Testing Assumptions, Non-parametric, Regression and Correlation
Gordon Ober
2024-07-17
The purpose of this R lab is to have you practice testing assumptions, interpretting output, practicing ways to deal with violations of assumptions and to dip into regression and correlation
NOTE: please refer to the hypothesis testing guide document for code examples!
Part 1: Testing assumptions
Create a code chunk(s) below to bring in “barnacle_data.csv” and complete the following actions. There are questions that will follow your coding. This data comes from some of my research looking at how things like microhabitat and shore height influence the growth and abundance of barnacles.
Actions/Questions: You are interested in seeing if there is an effect of shore height (‘Tide.Height’) on the growth of individual barnacles over a 6 month period.
- Question = What type of test would be appropriate to run to compare the means of ‘WidthChange’ by ‘Tide.Height’? (explain why)
- assuming that the sample data follows the 3 assumptions, I would run a two-sample t-test. The two sample t-test is the best option because there is one numerical variable and one categorical value which only has two levels.
- Code = Create code to test the data for normality (for this, create a histogram AND run a Shapiro-Wilks test)
barn <- read.table('barnacle_data_2.csv',sep=',',header=T)
barn## Tide.Height OperculumAug BasalAug WidthChange
## 1 H 5.258 7.098 68.01916033
## 2 H 5.615 9.256 18.65816768
## 3 H 5.483 8.289 0.97719870
## 4 H 5.065 11.578 6.36552081
## 5 H 5.229 9.563 12.21374046
## 6 H 5.645 11.291 7.41298379
## 7 H 6.367 8.750 1.06285714
## 8 H 5.740 11.798 6.32310561
## 9 H 5.714 9.890 8.24064712
## 10 H 3.821 6.072 45.25691700
## 11 H 3.642 6.293 1.43016050
## 12 H 3.971 8.611 3.79746835
## 13 H 5.323 8.826 26.50124632
## 14 H 4.708 7.784 16.00719424
## 15 H 3.472 6.029 22.64057058
## 16 H 3.235 5.521 42.25683753
## 17 H 3.881 5.820 30.20618557
## 18 H 1.848 3.368 89.60807601
## 19 H 4.865 6.001 40.19330112
## 20 H 5.073 5.813 12.98813005
## 21 H 2.857 3.483 7.69451622
## 22 H 4.771 8.944 12.94722719
## 23 H 4.422 6.262 16.33663366
## 24 H 4.384 7.715 3.30524951
## 25 H 4.898 6.371 3.32757809
## 26 H 4.722 6.874 7.53564155
## 27 H 4.261 7.039 14.98792442
## 28 H 4.604 7.817 9.49213253
## 29 H 4.558 8.892 16.64417454
## 30 H 5.303 8.467 1.29916145
## 31 H 4.723 9.030 6.36766334
## 32 H 3.758 9.147 8.54925112
## 33 H 4.908 8.703 32.64391589
## 34 H 4.361 9.779 19.20441763
## 35 H 4.348 10.218 15.02250930
## 36 H 5.249 10.126 15.40588584
## 37 H 3.956 6.552 11.75213675
## 38 H 4.457 8.149 18.33353786
## 39 H 4.164 8.804 15.54975011
## 40 H 4.088 9.363 0.58741856
## 41 H 3.656 8.790 5.77929465
## 42 H 3.755 8.400 5.83333333
## 43 H 4.026 8.218 8.42054028
## 44 H 3.663 5.287 94.15547570
## 45 H 4.284 6.053 30.81116802
## 46 H 4.672 9.284 7.71219302
## 47 H 3.911 4.594 30.40922943
## 48 L 3.470 10.315 3.46097916
## 49 L 3.215 6.568 21.26979294
## 50 L 3.957 6.979 34.46052443
## 51 L 3.936 7.290 21.38545953
## 52 L 3.585 7.513 32.31731665
## 53 L 3.778 7.208 37.19478357
## 54 L 4.316 10.376 13.97455667
## 55 L 2.288 5.088 55.09040881
## 56 L 2.874 6.361 20.40559660
## 57 L 4.518 9.353 23.69293275
## 58 L 4.056 6.387 97.96461563
## 59 L 3.256 4.375 32.96000000
## 60 