Lecture 31
We discussed the method of Benjamini and Hockberg for
controling the False Discover Rate using a simple step-down
procedure for the p-values of the tests involved in the comparison.
We also discussed the problem of power versus Type I errors.
The data are a fabricated microarray data set. The code for getting a column
of p-values is:
let c10 = (c2 + c3 + c4 + c5)/4
let c11 = (c6 + c7 + c8 + c9)/4
let c12 = sqrt(( (c2 - c10)**2 + (c3 - c10)**2 + (c4 - c10)**2 + (c5 - c10)**2 + (c6 - c11)**2 + (c7 - c11)**2 + (c8 - c11)**2 + (c9 - c11)**2 )/6)
let c13 = (c11 - c10)/(c12*sqrt(1/2))
let c13 = abs(c13)
CDF 't-statistic' 'p-value';
T 6.
let c14 = 1 - c14
The data are:
gene_number log_control_sample_1 log_control_sample__2 log_control_sample_3 log_control_sample_4 log_exp_sample_1 log_exp_sample_2 log_exp_sample_3 log_exp_sample_4
1 -4.04904 3.0308 1.08639 2.74121 -3.4393 -0.9115 -1.4331 -0.8713
2 0.40468 -1.3729 -0.32943 3.43345 -6.0143 -5.9454 -1.5425 -2.7858
3 3.62041 -3.2908 0.12409 0.34486 0.3675 2.6137 6.2017 -0.5384
4 -2.25582 0.5643 -2.43222 1.57450 3.7381 -1.2266 3.5018 1.1284
5 0.10346 -0.6506 4.45211 1.52784 -1.4561 2.9865 2.9484 0.8096
6 -2.45871 2.2088 3.01823 -2.80413 -7.5312 4.6511 -0.0481 -1.7405
7 -4.58612 3.4758 2.58870 -6.64682 -0.0550 -0.0195 -3.7101 -2.5874
8 1.34145 -0.8553 -1.24021 3.18623 -4.8549 3.9515 1.1938 1.3650
9 4.33324 0.8229 -2.19756 -2.67974 -0.2010 -1.5372 -0.4168 6.1412
10 2.01076 -3.7601 0.28522 -4.39140 -6.4550 -7.6508 -4.6853 -4.0344
11 0.53464 1.1887 -4.20233 3.59452 -2.6325 0.3546 0.9776 0.3552
12 0.05176 -1.7089 -0.00116 0.31837 6.1943 -0.9567 -2.7953 -3.3081
13 -2.75814 -1.6919 0.50680 2.71157 4.2860 -0.3019 -1.5837 -0.5308
14 -3.48628 1.5966 -1.19541 2.49992 -6.7113 -5.5809 -5.2116 -0.8058
15 -0.97308 2.9130 -1.82809 -3.95591 -1.7505 0.7165 1.5122 -2.0178
16 5.22481 -0.3159 1.42989 -0.15487 4.9589 -11.4341 0.6099 0.0865
17 -0.40815 1.2058 0.59316 1.16997 2.8466 5.4084 1.5904 -2.3411
18 0.62080 -1.5380 -0.97995 1.81420 1.2929 -3.0415 -0.0240 -1.2875
19 -2.53301 1.2023 -0.49349 2.11037 2.3774 2.6436 0.3237 -4.0414
20 -5.56998 7.0270 -0.51635 4.31800 2.2345 -4.0973 2.5019 -3.6022
21 0.98665 -4.2277 -2.52850 4.57872 -1.3016 -3.7859 0.5861 -2.5887
22 4.81402 3.8558 0.05826 -0.15172 5.3062 5.0008 3.5091 5.3430
23 -0.11555 3.1720 6.29521 0.25466 3.2517 -2.8571 1.2826 -0.2166
