Assignment 4
You are given two data sets (.xlsx files), stored the position of cancer cells during migration experiment in two different matrices, Collagen Matrix with a high concentration of collagen and Collagen Matrix with a low concentration of collagen. The structure of data in each file is as follows:
• The first three columns store the cell coordinate point (X,Y,Z), X coordinate stored in first, Y in the second and Z the third column
• Column four contain the information about the time step.
• Column five is the ID of cells. Each cell has a unique ID.
Using the provided data sets, answer the following questions:
a) How many cancer cells were analyzed in each matrix? Write a program to answer this question. b) How many cells have a full track of migration? Write a program to answer this question. c) Find the speed for each individual cell in each matrix using the following formula:
Speed= (Net Cell Displacement)/total time
** You may calculate the distance between two points in the space using:
���������������� = √(���� − ����)�� + (���� − ����)�� + (���� − ����)��
where (��1, ��1, ��1) is the coordinate of the first point and (��2, ��2, ��2) is the
coordinate of the second point. The interval between two consecutive
time steps is 40 mins or (2/3)hour.
d) For cells migrated in the two matrices:
I. Create a boxplot of the migration speed.
II. Find the mean, median, standard deviation of the migration speed in each matrix
III. To the boxplots of part (I.) add
(-) The relevant data points to each boxplot (-) Add Mean Line segment
e) Does really the concertation of collagen (low and high) have impact on cell migration speed? Support your answer by applying a proper hypothesis testing method. Clearly define the null and alternative hypothesis, explain response and predictor parameters used in your analysis.
Sheet1
Xposition Yposition Zposition Time Step ID
142.769 98.647 101.8 1 1001 110
169.472 203.963 103.326 1 1002 112
261.373 191.473 106.181 1 1003 113
102.487 259.923 107.066 1 1004 114
43.1146 307.178 113.755 1 1005 119
446.814 35.1064 103.254 1 1006 123
622.728 236.292 102.829 1 1007 125
330.804 317.066 101.024 1 1008 126
405.472 209.677 106.272 1 1009 130
522.96 225.651 104.839 1 1010 131
516.545 313.613 106.968 1 1011 133
820.223 107.746 102.279 1 1012 152
947.83 124.849 102.515 1 1013 155
846.538 247.822 103.583 1 1014 157
729.786 267.726 105.878 1 1015 162
761.28 238.089 108.758 1 1016 166
807.053 217.442 124.101 1 1017 170
118.724 427.571 110.909 1 1018 185
205.482 533.752 108.753 1 1019 187
129.492 461.46 112.14 1 1020 188
147.583 516.718 112.123 1 1021 189
159.428 619.891 117.321 1 1022 192
278.201 629.596 125.441 1 1023 195
422.281 495.796 103.625 1 1024 202
342.226 534.414 105.793 1 1025 205
534.033 529.789 109.073 1 1026 207
894.713 515.545 92.2559 1 1027 212
745.204 623.138 94.7204 1 1028 214