L 4.436 7.321 36.64799891
## 61 L 3.643 7.522 68.67854294
## 62 L 4.566 6.641 68.31802439
## 63 L 4.213 9.063 14.17852808
## 64 L 4.324 7.733 19.28100349
## 65 L 3.185 5.127 58.31870490
## 66 L 3.725 6.541 44.10640575
## 67 L 4.116 9.121 25.60026313
## 68 L 3.921 6.626 70.55538787
## 69 L 4.979 6.601 10.37721557
## 70 L 2.364 6.376 6.80677541
## 71 L 4.557 9.280 19.11637931
## 72 L 4.576 7.057 42.39761939
## 73 L 3.583 7.816 26.30501535
## 74 L 3.693 6.758 42.14264575
## 75 L 3.823 7.797 19.72553546
## 76 L 4.175 6.908 46.56919514
## 77 L 3.328 6.613 34.59851807
## 78 L 3.654 5.344 55.03368263
## 79 L 3.686 7.859 8.57615473
## 80 L 3.533 5.623 37.86235106
## 81 L 3.686 9.099 9.42960765
## 82 L 4.994 6.844 66.17475161
## 83 L 3.100 7.648 26.15062762
## 84 L 3.083 5.081 26.51052942
## 85 L 2.828 5.793 47.00500604
## 86 L 3.687 6.926 38.75252671
## 87 L 4.464 8.429 12.43326611
## 88 L 4.864 8.745 24.64265294
## 89 L 2.037 3.750 108.72000000
## 90 L 5.148 6.868 24.24286546
## 91 L 4.257 5.239 87.57396450
## 92 L 3.977 5.342 53.80007488
## 93 L 4.934 7.455 73.72233400
## 94 L 4.966 5.677 19.88726440
## 95 L 4.376 5.645 22.90522586
## 96 L 4.022 6.343 7.11020022
## 97 H 2.384 6.582 5.49984807
## 98 H 3.128 5.800 18.65517241
## 99 H 3.553 6.453 9.29800093
## 100 H 2.941 7.115 3.17638791
## 101 H 3.146 6.465 5.35189482
## 102 H 2.529 6.094 9.92779783
## 103 H 2.915 4.429 4.01896591
## 104 H 3.541 6.797 2.16271885
## 105 H 3.425 3.791 18.93959377
## 106 H 4.016 7.637 12.89773471
## 107 H 3.388 7.166 2.73513815
## 108 H 3.244 6.179 11.02120084
## 109 H 4.471 8.479 4.03349452
## 110 H 2.721 5.915 4.64919696
## 111 H 3.434 6.937 12.90183076
## 112 H 3.390 5.634 1.77493788
## 113 H 3.811 8.301 0.69871100
## 114 H 3.058 6.829 6.97027383
## 115 H 2.996 7.893 5.38451793
## 116 H 4.033 10.004 0.58976409
## 117 H 3.271 7.576 0.19799366
## 118 H 2.459 5.039 10.00198452
## 119 H 2.848 5.411 7.54019590
## 120 H 2.355 4.924 9.44354184
## 121 H 3.226 4.617 4.80831709
## 122 H 2.908 5.836 0.97669637
## 123 H 3.438 6.758 8.34566440
## 124 H 3.102 7.255 3.37698139
## 125 H 2.905 5.495 6.31483166
## 126 H 2.899 4.488 32.10784314
## 127 H 3.664 4.989 6.41411104
## 128 H 3.953 5.095 10.08832188
## 129 H 3.598 4.718 9.11403137
## 130 H 3.712 5.000 7.10000000
## 131 H 3.676 5.525 8.30769231
## 132 H 3.814 4.937 6.94753899
## 133 H 4.335 6.064 8.04749340
## 134 H 2.721 5.204 2.01767871
## 135 H 3.482 6.168 10.68417639
## 136 H 3.303 7.058 1.50184188
## 137 H 3.404 7.095 2.42424242
## 138 H 2.901 5.130 4.69785575
## 139 H 3.687 5.945 13.45668629
## 140 H 3.338 6.304 14.87944162
## 141 H 3.770 5.416 4.33899557
## 142 H 2.937 6.022 1.77681833
## 143 H 2.711 6.399 1.40646976
## 144 L 2.469 5.757 22.14695154
## 145 L 2.647 5.063 3.00217263
## 146 L 2.806 4.918 12.99308662
## 147 L 2.790 4.488 28.14171123
## 148 L 2.245 5.398 11.98592071
## 149 L 2.118 4.392 32.74134791
## 150 L 2.735 5.837 12.78053795
## 151 L 1.824 4.437 41.04124408
## 152 L 3.062 5.167 1.43216567
## 153 L 2.146 4.936 14.12074554
## 154 L 1.572 3.365 53.87815750
## 155 L 1.839 3.950 23.69620253
## 156 L 0.533 0.815 447.36196320
## 157 L 2.175 4.860 26.37860082
## 158 L 1.954 4.473 22.11044042
## 159 L 1.974 5.062 20.20940340
## 160 L 1.667 4.271 23.46054788
## 161 L 1.476 4.098 26.32991703
## 162 L 