24 3.48528 -0.5276 1.73219 4.77626 -2.6259 0.4812 1.0308 2.8795
25 3.25685 -3.5335 -2.44739 -0.21763 0.2098 0.2381 -0.7950 0.9140
26 -4.41156 -1.8755 -7.31815 -1.07975 -0.8422 -1.7827 2.7265 -5.0873
27 0.89766 -4.1166 1.71250 -1.03584 3.9281 0.5567 7.6290 8.0901
28 3.48195 -6.0563 -4.20032 -0.87687 -1.3021 -2.7594 -0.6183 3.6198
29 -5.37820 -1.5843 0.49746 2.27620 0.0196 4.2818 4.9821 4.0771
30 2.27514 2.2312 2.09261 0.63710 -0.4163 1.4633 -0.1155 3.1532
31 3.52364 4.2265 3.53395 3.03003 -0.9200 2.0064 0.5328 -0.5951
32 -3.15996 -2.8760 0.28729 4.91738 10.0663 4.9776 11.6573 2.8587
33 -0.49764 0.5154 -0.77778 0.08692 6.7969 2.4311 0.3280 1.5883
34 -7.92856 -0.1689 4.86542 2.10613 3.2002 -4.4369 -2.4083 -2.7648
35 1.16670 -5.2750 -1.99352 5.39064 -0.1095 0.2724 0.5925 -0.2971
36 1.71277 -3.6733 -4.62851 -3.75439 0.0359 1.0159 -7.1011 -0.6938
37 0.55225 3.9206 -3.61590 -6.52314 -1.4625 1.1055 -0.6335 4.1298
38 -1.62614 -0.0235 0.55817 1.49047 -0.4102 -5.2357 -2.1469 0.1391
39 2.32844 2.1162 -1.41329 -0.65276 -3.7473 5.0467 -0.2815 0.3916
40 3.42438 -1.5634 0.56920 1.46338 6.3295 4.8416 8.0398 10.9628
41 -0.10148 -0.7228 1.13399 4.26813 4.8342 4.5437 -4.0500 -4.9612
42 2.94352 0.8733 4.43493 -2.28263 1.4553 2.2616 -0.6151 -1.0222
43 -1.76824 2.1673 2.09802 -4.28054 2.2830 -1.5416 2.5856 0.6577
44 0.01084 4.4996 -1.19063 -2.81657 5.6018 -0.8538 -3.2416 -0.5733
45 4.57201 -3.9229 -3.13343 3.80066 1.2297 -4.6147 1.3465 -1.0958
46 6.11236 -3.4314 -3.85731 2.14385 0.9052 -3.5050 -1.2515 0.1557
47 -1.75507 -1.2482 -1.68896 -1.25402 0.3292 -2.2836 2.5486 3.5180
48 2.26497 -3.1065 0.47105 5.30359 -3.0601 -0.4203 0.0170 -1.1754
49 -3.92347 0.9401 -3.25458 5.22359 -1.0919 0.7225 0.7799 -0.5551
50 -3.99379 0.1806 -0.50796 -0.68958 -4.9349 -4.7648 -2.9009 4.4506
51 3.11766 3.3867 2.67698 -4.11043 1.1503 -2.4485 -4.9249 -3.4734
52 0.17264 4.3707 0.70439 2.92953 7.5536 3.5819 3.2090 12.4881
53 -0.83071 -2.5163 -2.64604 0.21478 -5.0617 0.3156 -3.3540 -6.8548
54 2.04152 2.1107 -1.86841 -0.67169 -4.9278 1.7048 2.1573 0.2783
55 -4.47357 1.2106 -7.63686 0.76218 0.0644 2.9199 -1.5140 2.0362
56 3.59439 -1.9062 1.81369 0.91059 1.8916 2.5681 1.8588 -4.1984
57 4.35074 -0.8864 -1.07223 0.10052 -0.0493 -1.3423 1.9132 -0.5888
58 2.41815 -1.2514 -2.86971 2.33382 7.2396 5.0748 5.5895 4.7780
59 1.07290 0.8020 -1.92715 3.57435 -0.3848 1.6566 1.7084 -0.0273
