Final Project
Yonatan Nega
11/27/2021
This project consisted of three parts, conducted throughout this semester. Part 1 is a designed experiment to determine the effect of the type of ball on the distance in which the ball is thrown. Part 2 is a designed experiment to determine the effect of Pin Elevation and Release Angle on distance in which a red ball is thrown when the Bungee Position is fixed at the second position. Settings one and three of Pin Elevation were investigated as a fixed effect, as well as settings of the Release Angle corresponding to 110, 140, and 170 degrees as a random effect. The design was replicated three times. Part 3 is a designed experiment to determine the effect of the available factors of Pin Elevation, Bungee Position, Release Angle, and Ball Type on distance in which a ball is thrown. This experiment was designed as a single replicate of a \(2^4\) factorial design.
Part 1
(1a)
Before collecting data, the number of samples needed for this experiment was determined by using the pwr.anova.test function available in R.
library(pwr)## Warning: package 'pwr' was built under R version 4.0.5pwr.anova.test(k=3,n=NULL,f=0.50*sqrt(3^2-1)/(2*3),sig.level=0.05,power=0.75)##
## Balanced one-way analysis of variance power calculation
##
## k = 3
## n = 52.55574
## f = 0.2357023
## sig.level = 0.05
## power = 0.75
##
## NOTE: n is number in each groupThe number of samples of required for each group is 53
(1b)
library(agricolae)## Warning: package 'agricolae' was built under R version 4.0.5trt1 <- c("ball 1","ball 2", "ball 3")
design<-design.crd(trt=trt1,r=53,seed=8238350)
design$book## plots r trt1
## 1 101 1 ball 2
## 2 102 2 ball 2
## 3 103 1 ball 3
## 4 104 3 ball 2
## 5 105 2 ball 3
## 6 106 4 ball 2
## 7 107 3 ball 3
## 8 108 4 ball 3
## 9 109 5 ball 2
## 10 110 6 ball 2
## 11 111 7 ball 2
## 12 112 1 ball 1
## 13 113 8 ball 2
## 14 114 5 ball 3
## 15 115 6 ball 3
## 16 116 9 ball 2
## 17 117 7 ball 3
## 18 118 10 ball 2
## 19 119 2 ball 1
## 20 120 3 ball 1
## 21 121 11 ball 2
## 22 122 8 ball 3
## 23 123 4 ball 1
## 24 124 9 ball 3
## 25 125 12 ball 2
## 26 126 10 ball 3
## 27 127 11 ball 3
## 28 128 13 ball 2
## 29 129 5 ball 1
## 30 130 12 ball 3
## 31 131 6 ball 1
## 32 132 14 ball 2
## 33 133 7 ball 1
## 34 134 13 ball 3
## 35 135 15 ball 2
## 36 136 8 ball 1
## 37 137 9 ball 1
## 38 138 14 ball 3
## 39 139 10 ball 1
## 40 140 11 ball 1
## 41 141 15 ball 3
## 42 142 16 ball 2
## 43 143 17 ball 2
## 44 144 12 ball 1
## 45 145 16 ball 3
## 46 146 13 ball 1
## 47 147 14 ball 1
## 48 148 17 ball 3
## 49 149 18 ball 3
## 50 150 19 ball 3
## 51 151 18 ball 2
## 52 152 19 ball 2
## 53 153 20 ball 2
## 54 154 21 ball 2
## 55 155 20 ball 3
## 56 156 15 ball 1
## 57 157 16 ball 1
## 58 158 22 ball 2
## 59 159 23 ball 2
## 60 160 24 ball 2
## 61 161 17 ball 1
## 62 162 21 ball 3
## 63 163 25 ball 2
## 64 164 18 ball 1
## 65 165 22 ball 3
## 66 166 19 ball 1
## 67 167 23 ball 3
## 68 168 20 ball 1
## 69 169 24 ball 3
## 70 170 21 ball 1
## 71 171 22 ball 1
## 72 172 25 ball 3
## 73 173 26 ball 3
## 74 174 26 ball 2
## 75 175 23 ball 1
## 76 176 27 ball 3
## 77 177 24 ball 1
## 78 178 27 ball 2
## 79 179 28 ball 3
## 80 180 28 ball 2
## 81 181 29 ball 3
## 82 182 29 ball 2
## 83 183 25 ball 1
## 84 184 26 ball 1
## 85 185 30 ball 2
## 86 186 