jonckheere-Terpstra -3.437 0.000589
#> Linear-by-linear exact conditional 0.000155
#> Linear-by-linear mid-P 0.000151
#> Jonckheere-Terpstra exact conditional 0.000155
#> Jonckheere-Terpstra mid-P 0.000151
#> ---------------------------------------------------------------
#>
#>
#> Correlation measures
#> -----------------------------------------------------------------------------------------
#> Pearson correlation coefficient -0.247 (95% CI -0.373 to -0.112)
#> Pearson correlation w / BCa bootstrap CI -0.247 (95% CI -0.389 to -0.097), nboot = 200
#>
#> Spearman correlation w / Fieller CI -0.244 (95% CI -0.378 to -0.101)
#> Spearman correlation w / Bonett-Wright CI -0.244 (95% CI -0.373 to -0.107)
#> Spearman correlation w / BCa bootstrap CI -0.244 (95% CI -0.425 to -0.117), nboot = 200
#>
#> The gamma coefficient -0.468
#> The gamma coefficient w / BCa bootstrap CI -0.468 (95% CI -0.686 to -0.221), nboot = 200
#>
#> Kendalls tau-b w / Fieller CI -0.230 (95% CI -0.316 to -0.141)
#> Kendalls tau-b w / BCa bootstrap CI -0.230 (95% CI -0.367 to -0.094), nboot = 200
#> -----------------------------------------------------------------------------------------
## Psychiatric diagnoses vs PA (Mangerud et al., 2004)
the_rxc_table(table_7.4, nboot = 0)
#>
#> Method Statistic P-value
#> -------------------------------------------------------------------
#> Unordered rxc tables
#> Pearson chi-square 11.687 (df=5) 0.039338
#> Likelihood ratio 11.851 (df=5) 0.036885
#> Fisher-Freeman-Halton asymptotic 11.542 (df=5) 0.041633
#> -------------------------------------------------------------------
#> Pearson residuals:
#> [,1] [,2]
#> [1,] 0.90342075 -1.27588328
#> [2,] 0.04289348 -0.06057761
#> [3,] -1.21560402 1.71677356
#> [4,] 1.07887352 -1.52367176
#> [5,] -0.66563137 0.94005804
#> [6,] 0.00532264 -0.00751706
#>
#> Standardized Pearson residuals:
#> [,1] [,2]
#> [1,] 1.697143624 -1.697143624
#> [2,] 0.086555318 -0.086555318
#> [3,] -2.147109879 2.147109879
#> [4,] 1.933370535 -1.933370535
#> [5,] -1.466663369 1.466663369
#> [6,] 0.009671725 -0.009671725
#>
#> The Scheffe-type simultaneous intervals
#> pi_1|1 - pi_1|2: estimate = 0.0780 (-0.1272 to 0.2832)
#> pi_1|1 - pi_1|3: estimate = 0.2924 (-0.0948 to 0.6797)
#> pi_1|1 - pi_1|4: estimate = -0.0638 (-0.3305 to 0.2028)
#> pi_1|1 - pi_1|5: estimate = 0.1184 (-0.0753 to 0.3121)
#> pi_1|1 - pi_1|6: estimate = 0.0803 (-0.1907 to 0.3513)
#> pi_1|2 - pi_1|3: estimate = 0.2144 (-0.1620 to 0.5908)
#> pi_1|2 - pi_1|4: estimate = -0.1418 (-0.3925 to 0.1088)
#> pi_1|2 - pi_1|5: estimate = 0.0404 (-0.1305 to 0.2113)
#> pi_1|2 - pi_1|6: estimate = 0.0023 (-0.2529 to 0.2575)
#> pi_1|3 - pi_1|4: estimate = -0.3563 (-0.7694 to 0.0568)
#> pi_1|3 - pi_1|5: estimate = -0.1740 (-0.5443 to 0.1962)
#> pi_1|3 - pi_1|6: estimate = -0.2121 (-0.6281 to 0.2038)
#> pi_1|4 - pi_1|5: estimate = 0.1822 (-0.0590 to 0.4235)
#> pi_1|4 - pi_1|6: estimate = 0.1441 (-0.1627 to 0.4510)
#> pi_1|5 - pi_1|6: estimate = -0.0381 (-0.2842 to 0.2080)
#>
#> The Bonferroni-type simultaneous intervals
#> pi_1|1 - pi_1|2: estimate = 0.0780 (-0.1030 to 0.2591)
#> pi_1|1 - pi_1|3: estimate = 0.2924 (-0.0492 to 0.6341)
#> pi_1|1 - pi_1|4: estimate = -0.0638 (-0.2991 to 0.1714)
#> pi_1|1 - pi_1|5: estimate = 0.1184 (-0.0525 to 0.2893)
#> pi_1|1 - pi_1|6: estimate = 0.0803 (-0.1588 to 0.3194)
#> pi_1|2 - pi_1|3: estimate = 0.2144 (-0.1176 to 0.5465)
#> pi_1|2 - pi_1|4: estimate = -0.1418 (-0.3629 to 0.0792)