900.804 389.645 104.037 1 1029 218
759.974 520.554 107.09 1 1030 219
698.275 541.254 108.257 1 1031 221
745.356 357.359 113.455 1 1032 222
269.569 777.331 101.164 1 1033 229
86.5101 645.935 118.342 1 1034 237
155.756 734.642 127.413 1 1035 238
520.556 716.887 91.0772 1 1036 239
460.665 641.721 94.0107 1 1037 240
492.111 653.427 93.0363 1 1038 241
349.116 704.307 93.7261 1 1039 242
401.193 773.59 92.2806 1 1040 244
522.242 684.346 99.2545 1 1041 245
344.758 638.968 102.127 1 1042 247
441.098 837.601 102.951 1 1043 248
513.554 858.238 104.83 1 1044 250
399.839 828.478 111.599 1 1045 251
763.659 805.128 87.8965 1 1046 257
845.602 837.232 88.5406 1 1047 259
741.285 657.861 123.42 1 1048 267
977.265 787.43 91.6551 1 1049 271
968.397 670.641 106.761 1 1050 273
16.7061 292.295 145.075 1 1051 300
757.636 166.183 134.152 1 1052 310
905.464 193.947 147.169 1 1053 315
214.589 360.986 138.658 1 1054 330
213.428 623.051 144.555 1 1055 331
7.70986 364.949 166.651 1 1056 334
648.408 383.908 139.355 1 1057 340
124.854 655.693 148.773 1 1058 352
476.199 641.478 156.91 1 1059 357
607.704 419.648 99.5265 1 1060 14004
739.976 417.792 109.838 1 1061 14010
517.858 155.815 120.331 1 1062 14019
534.424 426.964 94 1 1072 15501
526.425 442.958 126 1 1070 15524
546.626 425.517 95.2562 1 1073 15537
528.644 440.364 106 1 1074 15549
517.695 481.631 102 1 1075 15570
199.19 552.745 110 1 1065 15605
372.502 841.115 114 1 1069 15627
2.8678 383.09 126.062 1 1076 15637
855.611 662.011 130 1 1077 15660
849.415 654.238 122 1 1078 15683
694.982 476.902 98 1 1063 15706
569.288 431.996 98 1 1067 15724
116.05 103.418 99.0526 1 1080 15726
890.371 723.493 126 1 1083 15766
866.576 725.312 98 1 1081 15789
866.289 711.425 118 1 1082 15790
927.655 641.051 94 1 1084 15815
139.932 97.7205 96.7643 2 1001 14024
168.791 206.633 98.088 2 1002 14025
260.559 190.922 100.205 2 1003 14026
100.401 261.272 101.46 2 1004 14027
44.1278 305.558 108.414 2 1005 14028
454.571 25.9146 99.1869 2 1006 14029
626.358 238.293 97.7276 2 1007 14030
330.919 318.356 96.0599 2 1008 14031
407.965 207.041 102.039 2 1009 14032
523.583 224.52 100.136 2 1010 14033
514.652 308.713 101.559 2 1011 14034
815.992 107.391 96.6144 2 1012 14035
943.938 128.109 96.168 2 1013 14036
845.829 246.051 97.813 2 1014 14037
757.695 235.783 103.905 2 1016 14038
725.89 267.797 102.155 2 1015 14039
804.556 216.957 119.257 2 1017 14040
209.754 531.897 103.302 2 1019 14041
120.09 427.514 105.776 2 1018 14042
130.452 459.549 106.492 2 1020 14043
152.007 517.787 107.659 2 1021 14044
161.28 617.755 110.395 2 1022 14045
275.74 626.934 121.611 2 1023 14046
458.497 635.766 90.7697 2 1037 14047
421.563 494.364 98.5318 2 1024 14048
346.655 638.612 98.0187 2 1042 14049
532.767 528.321 103.878 2 1026 14050
341.173 534.047 101.467 2 1025 14051
888.721 515.42 87.2874 2 1027 14053
744.327 619.777 89.8204 2 1028 14054
689.056 462.418 97.9071 2 1063 14055