60 -1.57691 3.1612 -2.19931 -0.24512 -3.5468 -2.7525 -3.3208 -3.9453
61 0.31164 -3.3187 -2.83100 -2.08812 1.9905 2.0661 -0.2722 3.5117
62 -1.71758 -1.6021 3.46194 -0.26704 -0.0979 -4.3191 2.0251 5.3012
63 -5.71736 1.5581 -0.24492 -2.68918 -6.0947 -3.9496 -4.1203 -8.9401
64 2.37875 0.9209 -2.01033 -1.72665 2.4923 -2.1953 -7.9822 2.2815
65 -0.39230 -0.7965 -4.54384 3.46914 -7.2748 -3.4187 -6.5887 -6.6550
66 -0.28163 -2.2418 0.16576 -1.50826 -1.2708 -8.5501 -9.4964 -6.5343
67 3.08233 1.1683 -2.48196 0.00598 2.9940 3.0791 2.7482 -0.8339
68 2.59008 5.1222 -2.09303 3.18257 0.6733 1.0173 4.2281 -0.0512
69 0.83328 2.3940 6.43744 -6.75916 1.6421 -1.6269 -1.1920 1.6474
70 -0.88400 -1.5852 -2.13544 -0.97562 -6.2347 -1.6708 -6.7821 4.5811
71 -0.18155 0.9738 -3.35976 -0.76427 4.3262 -3.2296 2.6657 -0.3797
72 2.29213 0.0168 1.41595 -1.28652 -1.2272 5.6185 1.3751 -1.0800
73 -1.74143 7.6037 -0.86236 4.89908 -5.4021 2.6848 0.5140 0.0969
74 6.15403 0.1209 2.35216 1.29850 -0.8271 -3.9821 -3.4835 0.8277
75 3.12379 -0.8465 -1.92106 0.18640 7.5688 1.3192 1.7161 5.8164
76 -3.87816 -0.7646 2.19259 0.43450 -6.5864 -3.5575 -2.3776 -4.0648
77 -8.90415 0.7768 -3.39962 -3.31235 -7.2134 -3.4795 -2.8267 -12.1266
78 2.02442 3.2913 -2.64269 -1.26881 2.9005 1.7074 0.0156 -0.1644
79 -1.77287 0.2436 -0.43919 1.21838 2.0230 -5.7474 -3.9812 -4.0582
80 -1.63699 0.6630 -1.40551 -4.05299 1.3455 -3.3995 4.4555 5.1800
81 3.54674 5.7774 -1.45285 -3.37434 -3.2170 0.9042 -0.9426 2.4058
82 -2.23610 -3.3467 3.10545 0.94080 2.8336 2.2957 -5.4612 -1.1425
83 -0.36763 2.3096 6.01308 0.94594 2.2364 -4.1247 -2.4824 -2.7982
84 1.63531 -4.9418 -1.40948 2.60087 -4.1984 -2.5956 -5.6229 -9.7167
85 -4.59168 4.1369 2.55028 7.31253 -0.6531 3.1314 -0.0704 0.2434
86 -5.22158 3.4061 2.25058 -1.33371 1.1613 1.8061 1.2023 0.4511
87 -0.05939 0.4466 3.96505 -0.86364 -3.7753 -1.9809 -0.2306 -1.9594
88 3.97380 1.4060 -7.90471 3.25143 0.2470 -2.1633 -2.3976 0.8042
89 -0.70047 0.4946 -2.34662 0.13086 -3.0245 -1.0798 -1.8627 -2.9839
90 -4.61654 -4.3214 2.88711 -0.55543 -1.7370 0.5694 -0.3372 -0.7217
91 -7.36058 -9.2343 2.90244 -1.29067 2.0359 -0.3240 -7.2266 1.7704
92 -0.19510 0.9875 3.69895 2.64796 -0.0083 -1.5827 1.2187 2.4610
93 7.41453 4.9571 -4.03295 -3.63058 -5.7645 -3.3785 -11.0139 1.1923
94 3.14031 -3.4405 2.92407 -5.12105 -1.7364 -2.5825 -3.6041 -0.2752
95 1.30883 -0.3358 -4.23575 -1.64657 1.7488 -1.8595 4.3366 -0.0358