31 ball 2
## 87 187 27 ball 1
## 88 188 32 ball 2
## 89 189 30 ball 3
## 90 190 31 ball 3
## 91 191 33 ball 2
## 92 192 28 ball 1
## 93 193 32 ball 3
## 94 194 29 ball 1
## 95 195 33 ball 3
## 96 196 30 ball 1
## 97 197 31 ball 1
## 98 198 34 ball 3
## 99 199 32 ball 1
## 100 200 35 ball 3
## 101 201 33 ball 1
## 102 202 36 ball 3
## 103 203 34 ball 2
## 104 204 37 ball 3
## 105 205 34 ball 1
## 106 206 35 ball 1
## 107 207 35 ball 2
## 108 208 36 ball 1
## 109 209 38 ball 3
## 110 210 36 ball 2
## 111 211 37 ball 2
## 112 212 37 ball 1
## 113 213 38 ball 1
## 114 214 38 ball 2
## 115 215 39 ball 1
## 116 216 39 ball 2
## 117 217 39 ball 3
## 118 218 40 ball 3
## 119 219 41 ball 3
## 120 220 40 ball 2
## 121 221 41 ball 2
## 122 222 42 ball 2
## 123 223 43 ball 2
## 124 224 44 ball 2
## 125 225 42 ball 3
## 126 226 40 ball 1
## 127 227 45 ball 2
## 128 228 43 ball 3
## 129 229 41 ball 1
## 130 230 42 ball 1
## 131 231 46 ball 2
## 132 232 43 ball 1
## 133 233 47 ball 2
## 134 234 48 ball 2
## 135 235 49 ball 2
## 136 236 44 ball 1
## 137 237 44 ball 3
## 138 238 45 ball 3
## 139 239 45 ball 1
## 140 240 46 ball 1
## 141 241 47 ball 1
## 142 242 48 ball 1
## 143 243 49 ball 1
## 144 244 50 ball 2
## 145 245 46 ball 3
## 146 246 47 ball 3
## 147 247 51 ball 2
## 148 248 48 ball 3
## 149 249 49 ball 3
## 150 250 50 ball 1
## 151 251 52 ball 2
## 152 252 51 ball 1
## 153 253 50 ball 3
## 154 254 51 ball 3
## 155 255 53 ball 2
## 156 256 52 ball 3
## 157 257 53 ball 3
## 158 258 52 ball 1
## 159 259 53 ball 1After determining how many samples were needed from each population, a completely randomized design (CRD) was developed, with a randomized run order generated from the design.crd function in R
(1c)
The samples were collected using the randomized order determined above. After collecting the samples, a hypothesis test was done below to determine if the ball type affects the distance traveled when the ball is launched from a Statapult. In this test, the null hypothesis is that the mean distance traveled is the same between all groups, and the alternative hypothesis is that at least one mean differs from the others. To perform this hypothesis, ANOVA was performed on the collected data.
(1d)
path <- "C:/Users/Yonatan/OneDrive/Graduate Classes/Fall 2021 Semester Classes/Design of Experiments/Project/Part 1"
setwd(path)
dat <- read.csv("Project1_Part1_corrected.csv",header=TRUE)
dat <- as.data.frame(dat)
colnames(dat) <- c("trt","response")
dat$trt <- as.factor(dat$trt)
dat## trt response
## 1 1 97
## 2 2 87
## 3 3 77
## 4 1 83
## 5 3 67
## 6 2 67
## 7 1 72
## 8 1 106
## 9 3 77
## 10 2 71
## 11 3 69
## 12 2 68
## 13 2 63
## 14 1 114
## 15 1 119
## 16 2 66
## 17 3 75
## 18 2 73
## 19 1 121
## 20 2 65
## 21 3 68
## 22 3 68
## 23 3 65
## 24 3 62
## 25 3 65
## 26 2 69
## 27 2 71
## 28 3 68
## 29 1 100
## 30 3 100
## 31 3 82
## 32 2 83
## 33 1 108
## 34 3 75
## 35 1 106
## 36 1 97
## 37 1 115
## 38 3 117
## 39 3 122
## 40 1 116
## 41 3 74
## 42 2 73
## 43 3 85
## 44 1 106
## 45 2 82
## 46 2 80
## 47 2 75
## 48 2 72
## 49 1 120
## 50 1 114
## 51 2 84
## 52 3 82
## 53 1 114
## 54 1 85
## 55 2 82
## 56 2 80
## 57 2 78
## 58 1 140
## 59 1 115
## 60 2 83
## 61 1 105
## 62 3 87
## 63 2 85
## 64 2 72
## 65 3 87
## 66 2 84
## 67 1 119
## 68 3 108
## 69 1 121
## 70 3 106
## 71 2 86