900.833 389.923 101.422 2 1029 14056
760.824 517.753 101.624 2 1030 14057
699.644 537.262 102.999 2 1031 14058
744.489 356.923 108.643 2 1032 14059
268.37 776.752 96.107 2 1033 14060
185.685 789.188 98.3112 2 1064 14061
77.2644 654.245 112.419 2 1034 14062
157.921 727.525 123.753 2 1035 14063
519.137 714.163 86.2028 2 1036 14064
396.035 771.698 86.9347 2 1040 14065
498.166 654.561 88.6748 2 1038 14066
356.553 696.101 90.9732 2 1039 14067
527.185 682.584 94.9878 2 1041 14068
435.98 836.754 98.3017 2 1043 14069
511.47 854.769 98.7661 2 1044 14070
398.322 826.143 105.855 2 1045 14071
762.365 805.263 82.4831 2 1046 14072
837.553 834.001 83.4097 2 1047 14073
741.03 655.997 117.134 2 1048 14075
982.059 789.348 85.8143 2 1049 14076
967.854 668.773 101.09 2 1050 14077
12.6094 290.249 141.365 2 1051 14078
755.142 165.966 128.753 2 1052 14079
905.05 190.991 142.003 2 1053 14080
214.483 361.308 133.514 2 1054 14081
215.19 620.962 138.792 2 1055 14082
11.1929 363.416 161.843 2 1056 14083
647.235 381.914 135.082 2 1057 14084
124.508 653.872 143.795 2 1058 14085
473.229 638.953 151.809 2 1059 14086
610.199 425.017 97.4164 2 1060 14088
725.002 423.107 98.0173 2 1061 14089
517.858 156.803 115.712 2 1062 14090
532.258 426.091 90 2 1072 15502
527.863 438.455 114 2 1070 15525
550.9 418.03 95.5259 2 1073 15538
527.426 440.453 102 2 1074 15550
519.744 477.593 98 2 1075 15571
194.479 552.77 102 2 1065 15606
369.157 838.811 102 2 1069 15628
1.76135 383.09 109.336 2 1076 15638
854.93 660.095 118 2 1077 15661
845.259 654.189 106 2 1078 15684
558.87 434.401 94 2 1067 15725
118.546 104.121 96.3512 2 1080 15727
863.3 719.434 98 2 1081 15750
896.941 718.891 122 2 1083 15767
862.399 709.044 114 2 1082 15791
935.319 642.794 86 2 1084 15816
140.083 95.6273 92.7321 3 1001 14092
170.516 205.671 94.1654 3 1002 14093
102.54 261.638 94.8486 3 1004 14094
260.105 192.498 96.6066 3 1003 14095
41.7991 306.452 105.016 3 1005 14096
335.991 313.294 91.9232 3 1008 14097
455.055 21.2412 94.8506 3 1006 14098
523.023 224.239 95.7439 3 1010 14099
627.616 240.228 93.4112 3 1007 14100
407.22 206.702 98.5224 3 1009 14101
514.949 309.22 97.3162 3 1011 14102
814.052 106.897 91.9571 3 1012 14103
939.598 137.576 94.1156 3 1013 14104
845.041 249.259 94.148 3 1014 14105
756.606 233.128 99.5929 3 1016 14106
723.313 267.402 97.8365 3 1015 14107
803.492 215.008 115.688 3 1017 14108
753.889 166.837 124.511 3 1052 14109
215.006 526.621 98.9529 3 1019 14110
195.199 564.028 98.0527 3 1065 14111
121.078 424.466 101.058 3 1018 14112
133.155 457.772 102.488 3 1020 14113
156.963 546.737 102.698 3 1066 14114
154.463 516.145 104.031 3 1021 14115
159.936 619.083 105.784 3 1022 14116
271.797 627.76 116.498 3 1023 14117
457.109 635.925 85.4917 3 1037 14118
563.575 429.362 93.2606 3 1067 14119
423.678 493.751 93.4631 3 1024 14120
345.674 637.162 93.0601 3 1042 14121
