researcher hypothesized that cytokinins and auxins supplied by tumor-inducing insects lead to the production of tumors in plants. She performed experiments in which she hypodermically injected green pepper plants to determine if she could induce tumors. In one experiment she varied the concentration of cytokinin and

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A researcher hypothesized that cytokinins and auxins supplied by tumor-inducing insects lead to the production of tumors in plants. She performed experiments in which she hypodermically injected green pepper plants to determine if she could induce tumors.

In one experiment she varied the concentration of cytokinin and the ratio of auxin concentration to cytokinin concentration. She used 3 concentrations of cytokinin and 6 ratios of auxin/cytokinin. The concentrations are indexed (1-3) with 3 indicating the highest concentration of cytokinin. The 6 ratios of auxin/cytokinin varied from 0.125 to 5.0 with values greater than 1 indicating that auxin was in greater concentration than cytokinin.

The resulting data are in the date file "auxcyt.csv". The measured sizes of the tumors induced (relative to controls) are given in the 3rd column ('sumdiffd'). Analyze these data testing the appropriate hypotheses and interpret the results. (Note the unequal sample sizes.)

auxcyt data

  Concentration Ratio summdiffd
1 1 0.125 0.016666667
2 1 0.125 0.020877193
3 1 0.125 0.005438596
4 1 0.125 0.012280702
5 1 0.125 0.018596491
6 1 0.200 0.017017544
7 1 0.200 0.027017544
8 1 0.200 0.012982456
9 1 0.200 0.024210526
10 1 0.200 0.015824561
11 1 0.200 0.040877193
12 1 0.500 0.019473684
13 1 0.500 0.015789474
14 1 0.500 0.027017544
15 1 0.500 0.023157895
16 1 0.500 0.017017544
17 1 1.000 0.022807018
18 1 1.000 0.023684211
19 1 1.000 0.024385965
20 1 1.000 0.020526316
21 1 1.000 0.005263158
22 1 1.000 0.021578947
23 1 3.000 0.020526316
24 1 3.000 0.042280702
25 1 3.000 0.015087719
26 1 3.000 0.027894737
27 1 3.000 0.033157895
28 1 3.000 0.023157895
29 1 5.000 0.042280702
30 1 5.000 0.015614035
31 1 5.000 0.031403509
32 1 5.000 0.028771930
33 1 5.000 0.035964912
34 1 5.000 0.026666667
35 2 0.125 0.021052632
36 2 0.125 0.029824561
37 2 0.125 0.048245614
38 2 0.125 0.039473684
39 2 0.125 0.017192982
40 2 0.125 0.029824561
41 2 0.200 0.021578947
42 2 0.200 0.021929825
43 2 0.200 0.015964912
44 2 0.200 0.030350877
45 2 0.200 0.020350877
46 2 0.200 0.017192982
47 2 0.500 0.022456140
48 2 0.500 0.032280702
49 2 0.500 0.044912281
50 2 0.500 0.028070175
51 2 0.500 0.019122807
52 2 0.500 0.021929825
53 2 0.500 0.022280702
54 2 1.000 0.020701754
55 2 1.000 0.024912281
56 2 1.000 0.032631579
57 2 1.000 0.042105263
58 2 1.000 0.021929825
59 2 1.000 0.023508772
60 2 3.000 0.022982456
61 2 3.000 0.034035088
62 2 3.000 0.028245614
63 2 3.000 0.039824561
64 2 3.000 0.043157895
65 2 3.000 0.028771930
66 2 5.000 0.022631579
67 2 5.000 0.044736842
68 2 5.000 0.018245614
69 2 5.000 0.032982456
70 2 5.000 0.013859649
71 2 5.000 0.032105263
72 3 0.125 0.027017544
73 3 0.125 0.028421053
74 3 0.125 0.014561404
75 3 0.125 0.026315789
76 3 0.125 0.047719298
77 3 0.125 0.021052632
78 3 0.200 0.051578947
79 3 0.200 0.044385965
80 3 0.200 0.017192982
81 3 0.200 -0.007368421
82 3 0.200 0.025087719
83 3 0.200 0.020877193
84 3 0.500 0.033859649
85 3 0.500 0.053508772
86 3 0.500 0.009473684
87 3 0.500 0.069649123
88 3 0.500 0.039824561
89 3 0.500 0.016491228
90 3 1.000 0.048947368
91 3 1.000 0.057017544
92 3 1.000 0.032280702
93 3 1.000 0.038070175
94 3 1.000 0.054912281
95 3 1.000 0.043859649
96 3 3.000 0.033508772
97 3 3.000 0.028596491
98 3 3.000 0.047368421
99 3 3.000 0.025614035
100 3 3.000 0.049298246
101 3 5.000 0.056842105
102 3 5.000 0.053684211
103 3 5.000 0.048421053
104 3 5.000 0.042631579
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