## 72 3 110
## 73 2 82
## 74 2 84
## 75 2 81
## 76 2 86
## 77 3 90
## 78 2 83
## 79 1 137
## 80 1 132
## 81 3 97
## 82 2 85
## 83 3 95
## 84 2 85
## 85 1 123
## 86 1 130
## 87 1 129
## 88 1 135
## 89 3 115
## 90 1 127
## 91 2 81
## 92 1 135
## 93 2 86
## 94 3 104
## 95 1 136
## 96 3 121
## 97 1 135
## 98 1 137
## 99 2 96
## 100 2 81
## 101 1 134
## 102 1 131
## 103 1 138
## 104 1 136
## 105 1 136
## 106 2 85
## 107 1 134
## 108 3 103
## 109 2 80
## 110 1 134
## 111 2 81
## 112 3 104
## 113 2 82
## 114 3 96
## 115 3 97
## 116 3 94
## 117 3 91
## 118 3 110
## 119 3 89
## 120 3 89
## 121 1 120
## 122 1 118
## 123 1 117
## 124 2 77
## 125 3 104
## 126 2 82
## 127 3 102
## 128 3 108
## 129 2 82
## 130 3 99
## 131 1 98
## 132 2 101
## 133 1 135
## 134 3 116
## 135 2 82
## 136 1 133
## 137 2 89
## 138 1 124
## 139 2 83
## 140 1 136
## 141 2 106
## 142 2 84
## 143 3 104
## 144 3 108
## 145 3 144
## 146 3 107
## 147 1 147
## 148 3 138
## 149 1 126
## 150 1 130
## 151 1 137
## 152 2 85
## 153 3 97
## 154 3 114
## 155 2 87
## 156 2 85
## 157 2 83
## 158 3 109
## 159 3 119model <- aov(response~trt,data=dat)
summary(model)## Df Sum Sq Mean Sq F value Pr(>F)
## trt 2 43844 21922 95 <2e-16 ***
## Residuals 156 35997 231
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1plot(model)
A normal probability plot of the residuals was constructed and from this plot, it was determined that the samples follow a normal distribution. Additionally, the residual plots are of roughly the same width, implying that the variance is nearly constant between the three ball types. Therefore, no variance stabilizing transformations (VST) were performed on the data. From the ANOVA, the P-value was found to be much smaller than 0.05, nearly 0. At a significance level of 0.05, the null hypothesis can be rejected. This means that at least one mean must differ from the other means.
(1e)
To determine which means differ, pairwise comparisons were made using the Tukey HSD method.
TukeyHSD(model,conf.level = 0.95)## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = response ~ trt, data = dat)
##
## $trt
## diff lwr upr p adj
## 2-1 -40.18868 -47.171314 -33.20604 0.0e+00
## 3-1 -25.52830 -32.510936 -18.54567 0.0e+00
## 3-2 14.66038 7.677743 21.64301 5.2e-06 plot(TukeyHSD(model,conf.level = 0.95))
After performing the Tukey HSD test, all the pairs were found to have values that range only in the positive or only in the negative. This implies that the null hypothesis is rejected for all the pairs. This is supported with the p-values of the pairs, which are all much less than 0.05, the confidence level used in this experiment.
(1f)
The p-values determined in this experiment imply that ball type does have an effect on distance travelled. This is further supported by the difference in mean levels of treatment.
Part 2
(2a)
Model Equation: \(y_{ijk}\) = \(\mu\) + \(\alpha_{i}\) + \(\beta_{j}\) + \(\alpha \beta_{ij}\) + \(\epsilon_{ijk}\)
\(H_{0}\): All row treatments are equal, \(\alpha_{i}\) = 0
\(H_{1}\): At least one \(\alpha_{i}\) \(\neq\) 0
\(H_{0}\): All column treatments are equal, \(\beta_{j}\) = 0
\(H_{1}\): At least one \(\beta_{j}\) \(\neq\) 0
\(H_{0}\): (\(\alpha \beta_{ij}\)) = 0 for all i,j
\(H_{1}\): At least one (\(\alpha \beta_{ij}\)) \(\neq\) 0
We assume level of significance to be 0.1.