1.771 5.867 22.75438896
## 163 L 1.698 4.231 17.08815883
## 164 L 1.763 5.341 3.83823254
## 165 L 1.527 2.157 56.00370885
## 166 L 1.982 2.923 36.09305508
## 167 L 1.875 4.359 0.06882312
## 168 L 1.890 6.340 0.25236593
## 169 L 2.277 6.037 1.07669372
## 170 L 1.648 5.127 1.28730252
## 171 L 2.453 5.178 18.38547702
## 172 L 4.374 7.607 4.78506639
## 173 L 3.775 6.709 6.48382769
## 174 L 2.963 6.629 7.82923518
## 175 L 2.642 4.595 24.06964091
## 176 L 2.385 5.413 6.96471458
## 177 L 3.030 4.794 5.67375886
## 178 L 2.977 6.953 11.79347044
## 179 L 3.971 6.916 25.80971660
## 180 L 3.162 6.733 6.00029704
## 181 L 2.911 6.126 8.60267711
## 182 L 3.107 5.147 10.80240917
## 183 L 3.691 5.390 33.06122449
## 184 L 2.939 5.633 14.27303391
## 185 L 3.300 7.230 18.25726141
## 186 L 2.886 5.893 34.29492618
## 187 L 3.375 6.912 13.94675926
## 188 L 2.870 4.840 10.59917355
## 189 L 3.403 6.239 15.98012502
## 190 L 3.013 7.053 13.05827308
## 191 L 2.502 6.042 22.04568024shapiro.test(barn$WidthChange)##
## Shapiro-Wilk normality test
##
## data: barn$WidthChange
## W = 0.4299, p-value < 2.2e-16hist(barn$WidthChange)
- Question = what do the tests for normality tell you about the data? Is this assumption met?
- The shapiro test gave a p-value of 2.2e-16 which tells us to reject the null hypothesis. Meaning the data is not normally distributed. As further confirmation, the histogram is significantly skewed telling us the sample data is not normally distributed.
- Code = Create code to test the data for equal variance (use a Levene Test)
library(car)## Loading required package: carDataleveneTest(WidthChange ~ Tide.Height,
data = barn)## Warning in leveneTest.default(y = y, group = group, ...): group coerced to
## factor.## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 1 5.1557 0.0243 *
## 189
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1- Question = what does the test for equal variance tell you about the data? Is this assumption met?
- In order to support the null hypothesis that the variance among the groups are equal the levene test P-value would have to be greater than 0.05. In this case, the p-value is 0.0243 therefore the null hypothesis/assumption is not met. The varience between the groups is not equal.
- Code = log transform the WidthChange column
barn$log_WidthChange <- log(barn$WidthChange)
barn## Tide.Height OperculumAug BasalAug WidthChange log_WidthChange
## 1 H 5.258 7.098 68.01916033 4.21978944
## 2 H 5.615 9.256 18.65816768 2.92628400
## 3 H 5.483 8.289 0.97719870 -0.02306527
## 4 H 5.065 11.578 6.36552081 1.85089605
## 5 H 5.229 9.563 12.21374046 2.50256159
## 6 H 5.645 11.291 7.41298379 2.00323303
## 7 H 6.367 8.750 1.06285714 0.06096070
## 8 H 5.740 11.798 6.32310561 1.84421048
## 9 H 5.714 9.890 8.24064712 2.10907887
## 10 H 3.821 6.072 45.25691700 3.81235552
## 11 H 3.642 6.293 1.43016050 0.35778667
## 12 H 3.971 8.611 3.79746835 1.33433462
## 13 H 5.323 8.826 26.50124632 3.27719176
## 14 H 4.708 7.784 16.00719424 2.77303826
## 15 H 3.472 6.029 22.64057058 3.11974346
## 16 H 3.235 5.521 42.25683753 3.74376618
## 17 H 3.881 5.820 30.20618557 3.40804672
## 18 H 1.848 3.368 89.60807601 4.49544545
## 19 H 4.865 6.001 40.19330112 3.69370034
## 20 H 5.073 5.813 12.98813005 2.56403587
## 21 H 2.857 3.483 7.69451622 