96 -6.94042 5.3932 -1.89150 -1.17206 -7.7195 -0.1265 0.3884 -3.6204
97 3.09888 -3.6092 -0.58532 4.13761 -2.4928 0.0840 3.7807 0.8154
98 -0.36119 1.9745 -2.67092 4.07435 7.0461 7.8427 6.4301 3.4323
99 0.90718 -3.2693 0.24758 1.15487 1.7513 -1.4325 -6.2855 -2.6941
100 -0.82625 2.3810 -0.62931 2.24581 0.1990 1.0162 0.6190 -3.8730
101 -0.00063 0.8743 3.22897 -4.85731 4.7959 2.3044 0.2039 -4.4237
102 0.65658 -1.2040 -6.28483 1.08049 6.8633 5.3609 8.0714 3.6283
103 -5.55965 0.7939 0.27405 -2.00843 -1.8025 1.9267 0.8410 3.7505
104 1.42352 2.1747 0.87712 3.23243 1.0142 8.2280 6.9906 3.7308
105 4.24913 4.1235 -4.46737 -2.91070 0.6744 -1.9650 2.2420 -4.3554
106 3.25671 -2.8730 1.54653 1.53801 -2.8463 1.6097 3.5371 -0.0005
107 -6.02415 -2.1639 -1.78888 0.26263 4.8657 -0.2897 -2.4728 -3.0262
108 2.52130 2.2341 -3.73576 -3.18836 2.3966 -1.6319 4.2267 5.5507
109 -3.78865 6.9254 1.73600 -2.99985 2.0488 4.4721 -2.0150 -3.8319
110 1.88618 -0.4548 -0.03703 -0.86073 -2.2002 -1.2735 0.5887 -5.8589
111 -0.21059 5.7876 5.12504 1.05846 6.3683 -6.9024 -3.6782 4.7508
112 0.12939 -2.3078 -1.78179 0.49641 4.9072 -6.4098 -1.4616 1.4913
113 -2.17147 2.7836 5.17938 -1.78786 -2.1989 -0.6349 1.3365 1.1447
114 1.56761 2.1129 -1.53952 1.09569 0.9943 0.4818 4.4502 -1.9800
115 -4.50296 1.0239 1.73107 -1.71656 5.5881 3.9966 0.3402 4.0445
116 -1.48452 -3.7914 2.06815 -0.74207 -2.2742 -0.6451 -1.6937 -4.8197
117 -5.76082 2.8144 -2.09496 -4.12668 -1.3945 0.1147 0.3896 0.1917
118 1.34482 3.0335 5.46905 2.48493 -1.9755 -0.3722 -0.4906 -2.6760
119 -3.53996 5.2111 0.80292 -0.49878 3.6955 0.6769 4.3859 1.4796
120 1.77877 -3.6602 -1.76141 0.84905 1.9975 4.9908 -2.4586 -4.6015
121 -0.41246 -0.4803 1.88704 0.51354 0.1937 -7.4654 5.7458 3.1449
122 -0.03505 -0.8955 -3.63555 0.41323 0.7047 -7.0490 -8.6109 -3.9129
123 -1.19601 -4.6321 0.46706 -0.15045 0.8793 -5.5640 -1.3373 1.8314
124 -0.09119 2.6829 -1.12571 -5.88699 3.2392 -1.3755 0.6688 -1.9013
125 5.61039 -2.5857 1.65485 -0.51690 -2.7811 2.0415 -0.3794 3.2332
126 -1.21428 2.5795 -1.63141 0.68130 2.7841 -4.6743 -6.8231 0.1384
127 -1.46903 4.4050 1.11965 4.14755 0.6041 1.8155 -3.1391 -2.8167
128 -6.33946 -3.9489 -2.00524 -0.61439 -3.2622 -1.5643 -0.9322 2.7351
129 0.15858 -5.6573 2.36888 -2.17596 4.0339 2.9818 -4.0663 1.5382
130 1.28382 1.5604 5.36142 -3.21162 -1.9180 -0.9499 -0.8889 2.9062
131 3.53493 2.8725 1.01123 0.85959 -3.7860 -1.9132 3.2169 -5.4617