(2b)
library(agricolae)
trts<-c(2,3)
#Specify the K number of replications (r=3)
design <- design.ab(trt=trts, r=3, design="crd",seed=879879)
design$book## plots r A B
## 1 101 1 2 1
## 2 102 1 1 1
## 3 103 1 2 3
## 4 104 2 2 1
## 5 105 1 2 2
## 6 106 1 1 2
## 7 107 2 2 2
## 8 108 2 1 2
## 9 109 3 1 2
## 10 110 1 1 3
## 11 111 3 2 2
## 12 112 3 2 1
## 13 113 2 1 3
## 14 114 2 1 1
## 15 115 2 2 3
## 16 116 3 1 3
## 17 117 3 1 1
## 18 118 3 2 3Order is lay out in the list above. r denotes replicate. “A” denotes pin location, within which 1 denotes first location from bottom side, 2 denotes the third location from bottom side. “B” denotes degree, within which 1 denotes 110 degree, 2 denotes 140 degree, 3 denotes 170 degree.
(2c)
We collected the data from statapult, listed in the code.
library(GAD)## Warning: package 'GAD' was built under R version 4.0.5## Loading required package: matrixStats## Warning: package 'matrixStats' was built under R version 4.0.5## Loading required package: R.methodsS3## Warning: package 'R.methodsS3' was built under R version 4.0.3## R.methodsS3 v1.8.1 (2020-08-26 16:20:06 UTC) successfully loaded. See ?R.methodsS3 for help.Distance <- c(24,15,73,13.5,37,36,39,38,34,71,43,20,67,16,71,66,15,63)
Pin <- c(3,1,3,3,3,1,3,1,1,1,3,3,1,1,3,1,1,3)
Degree <- c(110,110,170,110,140,140,140,140,140,170,140,110,170,110,170,170,110,170)
Pin <- as.fixed(Pin)
Degree <- as.random(Degree)
model<-aov(Distance~Pin+Degree+Pin*Degree)
GAD::gad(model)## Analysis of Variance Table
##
## Response: Distance
## Df Sum Sq Mean Sq F value Pr(>F)
## Pin 1 36.1 36.1 9.5275 0.09088 .
## Degree 2 7981.4 3990.7 311.9750 4.514e-11 ***
## Pin:Degree 2 7.6 3.8 0.2964 0.74877
## Residual 12 153.5 12.8
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1plot (model)
(2d)
library(dplyr)## Warning: package 'dplyr' was built under R version 4.0.5##
## Attaching package: 'dplyr'## The following object is masked from 'package:matrixStats':
##
## count## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(tidyr)## Warning: package 'tidyr' was built under R version 4.0.5Distance <- c(24,15,73,13.5,37,36,39,38,34,71,43,20,67,16,71,66,15,63)
Pin <- c(3,1,3,3,3,1,3,1,1,1,3,3,1,1,3,1,1,3)
Degree <- c(110,110,170,110,140,140,140,140,140,170,140,110,170,110,170,170,110,170)
dat1 <- cbind(Distance,Pin,Degree)
dat1 <- as.data.frame(dat1)
Dist1<-dat1 %>% filter(Degree==110)%>% filter(Pin==1)
Dist2<-dat1 %>% filter(Degree==110)%>% filter(Pin==3)
Dist3<-dat1 %>% filter(Degree==140)%>% filter(Pin==1)
Dist4<-dat1 %>% filter(Degree==140)%>% filter(Pin==3)
Dist5<-dat1 %>% filter(Degree==170)%>% filter(Pin==1)
Dist6<-dat1 %>% filter(Degree==170)%>% filter(Pin==3)
Dist1 <- Dist1 %>% select(-Degree)%>% select(-Pin)
Dist1 <- as.numeric(Dist1$Distance)
Dist2 <- Dist2 %>% select(-Degree)%>% select(-Pin)