#> pi_1|2 - pi_1|5: estimate = 0.0404 (-0.1104 to 0.1912)
#> pi_1|2 - pi_1|6: estimate = 0.0023 (-0.2229 to 0.2275)
#> pi_1|3 - pi_1|4: estimate = -0.3563 (-0.7207 to 0.0082)
#> pi_1|3 - pi_1|5: estimate = -0.1740 (-0.5006 to 0.1526)
#> pi_1|3 - pi_1|6: estimate = -0.2121 (-0.5790 to 0.1548)
#> pi_1|4 - pi_1|5: estimate = 0.1822 (-0.0306 to 0.3951)
#> pi_1|4 - pi_1|6: estimate = 0.1441 (-0.1265 to 0.4148)
#> pi_1|5 - pi_1|6: estimate = -0.0381 (-0.2552 to 0.1790)
#> pi_1|6 - pi_1|6: estimate = 0.0000 (-0.2740 to 0.2740)
#>
#> Method Statistic P-value
#> ------------------------------------------------------------------
#> Singly ordered rxc tables
#> Kruskal-Wallis asymptotic 11.666 (df=5) 0.039668
#>
#>
#> Method Statistic P-value
#> ---------------------------------------------------------------
#> Doubly ordered rxc tables
#> Linear-by-linear 1.260 0.207815
#> Jonckheere-Terpstra 1.431 0.152534
#> ---------------------------------------------------------------
#>
#>
#> Correlation measures
#> -----------------------------------------------------------------------------------------
#> Pearson correlation coefficient 0.054 (95% CI -0.030 to 0.137)
#>
#> Spearman correlation w / Fieller CI 0.061 (95% CI -0.028 to 0.149)
#> Spearman correlation w / Bonett-Wright CI 0.061 (95% CI -0.023 to 0.144)
#>
#> The gamma coefficient 0.097
#>
#> Kendalls tau-b w / Fieller CI 0.056 (95% CI 0.000 to 0.111)
#> -----------------------------------------------------------------------------------------
# Singly ordered tables
## Psychiatric diag. vs BMI (Mangerud et al., 2004)
the_rxc_table(table_7.5, nboot = 0)
#>
#> Method Statistic P-value
#> -------------------------------------------------------------------
#> Unordered rxc tables
#> Pearson chi-square 25.092 (df=10) 0.005174
#> Likelihood ratio 24.272 (df=10) 0.006910
#> Fisher-Freeman-Halton asymptotic 23.770 (df=10) 0.008234
#> -------------------------------------------------------------------
#> Pearson residuals:
#> [,1] [,2] [,3]
#> [1,] -1.53043754 0.5236911 0.06719368
#> [2,] -1.32840101 1.0010884 -0.76324572
#> [3,] 3.07824372 0.1955264 -2.01247808
#> [4,] 0.92452195 -0.6207156 0.41693475
#> [5,] 0.09530522 -0.4109633 0.56456984
#> [6,] 1.20826157 -1.1035988 0.98441639
#>
#> Standardized Pearson residuals:
#> [,1] [,2] [,3]
#> [1,] -1.734762 0.9357843 0.08575454
#> [2,] -1.622368 1.9273863 -1.04951534
#> [3,] 3.285383 0.3289763 -2.41834590
#> [4,] 1.002982 -1.0615604 0.50927014
#> [5,] 0.127442 -0.8663136 0.84999783
#> [6,] 1.327766 -1.9118241 1.21798982
#>
#>
#> Method Statistic P-value
#> ------------------------------------------------------------------
#> Singly ordered rxc tables
#> Kruskal-Wallis asymptotic 11.965 (df=5) 0.035265
#>
#>
#> Testing the fit of a proportional odds model
#> Pearson goodness of fit: 11.505 (df=5) 0.042234
#> Likelihodd ratio (deviance): 11.289 (df=5) 0.045939
#>
#>
#> Testing the effect in a proportional odds model
#> Likelihood ratio 12.983 (df=5) 0.023540
#> ------------------------------------------------------------------
#>
#>
#> Comparing the rows Statistic P-value
#> --------------------------------------------------------
#> Wald (Z-statistic) row 2 vs row 1 -0.682 0.495121
#> Wald (Z-statistic) row 3 vs row 1 -3.482 0.000499
#> Wald (Z-statistic) row 4 vs row 1 -0.385 0.700454
#> Wald (Z-statistic) row 5 vs row 1 -0.330 0.741356
#> Wald (Z-statistic) row 6 vs row 1 -0.062 0.950912