132 0.47536 -3.0686 -0.84674 1.26413 1.2922 -0.7107 -2.0974 2.5919
133 8.35795 -1.1408 -0.47400 -0.53568 0.9892 -3.2697 -4.3582 -0.2148
134 0.32257 1.8492 9.04779 -0.72328 4.3722 0.2637 2.1904 0.5534
135 2.20800 -0.5685 -2.15915 1.61274 -1.6615 1.5957 1.6933 -0.8269
136 4.76522 3.4866 -0.03322 1.17398 -2.6305 -2.0199 4.5703 0.9936
137 -0.49139 -3.9962 0.83025 2.75279 3.2257 -2.3338 -3.9438 -2.9085
138 -0.39713 0.2481 -0.92736 -1.17436 -3.3692 -5.5156 -9.3683 -9.1251
139 5.14043 -2.0813 -3.04572 -2.71111 -0.0154 -0.5951 2.0127 -0.4882
140 0.32841 -4.6552 -2.49880 2.50234 1.2692 0.3293 -0.2189 0.3386
141 0.19551 -4.3252 2.56260 4.98727 2.3641 1.3886 3.5751 -4.2815
142 -1.77984 -7.1031 -0.06094 2.64440 1.4886 0.8337 -2.0265 -1.7001
143 6.40682 -2.7621 0.30210 2.48410 6.7907 4.1220 2.1564 5.3401
144 -0.64155 3.1899 -0.17672 -2.14048 1.2914 -4.1014 6.0483 -2.5302
145 -1.51433 1.8308 1.53747 0.72385 1.6452 0.4191 1.3571 2.8982
146 2.77479 -2.9545 -0.17790 1.93392 -0.5746 4.5640 0.2637 1.7566
147 -1.29913 -4.8869 6.39161 -3.22162 -1.0846 -2.0279 0.6422 0.9930
148 -3.71180 1.4199 -2.15267 0.81597 -3.0989 2.9047 2.6354 -0.3106
149 0.48670 0.8062 -1.70068 -2.81365 -0.5980 -0.7878 0.1098 2.2591
150 -1.45066 4.6846 -0.26509 0.59609 1.7210 0.4901 -4.5127 0.9193
151 1.65215 -4.3507 1.91076 -0.82065 -6.0627 1.3268 0.4877 0.1987
152 0.71825 2.3525 -4.33186 2.13277 1.2273 0.0412 -2.1559 0.8515
153 -3.20464 -1.1054 1.96315 -1.10677 11.1281 2.6991 9.8877 -2.1969
154 -0.15017 3.1275 1.00780 -3.03597 -2.7099 -3.6687 3.6661 4.8372
155 -5.07491 0.9402 0.20085 -6.17094 1.1079 -1.6962 -5.8551 -0.0392
156 0.60783 -3.2527 -1.50668 0.47122 0.8292 3.4583 0.0735 0.4199
157 -1.04149 -0.2426 -2.48234 -0.06819 0.4763 -1.9418 8.1460 -0.5231
158 0.15981 0.9182 -2.86135 -6.10082 1.8407 0.7138 -0.7777 3.8902
159 -1.24648 4.5095 1.16477 0.58172 -2.7475 3.3543 3.1609 1.2082
160 -2.06482 0.0727 1.00772 -3.81375 0.5059 0.7897 4.1629 2.4363
161 -3.79964 0.3996 0.43764 0.36770 -5.9733 -2.3137 -0.9395 -4.1601
162 3.19350 -0.1666 1.81474 2.03389 0.3008 -4.8246 -0.9443 -1.3740
163 -1.13435 2.0293 0.93700 -1.40033 2.0552 1.4587 0.6849 1.7032
164 3.20320 0.7288 1.01755 1.44605 -1.5736 1.3316 -1.1073 0.8309
165 6.62352 -0.6852 4.37085 1.10728 -3.1504 -6.2573 3.6374 -0.2251
166 -4.56029 -0.9321 -1.50611 2.48443 1.6821 0.0398 -1.9710 0.1423