2.04050790
## 22 H 4.771 8.944 12.94722719 2.56088165
## 23 H 4.422 6.262 16.33663366 2.79341005
## 24 H 4.384 7.715 3.30524951 1.19551197
## 25 H 4.898 6.371 3.32757809 1.20224474
## 26 H 4.722 6.874 7.53564155 2.01964397
## 27 H 4.261 7.039 14.98792442 2.70724484
## 28 H 4.604 7.817 9.49213253 2.25046330
## 29 H 4.558 8.892 16.64417454 2.81206028
## 30 H 5.303 8.467 1.29916145 0.26171902
## 31 H 4.723 9.030 6.36766334 1.85123258
## 32 H 3.758 9.147 8.54925112 2.14584369
## 33 H 4.908 8.703 32.64391589 3.48565850
## 34 H 4.361 9.779 19.20441763 2.95514034
## 35 H 4.348 10.218 15.02250930 2.70954970
## 36 H 5.249 10.126 15.40588584 2.73474963
## 37 H 3.956 6.552 11.75213675 2.46403508
## 38 H 4.457 8.149 18.33353786 2.90873205
## 39 H 4.164 8.804 15.54975011 2.74404457
## 40 H 4.088 9.363 0.58741856 -0.53201766
## 41 H 3.656 8.790 5.77929465 1.75428164
## 42 H 3.755 8.400 5.83333333 1.76358859
## 43 H 4.026 8.218 8.42054028 2.13067399
## 44 H 3.663 5.287 94.15547570 4.54494741
## 45 H 4.284 6.053 30.81116802 3.42787722
## 46 H 4.672 9.284 7.71219302 2.04280259
## 47 H 3.911 4.594 30.40922943 3.41474616
## 48 L 3.470 10.315 3.46097916 1.24155154
## 49 L 3.215 6.568 21.26979294 3.05728789
## 50 L 3.957 6.979 34.46052443 3.53981445
## 51 L 3.936 7.290 21.38545953 3.06271123
## 52 L 3.585 7.513 32.31731665 3.47560321
## 53 L 3.778 7.208 37.19478357 3.61616852
## 54 L 4.316 10.376 13.97455667 2.63723830
## 55 L 2.288 5.088 55.09040881 4.00897563
## 56 L 2.874 6.361 20.40559660 3.01580921
## 57 L 4.518 9.353 23.69293275 3.16517681
## 58 L 4.056 6.387 97.96461563 4.58460635
## 59 L 3.256 4.375 32.96000000 3.49529471
## 60 L 4.436 7.321 36.64799891 3.60135883
## 61 L 3.643 7.522 68.67854294 4.22943682
## 62 L 4.566 6.641 68.31802439 4.22417363
## 63 L 4.213 9.063 14.17852808 2.65172871
## 64 L 4.324 7.733 19.28100349 2.95912034
## 65 L 3.185 5.127 58.31870490 4.06592288
## 66 L 3.725 6.541 44.10640575 3.78660503
## 67 L 4.116 9.121 25.60026313 3.24260263
## 68 L 3.921 6.626 70.55538787 4.25639804
## 69 L 4.979 6.601 10.37721557 2.33961259
## 70 L 2.364 6.376 6.80677541 1.91791850
## 71 L 4.557 9.280 19.11637931 2.95054552
## 72 L 4.576 7.057 42.39761939 3.74709221
## 73 L 3.583 7.816 26.30501535 3.26975962
## 74 L 3.693 6.758 42.14264575 3.74106019
## 75 L 3.823 7.797 19.72553546 2.98191401
## 76 L 4.175 6.908 46.56919514 3.84093927
## 77 L 3.328 6.613 34.59851807 3.54381085
## 78 L 3.654 5.344 55.03368263 4.00794541
## 79 L 3.686 7.859 8.57615473 2.14898565
## 80 L 3.533 5.623 37.86235106 3.63395724
## 81 L 3.686 9.099 9.42960765 2.24385449
## 82 L 4.994 6.844 66.17475161 4.19229899
## 83 L 3.100 7.648 26.15062762 3.26387319
## 84 L 3.083 5.081 26.51052942 3.27754199
## 85 L 2.828 5.793 47.00500604 3.85025411
## 86 L 3.687 6.926 38.75252671 3.65719596
## 87 L 4.464 8.429 12.43326611 2.52037563
## 88 L 4.864 8.745 24.64265294 3.20447880
## 89 L 2.037 3.750 108.72000000 4.68877577
## 90 L 5.148 6.868 24.24286546 3.18812237
## 91 L 4.257 5.239 87.57396450 4.47248374
## 92 L 3.977 5.342 53.80007488 3.98527486
## 93 L 4.934 7.455 73.72233400 4.30030579
## 94 L 4.966 5.677 19.88726440 2.99007955
## 95 L 4.376 5.645 22.90522586 3.13136509
## 96 L 4.022 6.343 7.11020022 1.96153040
## 97 H 2.384 6.582 5.49984807 1.70472047
## 98 H 3.128 5.800 18.65517241 