#> --------------------------------------------------------
#>
#>
#> Comparing the rows Estimate (95% Wald CI) Odds ratio (95% Wald CI)
#> --------------------------------------------------------------------------
#> row 2 vs row 1: -0.189 (-0.732 to 0.354) 0.828 (0.481 to 1.425)
#> row 3 vs row 1: -1.742 (-2.722 to -0.761) 0.175 (0.066 to 0.467)
#> row 4 vs row 1: -0.156 (-0.954 to 0.641) 0.855 (0.385 to 1.898)
#> row 5 vs row 1: -0.086 (-0.599 to 0.427) 0.917 (0.549 to 1.532)
#> row 6 vs row 1: -0.023 (-0.744 to 0.698) 0.978 (0.475 to 2.011)
#> --------------------------------------------------------------------------
#>
#>
#> Method Statistic P-value
#> ---------------------------------------------------------------
#> Doubly ordered rxc tables
#> Linear-by-linear 0.105 0.916449
#> Jonckheere-Terpstra 0.245 0.806459
#> ---------------------------------------------------------------
#>
#>
#> Correlation measures
#> -----------------------------------------------------------------------------------------
#> Pearson correlation coefficient 0.004 (95% CI -0.079 to 0.088)
#>
#> Spearman correlation w / Fieller CI 0.011 (95% CI -0.077 to 0.100)
#> Spearman correlation w / Bonett-Wright CI 0.011 (95% CI -0.072 to 0.095)
#>
#> The gamma coefficient 0.015
#>
#> Kendalls tau-b w / Fieller CI 0.009 (95% CI -0.046 to 0.065)
#> -----------------------------------------------------------------------------------------
## Low birth weight vs psychiatric morbitidy (Lund et al., 2012)
the_rxc_table(table_7.6, nboot = 150)
#>
#> Method Statistic P-value
#> -------------------------------------------------------------------
#> Unordered rxc tables
#> Pearson chi-square 11.656 (df=4) 0.020105
#> Likelihood ratio 11.742 (df=4) 0.019379
#> Fisher-Freeman-Halton asymptotic 11.595 (df=4) 0.020629
#> -------------------------------------------------------------------
#> Pearson residuals:
#> [,1] [,2] [,3]
#> [1,] -0.6784534 -0.5422277 1.7210436
#> [2,] -0.8885338 1.2601632 0.5887594
#> [3,] 1.2510967 -0.6151158 -1.8087474
#>
#> Standardized Pearson residuals:
#> [,1] [,2] [,3]
#> [1,] -1.372700 -0.6798339 2.230360
#> [2,] -1.841286 1.6182279 0.781471
#> [3,] 2.909348 -0.8863952 -2.694080
#>
#>
#> Method Statistic P-value
#> ------------------------------------------------------------------
#> Singly ordered rxc tables
#> Kruskal-Wallis asymptotic 9.162 (df=2) 0.010242
#>
#>
#> Testing the fit of a proportional odds model
#> Pearson goodness of fit: 2.031 (df=2) 0.362245
#> Likelihodd ratio (deviance): 2.163 (df=2) 0.339122
#>
#>
#> Testing the effect in a proportional odds model
#> Likelihood ratio 9.579 (df=2) 0.008317
#> ------------------------------------------------------------------
#>
#>
#> Comparing the rows Statistic P-value
#> --------------------------------------------------------
#> Wald (Z-statistic) row 2 vs row 1 -0.185 0.853517
#> Wald (Z-statistic) row 3 vs row 1 -2.614 0.008960
#> --------------------------------------------------------
#>
#>
#> Comparing the rows Estimate (95% Wald CI) Odds ratio (95% Wald CI)
#> --------------------------------------------------------------------------
#> row 2 vs row 1: -0.080 (-0.934 to 0.773) 0.923 (0.393 to 2.166)
#> row 3 vs row 1: -1.170 (-2.047 to -0.293) 0.310 (0.129 to 0.746)
#> --------------------------------------------------------------------------
#>
#>
#> Method Statistic P-value
#> ---------------------------------------------------------------