167 -4.96745 -0.0540 1.15001 4.18691 -0.7568 -1.0543 -2.3511 0.4309
168 -0.14956 -1.5937 -4.56918 -2.62287 2.7007 5.0852 -1.3479 0.3857
169 -6.32652 2.4465 5.78626 1.02486 0.5149 -1.2890 -2.0013 0.4350
170 2.82423 0.0898 0.23520 -3.82794 -2.9763 1.8202 1.2273 -1.2253
171 -0.42438 3.7560 -0.12147 -1.72169 -2.7328 -0.4549 1.0049 2.8553
172 9.01397 2.6647 -0.24356 3.82000 0.0532 -1.9822 -3.5314 -0.6646
173 -0.25200 3.2325 4.07482 2.32643 -1.0215 -0.4742 -0.9597 1.2307
174 -1.07397 0.5600 -4.23150 1.64071 1.2450 -1.1972 1.9890 0.7520
175 -0.96768 -1.5975 1.06231 -1.78384 -2.8450 -2.3928 -3.2742 -5.6751
176 5.28274 -4.4698 -5.65150 -7.31644 1.6474 0.8061 -0.1888 4.3102
177 -3.16161 -1.4598 -0.04467 4.33599 2.1645 3.5172 -2.8338 4.9434
178 -6.96984 -4.0429 3.36599 0.17594 1.7290 1.3985 -7.4119 -3.9214
179 -3.20451 -1.8902 -1.32195 3.12276 -0.0888 -2.3688 -6.8714 -3.2909
180 0.90685 -3.6587 1.38665 -0.92837 -3.9625 4.3939 -4.8079 0.5967
181 -0.93810 -0.1579 3.16945 -0.29790 0.0538 2.8313 -6.2979 -5.4800
182 2.92650 4.1659 -8.13006 2.67091 3.3768 10.1700 -0.8726 -1.7233
183 -0.05107 0.5579 0.26281 0.67068 4.2581 -0.2518 2.6250 0.9940
184 5.12208 0.4588 2.66687 -5.98346 0.5175 4.8904 -2.5880 0.4565
185 0.07159 3.1478 0.20109 -3.00196 2.8215 0.0503 2.1860 1.1311
186 -0.45004 0.6040 1.61787 0.84118 -10.3886 -7.6414 -7.9004 -6.9968
187 -0.92841 2.3758 -0.54409 0.12885 -2.6402 6.9516 -6.1142 0.1923
188 -5.18153 7.4747 1.32658 1.68604 5.1282 -4.7770 -1.5649 -0.6469
189 1.58083 1.3587 2.49857 -2.36429 1.0080 3.1207 2.1831 0.8143
190 -1.21971 2.5142 -2.30005 -3.15743 -4.8446 -1.7210 -7.2225 -7.2345
191 1.43725 3.0947 -1.25083 7.01360 1.5271 2.4031 0.4125 -5.0414
192 0.00535 0.0413 2.79022 -4.47206 -0.4704 8.0502 4.8806 -2.9873
193 7.26482 -1.7159 -0.65456 3.81882 -10.9751 -2.2933 -6.6739 -4.0255
194 -1.22725 0.2476 -2.39373 2.44496 -0.3815 2.0133 4.5466 -0.9590
195 -3.89860 5.2293 3.41424 0.78387 0.0580 0.7098 -3.2092 -2.3159
196 -0.89850 -2.1502 1.60582 3.04878 -7.6854 0.8957 1.9904 3.1041
197 2.18582 3.1443 -1.50286 -4.13917 0.1006 1.1690 -0.1447 -3.2114
198 3.37246 -0.3454 0.84120 -2.11661 1.7264 -3.1066 0.6435 1.7719
199 2.68752 2.8829 -0.14448 -2.63927 -2.3903 3.5066 -6.2393 1.1180
200 -0.19781 -2.2783 3.46352 0.91332 -1.6058 2.4415 -2.3046 0.6163
201 0.38101 3.1085 -2.16147 0.91700 -4.1864 -3.2909 -4.3109 -3.2194
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