2.92612345
## 99 H 3.553 6.453 9.29800093 2.22979942
## 100 H 2.941 7.115 3.17638791 1.15574467
## 101 H 3.146 6.465 5.35189482 1.67745067
## 102 H 2.529 6.094 9.92779783 2.29533868
## 103 H 2.915 4.429 4.01896591 1.39102463
## 104 H 3.541 6.797 2.16271885 0.77136616
## 105 H 3.425 3.791 18.93959377 2.94125464
## 106 H 4.016 7.637 12.89773471 2.55705169
## 107 H 3.388 7.166 2.73513815 1.00618195
## 108 H 3.244 6.179 11.02120084 2.39982077
## 109 H 4.471 8.479 4.03349452 1.39463313
## 110 H 2.721 5.915 4.64919696 1.53669451
## 111 H 3.434 6.937 12.90183076 2.55736922
## 112 H 3.390 5.634 1.77493788 0.57376542
## 113 H 3.811 8.301 0.69871100 -0.35851807
## 114 H 3.058 6.829 6.97027383 1.94165451
## 115 H 2.996 7.893 5.38451793 1.68352779
## 116 H 4.033 10.004 0.58976409 -0.52803266
## 117 H 3.271 7.576 0.19799366 -1.61952025
## 118 H 2.459 5.039 10.00198452 2.30278353
## 119 H 2.848 5.411 7.54019590 2.02024816
## 120 H 2.355 4.924 9.44354184 2.24533110
## 121 H 3.226 4.617 4.80831709 1.57034715
## 122 H 2.908 5.836 0.97669637 -0.02357946
## 123 H 3.438 6.758 8.34566440 2.12174217
## 124 H 3.102 7.255 3.37698139 1.21698223
## 125 H 2.905 5.495 6.31483166 1.84290110
## 126 H 2.899 4.488 32.10784314 3.46910033
## 127 H 3.664 4.989 6.41411104 1.85850041
## 128 H 3.953 5.095 10.08832188 2.31137851
## 129 H 3.598 4.718 9.11403137 2.20981513
## 130 H 3.712 5.000 7.10000000 1.96009478
## 131 H 3.676 5.525 8.30769231 2.11718187
## 132 H 3.814 4.937 6.94753899 1.93838749
## 133 H 4.335 6.064 8.04749340 2.08536066
## 134 H 2.721 5.204 2.01767871 0.70194770
## 135 H 3.482 6.168 10.68417639 2.36876380
## 136 H 3.303 7.058 1.50184188 0.40669228
## 137 H 3.404 7.095 2.42424242 0.88551907
## 138 H 2.901 5.130 4.69785575 1.54710618
## 139 H 3.687 5.945 13.45668629 2.59947610
## 140 H 3.338 6.304 14.87944162 2.69998050
## 141 H 3.770 5.416 4.33899557 1.46764289
## 142 H 2.937 6.022 1.77681833 0.57482431
## 143 H 2.711 6.399 1.40646976 0.34108285
## 144 L 2.469 5.757 22.14695154 3.09769986
## 145 L 2.647 5.063 3.00217263 1.09933623
## 146 L 2.806 4.918 12.99308662 2.56441742
## 147 L 2.790 4.488 28.14171123 3.33725286
## 148 L 2.245 5.398 11.98592071 2.48373269
## 149 L 2.118 4.392 32.74134791 3.48863874
## 150 L 2.735 5.837 12.78053795 2.54792354
## 151 L 1.824 4.437 41.04124408 3.71457751
## 152 L 3.062 5.167 1.43216567 0.35918775
## 153 L 2.146 4.936 14.12074554 2.64764503
## 154 L 1.572 3.365 53.87815750 3.98672515
## 155 L 1.839 3.950 23.69620253 3.16531480
## 156 L 0.533 0.815 447.36196320 6.10336803
## 157 L 2.175 4.860 26.37860082 3.27255311
## 158 L 1.954 4.473 22.11044042 3.09604991
## 159 L 1.974 5.062 20.20940340 3.00614801
## 160 L 1.667 4.271 23.46054788 3.15532020
## 161 L 1.476 4.098 26.32991703 3.27070582
## 162 L 1.771 5.867 22.75438896 3.12475805
## 163 L 1.698 4.231 17.08815883 2.83838576
## 164 L 1.763 5.341 3.83823254 1.34501198
## 165 L 1.527 2.157 56.00370885 4.02541792
## 166 L 1.982 2.923 36.09305508 3.58610047
## 167 L 1.875 4.359 0.06882312 -2.67621547
## 168 L 1.890 6.340 0.25236593 -1.37687514
## 169 L 2.277 6.037 1.07669372 0.07389498
## 170 L 1.648 5.127 1.28730252 0.25254896
## 171 L 2.453 5.178 18.38547702 2.91156106
## 172 L 4.374 7.607 4.78506639 1.56549990
## 173 L 3.775 6.709 6.48382769 1.86931103
## 174 L 