Study: insecticide exposure results in increased levels of octopamine, demonstrated by a normal distribution.

1 - 3

treatment <- rnorm(n=30, mean=0, sd=1)
print(treatment)
##  [1]  1.22807429  0.42376645 -0.22337402 -0.57126069 -0.75398514 -0.17110028
##  [7] -0.67205841  1.52212995  0.10758333  0.31686733 -0.96869836 -0.39585329
## [13]  0.75384338  0.72968028 -0.26508610 -1.18146527 -1.09965968 -1.51453182
## [19] -0.69477996 -0.73027348 -0.07977261  0.75370980 -0.66585257 -0.01131366
## [25]  1.20604629 -0.05311278  0.48752228  0.16805724 -0.73123679  0.37960820
control<- rnorm(n=30, mean=0, sd=1)
print(control)
##  [1]  1.808398037  1.249693869  0.624341899  1.155743578 -1.398841210
##  [6] -0.324842981  0.199575032 -0.618993662 -0.390432297  0.534496026
## [11] -0.834429341 -0.137810383 -0.400486383  0.687891754  0.395392612
## [16] -0.484420929 -0.259640577  0.632945568  0.012875113  0.667856958
## [21]  1.043437539  0.305397540  1.150048870  0.792678215  0.123982010
## [26]  2.339817336  0.583287628 -0.005730008 -0.693668971  0.942790014
octopamine_data <- c(treatment, control)
print(octopamine_data)
##  [1]  1.228074285  0.423766452 -0.223374023 -0.571260687 -0.753985144
##  [6] -0.171100277 -0.672058413  1.522129950  0.107583327  0.316867334
## [11] -0.968698359 -0.395853293  0.753843384  0.729680279 -0.265086100
## [16] -1.181465266 -1.099659677 -1.514531819 -0.694779956 -0.730273483
## [21] -0.079772615  0.753709798 -0.665852571 -0.011313655  1.206046293
## [26] -0.053112782  0.487522283  0.168057235 -0.731236794  0.379608203
## [31]  1.808398037  1.249693869  0.624341899  1.155743578 -1.398841210
## [36] -0.324842981  0.199575032 -0.618993662 -0.390432297  0.534496026
## [41] -0.834429341 -0.137810383 -0.400486383  0.687891754  0.395392612
## [46] -0.484420929 -0.259640577  0.632945568  0.012875113  0.667856958
## [51]  1.043437539  0.305397540  1.150048870  0.792678215  0.123982010
## [56]  2.339817336  0.583287628 -0.005730008 -0.693668971  0.942790014
octopamine_data <- data.frame(octopamine_data)
print(octopamine_data)
##    octopamine_data
## 1      1.228074285
## 2      0.423766452
## 3     -0.223374023
## 4     -0.571260687
## 5     -0.753985144
## 6     -0.171100277
## 7     -0.672058413
## 8      1.522129950
## 9      0.107583327
## 10     0.316867334
## 11    -0.968698359
## 12    -0.395853293
## 13     0.753843384
## 14     0.729680279
## 15    -0.265086100
## 16    -1.181465266
## 17    -1.099659677
## 18    -1.514531819
## 19    -0.694779956
## 20    -0.730273483
## 21    -0.079772615
## 22     0.753709798
## 23    -0.665852571
## 24    -0.011313655
## 25     1.206046293
## 26    -0.053112782
## 27     0.487522283
## 28     0.168057235
## 29    -0.731236794
## 30     0.379608203
## 31     1.808398037
## 32     1.249693869
## 33     0.624341899
## 34     1.155743578
## 35    -1.398841210
## 36    -0.324842981
## 37     0.199575032
## 38    -0.618993662
## 39    -0.390432297
## 40     0.534496026
## 41    -0.834429341
## 42    -0.137810383
## 43    -0.400486383
## 44     0.687891754
## 45     0.395392612
## 46    -0.484420929
## 47    -0.259640577
## 48     0.632945568
## 49     0.012875113
## 50     0.667856958
## 51     1.043437539
## 52     0.305397540
## 53     1.150048870
## 54     0.792678215
## 55     0.123982010
## 56     2.339817336
## 57     0.583287628
## 58    -0.005730008
## 59    -0.693668971
## 60     0.942790014

Justifications:

4 - 5

one.way <- aov(treatment ~ control, data = octopamine_data)
summary(one.way)
##             Df Sum Sq Mean Sq F value Pr(>F)
## control      1  0.784  0.7844   1.363  0.253
## Residuals   28 16.115  0.5755

6

treatmenti <- rnorm(n=10, mean=0, sd=1)
print(treatment)
##  [1]  1.22807429  0.42376645 -0.22337402 -0.57126069 -0.75398514 -0.17110028
##  [7] -0.67205841  1.52212995  0.10758333  0.31686733 -0.96869836 -0.39585329
## [13]  0.75384338  0.72968028 -0.26508610 -1.18146527 -1.09965968 -1.51453182
## [19] -0.69477996 -0.73027348 -0.07977261  0.75370980 -0.66585257 -0.01131366
## [25]  1.20604629 -0.05311278  0.48752228  0.16805724 -0.73123679  0.37960820
controli<- rnorm(n=10, mean=0, sd=1)
print(control)
##  [1]  1.808398037  1.249693869  0.624341899  1.155743578 -1.398841210
##  [6] -0.324842981  0.199575032 -0.618993662 -0.390432297  0.534496026
## [11] -0.834429341 -0.137810383 -0.400486383  0.687891754  0.395392612
## [16] -0.484420929 -0.259640577  0.632945568  0.012875113  0.667856958
## [21]  1.043437539  0.305397540  1.150048870  0.792678215  0.123982010
## [26]  2.339817336  0.583287628 -0.005730008 -0.693668971  0.942790014
octopamine_datai <- c(treatmenti, controli)
print(octopamine_datai)
##  [1]  1.98622358 -0.27252682 -0.61515801  0.73185524 -3.61760935 -1.50488888
##  [7] -0.17640761 -0.43322014 -1.13223687  1.48959746 -0.27103042  0.02801763
## [13] -0.71846892  1.18262578  0.18985322  0.34375992  0.70582111  0.39809882
## [19]  0.22003534 -0.58194906
octopamine_datai <- data.frame(octopamine_datai)

one.wayi <- aov(treatment ~ control, data = octopamine_datai)
summary(one.wayi)
##             Df Sum Sq Mean Sq F value Pr(>F)
## control      1  0.784  0.7844   1.363  0.253
## Residuals   28 16.115  0.5755
for (i in octopamine_datai) {
  cat (runif(1), "\n")
}
## 0.01515622
for (i in octopamine_datai) {
  cat (runif(5), "\n")
}
## 0.8156116 0.6802734 0.5510175 0.2583638 0.4207502
for (i in octopamine_datai) {
  cat (runif(10), "\n")
}
## 0.3685087 0.7696729 0.3298483 0.4318846 0.07244364 0.7967316 0.2404264 0.4015762 0.3818391 0.4887981
for (i in octopamine_datai) {
  cat (runif(30), "\n")
}
## 0.3958549 0.3203885 0.9892471 0.005579167 0.02033918 0.7322405 0.03463807 0.6756334 0.9530099 0.3855874 0.5998217 0.2839669 0.6450383 0.3299902 0.5071298 0.05546348 0.36545 0.633249 0.4544673 0.3700083 0.1479238 0.2483389 0.05622335 0.8845427 0.9059982 0.60044 0.2591906 0.03934832 0.750318 0.4616841

5 samples is the smallest effective size needed to detect a significant pattern between the treatment and control.

7

for (i in octopamine_data) {
  cat (runif(1), "\n")
}
## 0.4425168
for (i in octopamine_data) {
  cat (runif(5), "\n")
}
## 0.125999 0.5320762 0.2821024 0.08010607 0.6181827
for (i in octopamine_data) {
  cat (runif(10), "\n")
}
## 0.4034153 0.5853156 0.1404649 0.6741628 0.9390835 0.1319064 0.9907421 0.9560928 0.8396608 0.6617118
for (i in octopamine_data) {
  cat (runif(30), "\n")
}
## 0.4827558 0.07852272 0.3077129 0.1807701 0.6742155 0.6598326 0.06910303 0.02597065 0.2857935 0.6956938 0.9027163 0.6446036 0.1312227 0.1625797 0.3647439 0.5952584 0.3321078 0.8540156 0.7283407 0.1809591 0.09919512 0.5392613 0.5247298 0.04480236 0.3683639 0.3966282 0.7542446 0.2295815 0.6075128 0.01814592

5 samples is the smallest effective size needed to detect a significant pattern between the treatment and control that were originally hypothesized.