#> Doubly ordered rxc tables
#> Linear-by-linear -2.867 0.004147
#> Jonckheere-Terpstra -2.865 0.004176
#> ---------------------------------------------------------------
#>
#>
#> Correlation measures
#> -----------------------------------------------------------------------------------------
#> Pearson correlation coefficient -0.239 (95% CI -0.387 to -0.079)
#> Pearson correlation w / BCa bootstrap CI -0.239 (95% CI -0.446 to -0.100), nboot = 150
#>
#> Spearman correlation w / Fieller CI -0.236 (95% CI -0.392 to -0.066)
#> Spearman correlation w / Bonett-Wright CI -0.236 (95% CI -0.386 to -0.073)
#> Spearman correlation w / BCa bootstrap CI -0.236 (95% CI -0.417 to -0.085), nboot = 150
#>
#> The gamma coefficient -0.364
#> The gamma coefficient w / BCa bootstrap CI -0.364 (95% CI -0.556 to -0.106), nboot = 150
#>
#> Kendalls tau-b w / Fieller CI -0.217 (95% CI -0.319 to -0.111)
#> Kendalls tau-b w / BCa bootstrap CI -0.217 (95% CI -0.397 to -0.086), nboot = 150
#> -----------------------------------------------------------------------------------------
# Doubly ordered tables
## Colorectal cancer (Jullumstroe et al., 2009)
the_rxc_table(table_7.7, nboot = 0)
#>
#> Method Statistic P-value
#> -------------------------------------------------------------------
#> Unordered rxc tables
#> Pearson chi-square 13.614 (df=9) 0.136734
#> Likelihood ratio 14.471 (df=9) 0.106516
#> Fisher-Freeman-Halton asymptotic 13.830 (df=9) 0.128509
#> -------------------------------------------------------------------
#> Pearson residuals:
#> [,1] [,2] [,3] [,4]
#> [1,] -0.65638953 -0.03163655 -0.6950590 1.4076349
#> [2,] -1.09582755 -2.05025498 0.5745765 0.7499116
#> [3,] 0.01113385 0.54613868 0.2603159 -0.7048281
#> [4,] 1.28267370 1.18967248 -0.4831628 -0.5135737
#>
#> Standardized Pearson residuals:
#> [,1] [,2] [,3] [,4]
#> [1,] -0.70111313 -0.03409375 -1.1548521 1.6902006
#> [2,] -1.28680170 -2.42905006 1.0495316 0.9899226
#> [3,] 0.01496521 0.74062699 0.5442724 -1.0649824
#> [4,] 1.56847093 1.46773239 -0.9190350 -0.7059677
#>
#>
#> Method Statistic P-value
#> ------------------------------------------------------------------
#> Singly ordered rxc tables
#> Kruskal-Wallis asymptotic 8.334 (df=3) 0.039582
#>
#>
#> Testing the fit of a proportional odds model
#> Pearson goodness of fit: 5.820 (df=6) 0.443643
#> Likelihodd ratio (deviance): 6.132 (df=6) 0.408616
#>
#>
#> Testing the effect in a proportional odds model
#> Likelihood ratio 8.340 (df=3) 0.039486
#> ------------------------------------------------------------------
#>
#>
#> Comparing the rows Statistic P-value
#> --------------------------------------------------------
#> Wald (Z-statistic) row 2 vs row 1 -0.470 0.638406
#> Wald (Z-statistic) row 3 vs row 1 -1.721 0.085308
#> Wald (Z-statistic) row 4 vs row 1 -1.996 0.045950
#> --------------------------------------------------------
#>
#>
#> Comparing the rows Estimate (95% Wald CI) Odds ratio (95% Wald CI)
#> --------------------------------------------------------------------------
#> row 2 vs row 1: -0.144 (-0.745 to 0.457) 0.866 (0.475 to 1.579)
#> row 3 vs row 1: -0.504 (-1.077 to 0.070) 0.604 (0.341 to 1.073)
#> row 4 vs row 1: -0.604 (-1.198 to -0.011) 0.546 (0.302 to 0.989)
#> --------------------------------------------------------------------------
#>
#>
#> Method Statistic P-value
#> ---------------------------------------------------------------
#> Doubly ordered rxc tables