2.963 6.629 7.82923518 2.05786483
## 175 L 2.642 4.595 24.06964091 3.18095133
## 176 L 2.385 5.413 6.96471458 1.94085663
## 177 L 3.030 4.794 5.67375886 1.73585184
## 178 L 2.977 6.953 11.79347044 2.46754603
## 179 L 3.971 6.916 25.80971660 3.25075103
## 180 L 3.162 6.733 6.00029704 1.79180898
## 181 L 2.911 6.126 8.60267711 2.15207345
## 182 L 3.107 5.147 10.80240917 2.37976918
## 183 L 3.691 5.390 33.06122449 3.49836113
## 184 L 2.939 5.633 14.27303391 2.65837202
## 185 L 3.300 7.230 18.25726141 2.90456289
## 186 L 2.886 5.893 34.29492618 3.53499742
## 187 L 3.375 6.912 13.94675926 2.63524717
## 188 L 2.870 4.840 10.59917355 2.36077603
## 189 L 3.403 6.239 15.98012502 2.77134576
## 190 L 3.013 7.053 13.05827308 2.56942189
## 191 L 2.502 6.042 22.04568024 3.09311668- Code = run a shaprio-wilks and levene test on the transformed data
shapiro.test(barn$log_WidthChange)##
## Shapiro-Wilk normality test
##
## data: barn$log_WidthChange
## W = 0.95978, p-value = 2.894e-05library(car)
leveneTest(log_WidthChange ~ Tide.Height,
data = barn)## Warning in leveneTest.default(y = y, group = group, ...): group coerced to
## factor.## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 1 0.225 0.6358
## 189- Question = what did the transformation do to your assumptions? Have they all been met?
- After doing the log transformation, the shapiro test gave a p-value of 2.894e-05 which is greatly improved, but still not enough to fulfill the assumption of normality. On the other hand, the levene test gave a p-value of 0.6358 which passes the assumption of equal variance. So although improved, not all of the assumptions have been met.
- Question = given the outcome, what type of non-parametric test should be run?
- Given the outcome I would run the Mann-Whitney U-test (AKA Wilcoxon test) used for two-sample t-tests.
- Code = code for the test you decided in Q9
wilcox.test(log_WidthChange ~ Tide.Height, data = barn)##
## Wilcoxon rank sum test with continuity correction
##
## data: log_WidthChange by Tide.Height
## W = 2200, p-value = 6.623e-10
## alternative hypothesis: true location shift is not equal to 0- Question = interpret the outcome of the code from Q10
- The wilcox test gave a p-value of 6.623e-10 therefore we reject the null hypothesis. Meaning that there is a significant difference between samples.
- Code = create an appropriate visual to show WidthChange by Tide.Height
boxplot(log_WidthChange ~ Tide.Height,
data = barn)
Part 2: Correlation
The barnacle data set had measured key size metric for this species over time. In Part 1, you explored how tide height would impact the growht of one of these metrics, basal width. However, we collected two types of size data on the barnacles, their basal width and their operculum length. Much like we see body and brain size correlate, do we see basal width and operculum length do the same thing?
Actions/Questions: Complete the following using one or several code chunks with the ‘barnacle_data.csv’ file
- Code: create a scatter plot of OperculumAug vs. BasalAug
plot(barn$OperculumAug, barn$BasalAug, pch = 16, col="blue")
- Question: what do you suspect the correlation is? Does it look positive or negative? Does it look strong or weak?
- This looks to be a semi-strong, positive correlation close to zero.