Dist2 <- as.numeric(Dist2$Distance)
Dist3 <- Dist3 %>% select(-Degree)%>% select(-Pin)
Dist3 <- as.numeric(Dist3$Distance)
Dist4 <- Dist4 %>% select(-Degree)%>% select(-Pin)
Dist4 <- as.numeric(Dist4$Distance)
Dist5 <- Dist5 %>% select(-Degree)%>% select(-Pin)
Dist5 <- as.numeric(Dist5$Distance)
Dist6 <- Dist6 %>% select(-Degree)%>% select(-Pin)
Dist6 <- as.numeric(Dist6$Distance)
avg1 <- ave(Dist1)
avg2 <- ave(Dist2)
avg3 <- ave(Dist3)
avg4 <- ave(Dist4)
avg5 <- ave(Dist5)
avg6 <- ave(Dist6)
Deg <- c(110,110,110,140,140,140,170,170,170)
Deg1 <- c(110,110,110)
Deg2<- c(140,140,140)
Deg3 <- c(170,170,170)
plot(Deg, c(Dist1,Dist3,Dist5),main="Scatterplot with average", xlab="Degree",ylab="Distance", pch=19, col="red")
lines(Deg, c(avg1,avg3,avg5), type = "b", col = "red", lwd = 3, pch = 15)
points(Deg,c(Dist2,Dist4,Dist6),pch = 19,col="blue")
lines(Deg, c(avg2,avg4,avg6), type = "b", col = "blue", lwd = 3, pch = 15)
legend(x=110,y=60,c("Pin Location=1","Pin Location=3"),pch=c(19,19),col = c("red","blue"))
Since P-value of Pin:Degree=0.74877 >0.1, fail to reject null hypothesis, no interaction. We also provide the interaction plot desipte it is not required in this case, since we drew the conclusion of no interaction. From the interaction plot, we also know that they are also almost in parallel, we confirm no interaction.
P-value of Degree= 4.514e-11 <0.1, reject null hypothesis, degree has impact on means. P-value of Degree= 0.09088 <0.1, reject null hypothesis, pin location has impact on means. However, this is highly dependent upon the alpha value. If we assume this threshold to be 0.05, pin location impact would turn to be insignificant.
Even if we are required by question to use the raw data regardless of normality and variance constancy, we provide a few insights herein as supplimentary.
From Normality Plot, we can see it passes fat pencil test, so it is normally distributed. From the Residue Plot, we can say, constancy of variance is not perfect but still accepable, but since we only have 3 replicates for each condition, it is recommended to run the experiments for more times to stabalize the redisue plot to boost our confidence of drawing conclusions.
Part 3
(3a)
Data collection layout is listed as in the results.
library(agricolae)
trts<-c(2,2,2,2)
#Specify the K number of replications (r=1)
design <- design.ab(trt=trts, r=1, design="crd",seed=879879)
design$book## plots r A B C D
## 1 101 1 2 1 2 1
## 2 102 1 2 1 1 1
## 3 103 1 1 1 1 1
## 4 104 1 2 1 2 2
## 5 105 1 1 1 2 2
## 6 106 1 2 2 1 1
## 7 107 1 1 2 1 1
## 8 108 1 1 2 1 2
## 9 109 1 1 2 2 1
## 10 110 1 1 1 2 1
## 11 111 1 2 2 1 2
## 12 112 1 2 2 2 2
## 13 113 1 2 1 1 2
## 14 114 1 1 1 1 2
## 15 115 1 1 2 2 2
## 16 116 1 2 2 2 1(3b)
Data are collected as listed in code below.