#> Linear-by-linear -2.854 0.004321
#> Jonckheere-Terpstra -2.710 0.006720
#> ---------------------------------------------------------------
#>
#>
#> Correlation measures
#> -----------------------------------------------------------------------------------------
#> Pearson correlation coefficient -0.102 (95% CI -0.171 to -0.032)
#>
#> Spearman correlation w / Fieller CI -0.096 (95% CI -0.169 to -0.022)
#> Spearman correlation w / Bonett-Wright CI -0.096 (95% CI -0.165 to -0.026)
#>
#> The gamma coefficient -0.139
#>
#> Kendalls tau-b w / Fieller CI -0.086 (95% CI -0.132 to -0.040)
#> -----------------------------------------------------------------------------------------
## Breast Tumor (Bofin et al., 2004)
the_rxc_table(table_7.8, nboot = 200)
#>
#> Method Statistic P-value
#> -------------------------------------------------------------------
#> Unordered rxc tables
#> Pearson chi-square 64.338 (df=8) 0.000000
#> Likelihood ratio 76.221 (df=8) 0.000000
#> Fisher-Freeman-Halton asymptotic 68.473 (df=8) 0.000000
#> -------------------------------------------------------------------
#> Pearson residuals:
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 1.9667391 3.107810 0.54540721 -1.752936 -3.1718074
#> [2,] -0.9368691 -1.617342 -0.02110825 1.627276 0.8295151
#> [3,] -2.0224306 -3.063243 -0.79197165 1.035477 3.9213814
#>
#> Standardized Pearson residuals:
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 3.084420 5.414349 0.82730534 -2.917449 -5.496684
#> [2,] -1.139943 -2.186105 -0.02484131 2.101240 1.115310
#> [3,] -2.485053 -4.181273 -0.94121696 1.350245 5.324370
#>
#>
#> Method Statistic P-value
#> ------------------------------------------------------------------
#> Singly ordered rxc tables
#> Kruskal-Wallis asymptotic 57.044 (df=2) 0.000000
#>
#>
#> Testing the fit of a proportional odds model
#> Pearson goodness of fit: 6.187 (df=6) 0.402576
#> Likelihodd ratio (deviance): 7.610 (df=6) 0.268096
#>
#>
#> Testing the effect in a proportional odds model
#> Likelihood ratio 68.611 (df=2) 0.000000
#> ------------------------------------------------------------------
#>
#>
#> Comparing the rows Statistic P-value
#> --------------------------------------------------------
#> Wald (Z-statistic) row 2 vs row 1 4.921 0.000001
#> Wald (Z-statistic) row 3 vs row 1 7.082 0.000000
#> --------------------------------------------------------
#>
#>
#> Comparing the rows Estimate (95% Wald CI) Odds ratio (95% Wald CI)
#> --------------------------------------------------------------------------
#> row 2 vs row 1: 2.215 ( 1.333 to 3.098) 9.165 (3.793 to 22.148)
#> row 3 vs row 1: 3.543 ( 2.562 to 4.523) 34.563 (12.966 to 92.137)
#> --------------------------------------------------------------------------
#>
#>
#> Method Statistic P-value
#> ---------------------------------------------------------------
#> Doubly ordered rxc tables
#> Linear-by-linear 6.560 0.000000
#> Jonckheere-Terpstra 7.658 0.000000
#> ---------------------------------------------------------------
#>
#>
#> Correlation measures
#> -----------------------------------------------------------------------------------------
#> Pearson correlation coefficient 0.571 (95% CI 0.444 to 0.676)
#> Pearson correlation w / BCa bootstrap CI 0.571 (95% CI 0.471 to 0.680), nboot = 200
#>
#> Spearman correlation w / Fieller CI 0.657 (95% CI 0.541 to 0.749)
#> Spearman correlation w / Bonett-Wright CI 0.657 (95% CI 0.536 to 0.752)