533.974 527.214 98.3678 3 1026 14122
338.571 533.962 96.2657 3 1025 14123
887.322 514.533 84.2526 3 1027 14125
740.1 621.632 85.5414 3 1028 14126
693.535 461.969 95.4221 3 1063 14127
899.715 387.587 96.9785 3 1029 14128
759.722 515.814 98.082 3 1030 14129
699.241 537.528 99.0588 3 1031 14130
748.495 353.631 102.235 3 1032 14131
267.755 777.237 91.9206 3 1033 14132
179.654 792.898 93.1336 3 1064 14133
72.6034 661.144 107.343 3 1034 14134
161.188 724.45 120.749 3 1035 14135
496.185 650.901 82.0183 3 1038 14136
362.873 698.658 83.4657 3 1039 14137
520.061 714.048 81.5699 3 1036 14138
397.323 773.095 82.3411 3 1040 14139
529.264 684.148 88.7572 3 1041 14140
431.867 837.609 94.4647 3 1043 14141
510.271 854.618 94.6541 3 1044 14142
397.64 826.281 101.625 3 1045 14143
760.982 803.732 78.0965 3 1046 14144
838.211 835.158 78.9155 3 1047 14145
741.893 657.128 113.133 3 1048 14147
982.059 788.121 81.8982 3 1049 14148
968 668.842 96.5492 3 1050 14149
12.5135 289.966 137.408 3 1051 14150
904.685 190.661 137.494 3 1053 14151
214.101 360.379 129.294 3 1054 14152
214.375 621.212 134.67 3 1055 14153
8.11742 363.196 157.653 3 1056 14154
647.074 382.579 131.4 3 1057 14155
124.101 655.061 138.661 3 1058 14156
472.906 639.857 147.108 3 1059 14157
612.695 420.936 94.3978 3 1060 14159
727.497 421.397 94.567 3 1061 14160
512.867 149.842 116.533 3 1062 14161
530.301 428.856 90 3 1072 15503
524.746 441.62 114 3 1070 15526
550.732 413.039 94.2856 3 1073 15539
529.36 440.422 98 3 1074 15551
519.282 480.511 90 3 1075 15572
366.768 832.264 98 3 1069 15629
3.44788 370.612 98.0952 3 1076 15639
855.08 661.302 106 3 1077 15662
849.996 653.991 114 3 1078 15685
123.537 101.58 99.2593 3 1080 15728
865.458 718.908 94 3 1081 15751
890.819 728.116 110 3 1083 15768
862.399 709.044 114 3 1082 15792
935.399 638.986 86 3 1084 15817
141.766 97.1253 90.1175 4 1001 14163
167.399 208.151 90.5057 4 1002 14164
99.8863 263.591 90.5291 4 1004 14165
254.672 196.469 94.1095 4 1003 14166
37.8868 307.298 101.924 4 1005 14167
458.021 20.5802 91.0557 4 1006 14168
524.213 224.934 90.8485 4 1010 14169
630.416 243.717 90.6805 4 1007 14170
336.984 313.383 88.8374 4 1008 14171
399.427 209.083 94.1638 4 1009 14172
514.707 309.721 93.448 4 1011 14173
501.085 142.903 113.191 4 1062 14174
815.073 108.248 89.1691 4 1012 14175
845.61 248.143 91.4444 4 1014 14176
940.503 148.461 94.3557 4 1013 14177
722.008 268.797 95.4339 4 1015 14178
752.333 230.01 96.9587 4 1016 14179
800.785 212.835 112.578 4 1017 14180
755.737 167.362 122.465 4 1052 14181
214.55 521.171 95.3877 4 1019 14182
125.848 425.507 98.7477 4 1018 14183
133.412 456.382 99.566 4 1020 14184
161.03 551.493 99.8891 4 1066 14185
187.584 574.527 96.3852 4 1065 14186
154.171 516.484 102.262 4 1021 14187
159.674 620.31 103.403 4 1022 14188
274.543 627.701 114.445 4 1023 14189
212.566 360.106 125.985 4 1054 14190
455.636 635.251 82.6713 4 1037 14191