obs <- c(60,36,29,62,41,37,35,29,48,42,45,71,40,31,53,61)
A <- c(1,1,-1,1,-1,1,-1,-1,-1,-1,1,1,1,-1,-1,1)
B <- c(-1,-1,-1,-1,-1,1,1,1,1,-1,1,1,-1,-1,1,1)
C <- c(1,-1,-1,1,1,-1,-1,-1,1,1,-1,1,-1,-1,1,1)
D <- c(-1,-1,-1,1,1,-1,-1,1,-1,-1,1,1,1,1,1,-1)
library(DoE.base)## Warning: package 'DoE.base' was built under R version 4.0.5## Loading required package: grid## Loading required package: conf.design## Warning: package 'conf.design' was built under R version 4.0.3## Registered S3 method overwritten by 'DoE.base':
## method from
## factorize.factor conf.design##
## Attaching package: 'DoE.base'## The following objects are masked from 'package:stats':
##
## aov, lm## The following object is masked from 'package:graphics':
##
## plot.design## The following object is masked from 'package:base':
##
## lengthsdat1 <- cbind(A,B,C,D,obs)
dat1 <- data.frame(dat1)
mod <- lm(obs~A*B*C*D,data = dat1)
coef(mod)## (Intercept) A B C D A:B
## 45.000 6.500 2.375 9.750 1.500 -0.375
## A:C B:C A:D B:D C:D A:B:C
## 2.250 1.125 1.500 0.625 0.500 -0.625
## A:B:D A:C:D B:C:D A:B:C:D
## 0.875 -0.500 1.125 -0.625halfnormal(mod)##
## Significant effects (alpha=0.05, Lenth method):## [1] C A
### (3c)
model equation: \(y_{ijklm}\) = \(\mu\) + \(\alpha_{i}\) + \(\beta_{j}\) + \(\gamma_{k}\) + \(\delta_{l}\) + \(\alpha \beta_{ij}\) + \(\alpha\gamma_{ik}\) + \(\alpha\delta_{il}\) + \(\beta\gamma_{jk}\) + \(\beta\delta_{jl}\) + \(\gamma\delta_{kl}\) + \(\alpha\beta\gamma_{ijk}\) + \(\alpha\beta\delta_{ijl}\) + \(\alpha\gamma\delta_{ikl}\) + \(\beta\gamma\delta_{jkl}\) + \(\alpha\beta\gamma\delta_{ijkl}\) + \(\epsilon_{ijklm}\)
From the halfnorm plot, we know that A and C has the significance.
dat1$A <- as.factor(dat1$A)
dat1$B <- as.factor(dat1$B)
dat1$C <- as.factor(dat1$C)
dat1$D <- as.factor(dat1$D)
model<-aov(obs~A+C+A*C,data=dat1)
summary(model)## Df Sum Sq Mean Sq F value Pr(>F)
## A 1 676 676.0 33.246 8.94e-05 ***
## C 1 1521 1521.0 74.803 1.68e-06 ***
## A:C 1 81 81.0 3.984 0.0692 .
## Residuals 12 244 20.3
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1(3d)
\(y_{ikm}\) = \(\mu\) + \(\alpha_{i}\) + \(\gamma_{k}\) + \(\alpha\gamma_{ik}\) + \(\epsilon_{ikm}\)
From ANOVA, p(a:c)=0.0692>0.05, so interaction between A and C is not significant. So we investigate the main effect A and C. Since P(A)=8.94e-05<0.05, P(B)=1.68e-06<0.05, they are significant. Both A and C do affect the means.
\(y_{ikm}\) = \(\mu\) + \(\alpha_{i}\) + \(\gamma_{k}\) + \(\epsilon_{ikm}\)
R Code
library(pwr)
pwr.anova.test(k=3,n=NULL,f=0.50*sqrt(3^2-1)/(2*3),sig.level=0.05,power=0.75)
library(agricolae)
trt1 <- c("ball 1","ball 2", "ball 3")
design<-design.crd(trt=trt1,r=53,seed=8238350)
design$book
path <- "C:/Users/Yonatan/OneDrive/Graduate Classes/Fall 2021 Semester Classes/Design of Experiments/Project/Part 1"
setwd(path)
dat <- read.csv("Project1_Part1_corrected.csv",header=TRUE)
dat <- as.data.frame(dat)
colnames(dat) <- c("trt","response")
dat$trt <- as.factor(dat$trt)
dat
model <- aov(response~trt,data=dat)
summary(model)
plot(model)