- Code: Run a correlation test on this relationship
cor(x = barn$OperculumAug, y = barn$BasalAug) ## [1] 0.7152863cor.test(x = barn$OperculumAug, y = barn$BasalAug) ##
## Pearson's product-moment correlation
##
## data: barn$OperculumAug and barn$BasalAug
## t = 14.071, df = 189, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.6381109 0.7782316
## sample estimates:
## cor
## 0.7152863- Question: interpret the p-value and tell me what this means for this relationship.
- The p-value is 2.2e-16 so the correlation is statistically significant.
Part 3: Regression
Load the data ‘environmental.csv’, this dataset has tracked environmental parameters in NYC throughout the course of a summer. You are interested developing a predictive model that tracks how radiation influences temperature. This would allow you to better hone in on weather forecasting.
Actions/Questions: Complete the following using one or several code chunks
- Code: create a scatter plot of ‘radiation’ vs. ‘temperature’ (x axis should be radiation)
envir <- read.table('environmental.csv', ',', header=T)
envir## rownames ozone radiation temperature wind
## 1 1 41 190 67 7.4
## 2 2 36 118 72 8.0
## 3 3 12 149 74 12.6
## 4 4 18 313 62 11.5
## 5 5 23 299 65 8.6
## 6 6 19 99 59 13.8
## 7 7 8 19 61 20.1
## 8 8 16 256 69 9.7
## 9 9 11 290 66 9.2
## 10 10 14 274 68 10.9
## 11 11 18 65 58 13.2
## 12 12 14 334 64 11.5
## 13 13 34 307 66 12.0
## 14 14 6 78 57 18.4
## 15 15 30 322 68 11.5
## 16 16 11 44 62 9.7
## 17 17 1 8 59 9.7
## 18 18 11 320 73 16.6
## 19 19 4 25 61 9.7
## 20 20 32 92 61 12.0
## 21 21 23 13 67 12.0
## 22 22 45 252 81 14.9
## 23 23 115 223 79 5.7
## 24 24 37 279 76 7.4
## 25 25 29 127 82 9.7
## 26 26 71 291 90 13.8
## 27 27 39 323 87 11.5
## 28 28 23 148 82 8.0
## 29 29 21 191 77 14.9
## 30 30 37 284 72 20.7
## 31 31 20 37 65 9.2
## 32 32 12 120 73 11.5
## 33 33 13 137 76 10.3
## 34 34 135 269 84 4.0
## 35 35 49 248 85 9.2
## 36 36 32 236 81 9.2
## 37 37 64 175 83 4.6
## 38 38 40 314 83 10.9
## 39 39 77 276 88 5.1
## 40 40 97 267 92 6.3
## 41 41 97 272 92 5.7
## 42 42 85 175 89 7.4
## 43 43 10 264 73 14.3
## 44 44 27 175 81 14.9
## 45 45 7 48 80 14.3
## 46 46 48 260 81 6.9
## 47 47 35 274 82 10.3
## 48 48 61 285 84 6.3
## 49 49 79 187 87 5.1
## 50 50 63 220 85 11.5
## 51 51 16 7 74 6.9
## 52 52 80 294 86 8.6
## 53 53 108 223 85 8.0
## 54 54 20 81 82 8.6
## 55 55 52 82 86 12.0
## 56 56 82 213 88 7.4
## 57 57 50 275 86 7.4
## 58 58 64 253 83 7.4
## 59 59 59 254 81 9.2
## 60 60 39 83 81 6.9
## 61 61 9 24 81 13.8
## 62 62 16 77 82 7.4
## 63 63 122 255 89 4.0
## 64 64 89 229 90 10.3
## 65 65 110 207 90 8.0
## 66 66 44 192 86 11.5
## 67 67 28 273 82 11.5
## 68 68 65 157 80 9.7
## 69 69 22 71 77 10.3
## 70 70 59 51 79 6.3
## 71 71 23 115 76 7.4
## 72 72 31 244 78 10.9
## 73 73 44 190 78 10.3
## 74 74 21 259 77 15.5
## 75 75 9 36 72 14.3
## 76 76 45 212 79 9.7
## 77 77 168 238 81 3.4
## 78 78 73 215 86 8.0
## 79 79 76 203 97 9.7
## 80 80 118 225 94 2.3
## 81 81 84 237 96 6.3
## 82 82 85 188 94 6.3
## 83 83 96 167 91 6.9
## 84 84 78 197 92 5.1
## 85 85 73 183 93 2.8
## 86 86 91 189 93 4.6
## 87 87 47 95 87 7.4
## 88 88 32 92 84 15.5
## 89 89 20 252 80 10.9
## 90 90 23 220 78 10.3
## 91 91 21 230 75 10.9
## 92 92 24 259 73 9.7
## 93 93 44 236 81 14.9
## 94 94 21 259 76 