567.523 429.312 89.9083 4 1067 14192
421.122 494.039 90.9631 4 1024 14193
344.909 638.046 90.2583 4 1042 14194
532.733 527.194 95.3264 4 1026 14195
336.699 535.601 92.9828 4 1025 14196
889.971 513.112 81.1932 4 1027 14198
740.426 622.789 81.7347 4 1028 14199
891.755 386.734 93.3426 4 1029 14200
689.244 450.305 93.9818 4 1063 14201
759.196 514.263 94.9938 4 1030 14202
698.54 537.734 94.9779 4 1031 14203
744.692 347.988 98.1175 4 1032 14204
267.013 777.167 88.5963 4 1033 14205
183.524 793.023 90.338 4 1064 14206
65.7634 671.21 106.14 4 1034 14207
155.811 736.446 113.14 4 1068 14208
166.896 718.302 121.359 4 1035 14209
495.288 650.961 79.4938 4 1038 14210
520.948 713.269 78.9362 4 1036 14211
397.905 772.17 79.2664 4 1040 14212
365.229 693.433 80.9539 4 1039 14213
530.846 685.253 84.8762 4 1041 14214
431.916 837.13 91.1102 4 1043 14215
510.767 853.642 91.1309 4 1044 14216
397.732 825.259 99.1514 4 1045 14217
756.287 803.875 75.0165 4 1046 14218
841.85 837.322 75.5621 4 1047 14219
740.661 657.99 109.045 4 1048 14220
982.059 788.06 78.6433 4 1049 14222
968.778 667.512 93.9737 4 1050 14223
14.2808 290.913 134.404 4 1051 14224
901.055 191.455 134.081 4 1053 14225
212.116 624.11 131.497 4 1055 14226
6.76659 363.081 155.06 4 1056 14227
645.384 383.035 129.265 4 1057 14228
125.348 653.443 136.151 4 1058 14229
476.372 640.513 145.383 4 1059 14230
632.661 426.159 88.2772 4 1060 14232
727.497 420.698 91.2256 4 1061 14233
526.961 424.691 86 4 1072 15504
525.227 440.721 110 4 1070 15527
550.178 413.039 88.7562 4 1073 15540
529.02 441.146 102 4 1074 15552
521.583 481.68 82 4 1075 15573
369.155 833.802 90 4 1069 15630
2.53796 368.116 105.691 4 1076 15640
857.202 661.544 110 4 1077 15663
851.266 655.228 110 4 1078 15686
121.042 103.809 89.1946 4 1080 15729
887.366 723.094 110 4 1083 15769
857.081 709.858 106 4 1082 15794
870.116 725.096 98 4 1081 15795
936.652 643.279 78 4 1084 15818
138.122 98.3515 86.5617 5 1001 14235
166.229 206.991 87.7511 5 1002 14236
96.2245 265.299 87.8394 5 1004 14237
249.85 199.586 90.3256 5 1003 14238
34.5731 310.82 99.4736 5 1005 14239
461.682 20.8551 86.9701 5 1006 14240
336.618 317.815 86.4055 5 1008 14241
405.412 208.457 90.7501 5 1009 14242
523.013 223.65 88.3145 5 1010 14243
631.406 245.27 88.2428 5 1007 14244
516.448 311.887 90.484 5 1011 14245
498.864 147.435 109.428 5 1062 14246
815.504 107.213 86.9579 5 1012 14247
845.638 249.371 89.6452 5 1014 14248
941.196 150.295 93.8783 5 1013 14249
746.668 224.247 94.5955 5 1016 14250
721.669 269.201 92.9694 5 1015 14251
797.826 211.34 111.681 5 1017 14252
760.088 170.193 121.201 5 1052 14253
214.258 514.33 92.1432 5 1019 14254
125.594 426.193 97.0572 5 1018 14255
133.954 456.135 97.9881 5 1020 14256
165.383 549.083 98.7594 5 1066 14257
197.906 578.911 96.3898 5 1065 14258
153.368 516.596 101.724 5 1021 14259
162.55 617.394 101.949 5 1022 14260