TukeyHSD(model,conf.level = 0.95)
plot(TukeyHSD(model,conf.level = 0.95))
library(agricolae)
trts<-c(2,3)
#Specify the K number of replications (r=3)
design <- design.ab(trt=trts, r=3, design="crd",seed=879879)
design$book
######
library(GAD)
Distance <- c(24,15,73,13.5,37,36,39,38,34,71,43,20,67,16,71,66,15,63)
Pin <- c(3,1,3,3,3,1,3,1,1,1,3,3,1,1,3,1,1,3)
Degree <- c(110,110,170,110,140,140,140,140,140,170,140,110,170,110,170,170,110,170)
Pin <- as.fixed(Pin)
Degree <- as.random(Degree)
model<-aov(Distance~Pin+Degree+Pin*Degree)
GAD::gad(model)
plot (model)
######
library(dplyr)
library(tidyr)
Distance <- c(24,15,73,13.5,37,36,39,38,34,71,43,20,67,16,71,66,15,63)
Pin <- c(3,1,3,3,3,1,3,1,1,1,3,3,1,1,3,1,1,3)
Degree <- c(110,110,170,110,140,140,140,140,140,170,140,110,170,110,170,170,110,170)
dat1 <- cbind(Distance,Pin,Degree)
dat1 <- as.data.frame(dat1)
Dist1<-dat1 %>% filter(Degree==110)%>% filter(Pin==1)
Dist2<-dat1 %>% filter(Degree==110)%>% filter(Pin==3)
Dist3<-dat1 %>% filter(Degree==140)%>% filter(Pin==1)
Dist4<-dat1 %>% filter(Degree==140)%>% filter(Pin==3)
Dist5<-dat1 %>% filter(Degree==170)%>% filter(Pin==1)
Dist6<-dat1 %>% filter(Degree==170)%>% filter(Pin==3)
Dist1 <- Dist1 %>% select(-Degree)%>% select(-Pin)
Dist1 <- as.numeric(Dist1$Distance)
Dist2 <- Dist2 %>% select(-Degree)%>% select(-Pin)
Dist2 <- as.numeric(Dist2$Distance)
Dist3 <- Dist3 %>% select(-Degree)%>% select(-Pin)
Dist3 <- as.numeric(Dist3$Distance)
Dist4 <- Dist4 %>% select(-Degree)%>% select(-Pin)
Dist4 <- as.numeric(Dist4$Distance)
Dist5 <- Dist5 %>% select(-Degree)%>% select(-Pin)
Dist5 <- as.numeric(Dist5$Distance)
Dist6 <- Dist6 %>% select(-Degree)%>% select(-Pin)
Dist6 <- as.numeric(Dist6$Distance)
avg1 <- ave(Dist1)
avg2 <- ave(Dist2)
avg3 <- ave(Dist3)
avg4 <- ave(Dist4)
avg5 <- ave(Dist5)
avg6 <- ave(Dist6)
Deg <- c(110,110,110,140,140,140,170,170,170)
Deg1 <- c(110,110,110)
Deg2<- c(140,140,140)
Deg3 <- c(170,170,170)
plot(Deg, c(Dist1,Dist3,Dist5),main="Scatterplot with average", xlab="Degree",ylab="Distance", pch=19, col="red")
lines(Deg, c(avg1,avg3,avg5), type = "b", col = "red", lwd = 3, pch = 15)
points(Deg,c(Dist2,Dist4,Dist6),pch = 19,col="blue")
lines(Deg, c(avg2,avg4,avg6), type = "b", col = "blue", lwd = 3, pch = 15)
legend(x=110,y=60,c("Pin Location=1","Pin Location=3"),pch=c(19,19),col = c("red","blue"))
library(agricolae)
trts<-c(2,2,2,2)
#Specify the K number of replications (r=1)
design <- design.ab(trt=trts, r=1, design="crd",seed=879879)
design$book
obs <- c(60,36,29,62,41,37,35,29,48,42,45,71,40,31,53,61)
A <- c(1,1,-1,1,-1,1,-1,-1,-1,-1,1,1,1,-1,-1,1)
B <- c(-1,-1,-1,-1,-1,1,1,1,1,-1,1,1,-1,-1,1,1)
C <- c(1,-1,-1,1,1,-1,-1,-1,1,1,-1,1,-1,-1,1,1)
D <- c(-1,-1,-1,1,1,-1,-1,1,-1,-1,1,1,1,1,1,-1)
library(DoE.base)
dat1 <- cbind(A,B,C,D,obs)
dat1 <- data.frame(dat1)
mod <- lm(obs~A*B*C*D,data = dat1)
coef(mod)
halfnormal(mod)
dat1$A <- as.factor(dat1$A)
dat1$B <- as.factor(dat1$B)
dat1$C <- as.factor(dat1$C)
dat1$D <- as.factor(dat1$D)
model<-aov(obs~A+C+A*C,data=dat1)
summary(model)