15.5
## 95 95 28 238 77 6.3
## 96 96 9 24 71 10.9
## 97 97 13 112 71 11.5
## 98 98 46 237 78 6.9
## 99 99 18 224 67 13.8
## 100 100 13 27 76 10.3
## 101 101 24 238 68 10.3
## 102 102 16 201 82 8.0
## 103 103 13 238 64 12.6
## 104 104 23 14 71 9.2
## 105 105 36 139 81 10.3
## 106 106 7 49 69 10.3
## 107 107 14 20 63 16.6
## 108 108 30 193 70 6.9
## 109 109 14 191 75 14.3
## 110 110 18 131 76 8.0
## 111 111 20 223 68 11.5plot(envir$radiation, envir$temperature, pch = 16, col="blue")
- Code: create and run a linear regression model for ‘radiation’ vs. ‘temperature’
plot(x = envir$radiation, y = envir$temperature)
envir.lm <- lm(formula = radiation ~ temperature, data = envir)
summary(envir.lm)##
## Call:
## lm(formula = radiation ~ temperature, data = envir)
##
## Residuals:
## Min 1Q Median 3Q Max
## -169.823 -54.259 7.112 65.960 187.996
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -34.0209 68.6223 -0.496 0.62105
## temperature 2.8129 0.8756 3.212 0.00173 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 87.52 on 109 degrees of freedom
## Multiple R-squared: 0.08649, Adjusted R-squared: 0.07811
## F-statistic: 10.32 on 1 and 109 DF, p-value: 0.001731- Question: how do you interpret the p-value? How do you interpret the R^2 value?
- The p-value is 0.001731 which is less than 0.05 suggesting a significant relationship between the two variables. The adjusted R squared value is 0.07811 (on a scale of 0-1) telling us that X can predict most of the variation of Y.
- Code: add a least squares regression line to your plot
plot(x = envir$radiation, y = envir$temperature)
envir.lm <- lm(radiation ~ temperature, data = envir)
abline(envir.lm, col ='red') 
- Code: create code that predicts what the temperature in NYC will be with a radiation value of 180
envir.lm <- lm(radiation ~ temperature, data = envir)
predict(envir.lm, radiation = 180)## 1 2 3 4 5 6 7 8
## 154.4429 168.5073 174.1331 140.3784 148.8171 131.9397 137.5655 160.0686
## 9 10 11 12 13 14 15 16
## 151.6300 157.2557 129.1268 146.0042 151.6300 126.3139 157.2557 140.3784
## 17 18 19 20 21 22 23 24
## 131.9397 171.3202 137.5655 137.5655 154.4429 193.8233 188.1975 179.7589
## 25 26 27 28 29 30 31 32
## 196.6362 219.1393 210.7007 196.6362 182.5718 168.5073 148.8171 171.3202
## 33 34 35 36 37 38 39 40
## 179.7589 202.2620 205.0749 193.8233 199.4491 199.4491 213.5136 224.7651
## 41 42 43 44 45 46 47 48
## 224.7651 216.3265 171.3202 193.8233 191.0104 193.8233 196.6362 202.2620
## 49 50 51 52 53 54 55 56
## 210.7007 205.0749 174.1331 207.8878 205.0749 196.6362 207.8878 213.5136
## 57 58 59 60 61 62 63 64
## 207.8878 199.4491 193.8233 193.8233 193.8233 196.6362 216.3265 219.1393
## 65 66 67 68 69 70 71 72
## 219.1393 207.8878 196.6362 191.0104 182.5718 188.1975 179.7589 185.3847
## 73 74 75 76 77 78 79 80
## 185.3847 182.5718 168.5073 188.1975 193.8233 207.8878 238.8296 230.3909
## 81 82 83 84 85 86 87 88
## 236.0167 230.3909 221.9522 224.7651 227.5780 227.5780 210.7007 202.2620
## 89 90 91 92 93 94 95 96
## 191.0104 185.3847 176.9460 171.3202 193.8233 179.7589 182.5718 165.6944
## 97 98 99 100 101 102 103 104
## 165.6944 185.3847 154.4429 179.7589 157.2557 196.6362 146.0042 165.6944
## 105 106 107 108 109 110 111
## 193.8233 160.0686 143.1913 162.8815 176.9460 179.7589 157.2557