275.079 627.123 113.059 5 1023 14261
211.189 360.484 124.265 5 1054 14262
458.442 636.821 80.3224 5 1037 14263
343.769 637.88 87.9484 5 1042 14264
570.92 431.376 88.9191 5 1067 14265
420.401 494.592 88.8661 5 1024 14266
332.588 535.534 91.0139 5 1025 14267
532.982 527.92 92.8278 5 1026 14269
895.372 512.972 78.6777 5 1027 14271
739.622 622.433 78.9462 5 1028 14272
894.128 383.997 91.3356 5 1029 14273
693.695 457.695 91.3243 5 1063 14274
760.131 515.177 95.4887 5 1030 14275
700.842 535.464 93.1978 5 1031 14276
743.435 348.785 97.53 5 1032 14277
647.322 382.615 126.687 5 1057 14278
269.161 778.306 86.5417 5 1033 14279
183.205 794.94 88.9856 5 1064 14280
68.9893 679.832 102.862 5 1034 14281
158.96 737.998 110.951 5 1068 14282
168.575 719.028 121.255 5 1035 14283
488.939 648.279 76.7312 5 1038 14284
350.898 685.145 78.7809 5 1039 14285
520.013 714.397 77.0997 5 1036 14286
398.691 773.169 77.6063 5 1040 14287
532.397 686.083 83.1709 5 1041 14288
427.219 838.462 90.2942 5 1043 14289
509.766 854.917 89.5503 5 1044 14290
397.879 826.507 98.6067 5 1045 14291
755.608 805.608 72.6982 5 1046 14292
841.964 838.177 73.4045 5 1047 14293
740.879 658.489 106.258 5 1048 14294
982.059 786.776 76.9332 5 1049 14296
968.834 667.346 91.6643 5 1050 14297
13.2823 291.416 131.976 5 1051 14298
900.127 191.445 131.621 5 1053 14299
214.582 623.021 129.063 5 1055 14300
8.03457 362.667 153.001 5 1056 14301
124.31 653.971 134.132 5 1058 14302
479.24 641.923 141.587 5 1059 14303
635.156 429.122 95.854 5 1060 14305
727.497 418.517 92.6385 5 1061 14306
528.685 428.002 86 5 1072 15505
529 443.536 102 5 1070 15528
547.686 410.543 87.323 5 1073 15541
538.972 449.484 118 5 1074 15553
519.929 485.573 82 5 1075 15574
368.267 833.405 90 5 1069 15631
1.94373 380.595 100.642 5 1076 15641
857.933 655.923 118 5 1077 15664
846.522 655.441 102 5 1078 15687
118.546 103.226 85.9458 5 1080 15730
856.788 715.082 94 5 1082 15753
888.635 719.926 114 5 1083 15770
868.167 730.564 86 5 1081 15796
931.118 635.739 82 5 1084 15819
137.614 97.5864 84.97 6 1001 14308
166.089 208.573 87.6867 6 1002 14309
94.0816 264.39 85.3201 6 1004 14310
246.695 199.299 88.6455 6 1003 14311
31.5823 310.685 97.2422 6 1005 14312
458.962 18.7711 85.7145 6 1006 14313
523.801 224.761 85.1925 6 1010 14314
630.068 241.761 85.2427 6 1007 14315
338.034 316.257 84.2406 6 1008 14316
404.637 204.89 88.8995 6 1009 14317
518.459 313.339 88.3263 6 1011 14318
502.536 148.975 107.844 6 1062 14319
815.479 107.475 86.1773 6 1012 14320
846.387 254.019 87.1463 6 1014 14321
724.914 271.035 90.8227 6 1015 14322
943.079 149.899 93.1926 6 1013 14323
748.094 225.866 92.5027 6 1016 14324
799.535 210.288 109.392 6 1017 14325
764.498 170.905 120.393 6 1052 14326
227.034 511.619 87.4172 6 1019 14327
127.136 425.389 94.8595 6 1018 14328
134.522 456.379 95.798 6 1020 14329
165.147 516.321 94.1562 6 1021 14330
199.833 577.824 95