#> Spearman correlation w / BCa bootstrap CI 0.657 (95% CI 0.550 to 0.738), nboot = 200
#>
#> The gamma coefficient 0.776
#> The gamma coefficient w / BCa bootstrap CI 0.776 (95% CI 0.658 to 0.876), nboot = 200
#>
#> Kendalls tau-b w / Fieller CI 0.575 (95% CI 0.493 to 0.646)
#> Kendalls tau-b w / BCa bootstrap CI 0.575 (95% CI 0.397 to 0.623), nboot = 200
#> -----------------------------------------------------------------------------------------
## Self-rated health (Breidablik et al., 2008)
the_rxc_table(table_7.9, nboot = 0)
#>
#> Method Statistic P-value
#> -------------------------------------------------------------------
#> Unordered rxc tables
#> Pearson chi-square 361.420 (df=9) 0.000000
#> Likelihood ratio 296.140 (df=9) 0.000000
#> Fisher-Freeman-Halton asymptotic 299.161 (df=9) 0.000000
#> -------------------------------------------------------------------
#> Pearson residuals:
#> [,1] [,2] [,3] [,4]
#> [1,] 7.0312583 1.535737 -1.420054 0.006404978
#> [2,] 0.7647562 8.561983 -0.611197 -4.788498683
#> [3,] -0.4391961 0.299126 4.097410 -6.244697301
#> [4,] -0.6064165 -4.558824 -4.932546 10.433734978
#>
#> Standardized Pearson residuals:
#> [,1] [,2] [,3] [,4]
#> [1,] 7.0719229 1.6366932 -2.267789 0.007522952
#> [2,] 0.7971267 9.4563765 -1.011530 -5.828676663
#> [3,] -0.6831955 0.4930452 10.120206 -11.343945914
#> [4,] -0.7479617 -5.9580910 -9.659905 15.028454866
#>
#>
#> Method Statistic P-value
#> ------------------------------------------------------------------
#> Singly ordered rxc tables
#> Kruskal-Wallis asymptotic 250.843 (df=3) 0.000000
#>
#>
#> Testing the fit of a proportional odds model
#> Pearson goodness of fit: 36.508 (df=6) 0.000002
#> Likelihodd ratio (deviance): 26.422 (df=6) 0.000186
#>
#>
#> Testing the effect in a proportional odds model
#> Likelihood ratio 269.718 (df=3) 0.000000
#> ------------------------------------------------------------------
#>
#>
#> Comparing the rows Statistic P-value
#> --------------------------------------------------------
#> Wald (Z-statistic) row 2 vs row 1 0.209 0.834621
#> Wald (Z-statistic) row 3 vs row 1 1.797 0.072354
#> Wald (Z-statistic) row 4 vs row 1 3.449 0.000563
#> --------------------------------------------------------
#>
#>
#> Comparing the rows Estimate (95% Wald CI) Odds ratio (95% Wald CI)
#> --------------------------------------------------------------------------
#> row 2 vs row 1: 0.156 (-1.305 to 1.616) 1.168 (0.271 to 5.032)
#> row 3 vs row 1: 1.316 (-0.119 to 2.752) 3.729 (0.887 to 15.668)
#> row 4 vs row 1: 2.536 ( 1.095 to 3.977) 12.625 (2.988 to 53.339)
#> --------------------------------------------------------------------------
#>
#>
#> Method Statistic P-value
#> ---------------------------------------------------------------
#> Doubly ordered rxc tables
#> Linear-by-linear 15.421 0.000000
#> Jonckheere-Terpstra 15.985 0.000000
#> ---------------------------------------------------------------
#>
#>
#> Correlation measures
#> -----------------------------------------------------------------------------------------
#> Pearson correlation coefficient 0.318 (95% CI 0.281 to 0.354)
#>
#> Spearman correlation w / Fieller CI 0.326 (95% CI 0.287 to 0.364)
#> Spearman correlation w / Bonett-Wright CI 0.326 (95% CI 0.289 to 0.363)
#>
#> The gamma coefficient 0.526
#>
#> Kendalls tau-b w / Fieller CI 0.308 (95% CI 0.283 to 0.332)
#> -----------------------------------------------------------------------------------------