EX1
library(readr)
rat <- read_csv("E:/XJTLU/3/S2/ENV222/Friedman test/rats.csv")
library(tidyr)
longrat <- gather(rat, Temp, Speed, -Animal)
friedman.test(longrat$Speed, longrat$Temp, longrat$Animal)
##
## Friedman rank sum test
##
## data: longrat$Speed, longrat$Temp and longrat$Animal
## Friedman chi-squared = 21.95, df = 4, p-value = 0.0002051
pairwise.wilcox.test(longrat$Speed, longrat$Temp,
p.adj="none",
paired=TRUE,
exact=FALSE,
correct=FALSE)
##
## Pairwise comparisons using Wilcoxon signed rank test
##
## data: longrat$Speed and longrat$Temp
##
## ...1 X20C X24C X27C
## X20C 0.028 - - -
## X24C 0.028 0.453 - -
## X27C 0.028 0.026 0.027 -
## X32C 0.028 0.027 0.026 0.336
##
## P value adjustment method: none
## ...1 Animal X20C X24C X27C
## Min. :1.00 Min. :1.00 Min. :25.00 Min. :25.0 Min. :18.00
## 1st Qu.:2.25 1st Qu.:2.25 1st Qu.:29.50 1st Qu.:27.5 1st Qu.:21.00
## Median :3.50 Median :3.50 Median :32.50 Median :31.0 Median :26.50
## Mean :3.50 Mean :3.50 Mean :32.33 Mean :31.5 Mean :25.83
## 3rd Qu.:4.75 3rd Qu.:4.75 3rd Qu.:35.50 3rd Qu.:36.0 3rd Qu.:29.75
## Max. :6.00 Max. :6.00 Max. :39.00 Max. :38.0 Max. :34.00
## X32C
## Min. :19.00
## 1st Qu.:20.50
## Median :23.00
## Mean :24.83
## 3rd Qu.:29.25
## Max. :33.00
#graph
library(ggplot2)
ggplot(longrat)+
geom_point(aes(y=Speed,x=Temp,fill=Temp,shape=Temp,color=Temp))+
geom_hline(aes(yintercept=32.33),color="red",linetype="dashed")+
geom_hline(aes(yintercept=31.5),color="green",linetype="dashed")+
geom_hline(aes(yintercept=25.83),color="blue",linetype="dashed")+
geom_hline(aes(yintercept=24.83),color="purple",linetype="dashed")
#ANOVA
shapiro.test(rat$X20C)
##
## Shapiro-Wilk normality test
##
## data: rat$X20C
## W = 0.99065, p-value = 0.9907
##
## Shapiro-Wilk normality test
##
## data: rat$X24C
## W = 0.92461, p-value = 0.5392
##
## Shapiro-Wilk normality test
##
## data: rat$X27C
## W = 0.95015, p-value = 0.7415
##
## Shapiro-Wilk normality test
##
## data: rat$X32C
## W = 0.8807, p-value = 0.2723
longrat$Animal <- as.factor(longrat$Animal)
longrat$Temp <- as.factor(longrat$Temp)
longrat$Speed <- as.numeric(longrat$Speed)
str(longrat)
## tibble [30 x 3] (S3: tbl_df/tbl/data.frame)
## $ Animal: Factor w/ 6 levels "1","2","3","4",..: 1 2 3 4 5 6 1 2 3 4 ...
## $ Temp : Factor w/ 5 levels "...1","X20C",..: 1 1 1 1 1 1 2 2 2 2 ...
## $ Speed : num [1:30] 1 2 3 4 5 6 39 29 36 25 ...
attach(longrat)
library(ez)
model <- ezANOVA(longrat, dv = Speed, wid = Animal, within = Temp, type = 2,detailed = T)
model
## $ANOVA
## Effect DFn DFd SSn SSd F p p<.05 ges
## 1 (Intercept) 1 5 16708.8 440 189.87273 3.613664e-05 * 0.9624441
## 2 Temp 4 20 3295.2 212 77.71698 6.770175e-12 * 0.8348196
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 Temp 0.03552377 0.3019756
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF] p[HF]<.05
## 2 Temp 0.4663298 1.787575e-06 * 0.7330824 3.39521e-09 *
EX2
cancer <- read_csv("E:/XJTLU/3/S2/ENV222/Friedman test/cancer.csv")
longcancer <- gather(cancer, time, PSA, -Patient_no)
friedman.test(longcancer$PSA, longcancer$time, longcancer$Patient_no)
##
## Friedman rank sum test
##
## data: longcancer$PSA, longcancer$time and longcancer$Patient_no
## Friedman chi-squared = 4.0787, df = 3, p-value = 0.2531
pairwise.wilcox.test(longcancer$PSA, longcancer$time,
p.adj="none",
paired=TRUE,
exact=FALSE,
correct=FALSE)
##
## Pairwise comparisons using Wilcoxon signed rank test
##
## data: longcancer$PSA and longcancer$time
##
## ...1 First_PSA_ng_ml Second_PSA_ng_ml
## First_PSA_ng_ml 0.066 - -
## Second_PSA_ng_ml 0.110 0.214 -
## Third_PSA_ng_ml 0.374 0.374 0.327
##
## P value adjustment method: none
## ...1 Patient_no First_PSA_ng_ml Second_PSA_ng_ml Third_PSA_ng_ml
## Min. :1 Min. :1 Min. :0.620 Min. :0.300 Min. : 0.100
## 1st Qu.:3 1st Qu.:3 1st Qu.:1.800 1st Qu.:1.670 1st Qu.: 0.420
## Median :5 Median :5 Median :1.800 Median :2.100 Median : 2.540
## Mean :5 Mean :5 Mean :2.424 Mean :2.947 Mean : 3.604
## 3rd Qu.:7 3rd Qu.:7 3rd Qu.:3.700 3rd Qu.:3.950 3rd Qu.: 4.950
## Max. :9 Max. :9 Max. :3.900 Max. :7.680 Max. :13.500
#graph
library(ggplot2)
ggplot(longcancer)+
geom_point(aes(y=PSA,x=time,fill=time,shape=time,color=time))+
geom_hline(aes(yintercept=2.424),color="red",linetype="dashed")+
geom_hline(aes(yintercept=2.947),color="green",linetype="dashed")+
geom_hline(aes(yintercept=3.604),color="blue",linetype="dashed")
#ANOVA
shapiro.test(cancer$First_PSA_ng_ml)
##
## Shapiro-Wilk normality test
##
## data: cancer$First_PSA_ng_ml
## W = 0.84226, p-value = 0.06119
shapiro.test(cancer$Second_PSA_ng_ml)
##
## Shapiro-Wilk normality test
##
## data: cancer$Second_PSA_ng_ml
## W = 0.91631, p-value = 0.3626
shapiro.test(cancer$Third_PSA_ng_ml)
##
## Shapiro-Wilk normality test
##
## data: cancer$Third_PSA_ng_ml
## W = 0.80817, p-value = 0.0253
longcancer$Patient_no <- as.factor(longcancer$Patient_no)
longcancer$time <- as.factor(longcancer$time)
longcancer$PSA <- as.numeric(longcancer$PSA)
str(longcancer)
## tibble [36 x 3] (S3: tbl_df/tbl/data.frame)
## $ Patient_no: Factor w/ 9 levels "1","2","3","4",..: 1 2 3 4 5 6 7 8 9 1 ...
## $ time : Factor w/ 4 levels "...1","First_PSA_ng_ml",..: 1 1 1 1 1 1 1 1 1 2 ...
## $ PSA : num [1:36] 1 2 3 4 5 6 7 8 9 3.9 ...
attach(longcancer)
library(ez)
model <- ezANOVA(longcancer, dv = PSA, wid = Patient_no, within = time, type = 2, detailed = T)
model
## $ANOVA
## Effect DFn DFd SSn SSd F p p<.05 ges
## 1 (Intercept) 1 8 439.46134 116.8805 30.079372 0.0005843641 * 0.6201755
## 2 time 3 24 33.51381 152.2662 1.760801 0.1815276068 0.1107307
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 time 0.04575848 0.001044556 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF] p[HF]<.05
## 2 time 0.5523613 0.210953 0.6786445 0.2028351