R version 4.0.4 (2021-02-15) -- "Lost Library Book"
Copyright (C) 2021 The R Foundation for Statistical Computing
dataset<-read.table(file="C:/Users/clsgsr12/Desktop/EXERCISES.csv", header=TRUE, sep=",")
attach(dataset)
summary(dataset)
# GROUP GENDER AGE PREOP_CCT POSTOP_CCT_1M
# Min. :1.0 Min. :1.000 Min. :21.00 Min. :378.0 Min. :493.0
# 1st Qu.:1.0 1st Qu.:1.000 1st Qu.:27.00 1st Qu.:397.0 1st Qu.:509.0
# Median :1.5 Median :1.000 Median :33.50 Median :470.0 Median :518.0
# Mean :1.5 Mean :1.422 Mean :33.14 Mean :459.3 Mean :518.1
# 3rd Qu.:2.0 3rd Qu.:2.000 3rd Qu.:39.00 3rd Qu.:518.0 3rd Qu.:527.0
# Max. :2.0 Max. :2.000 Max. :45.00 Max. :541.0 Max. :541.0
# SMOKING_STATUS BMI
# Min. :1.000 Min. :18.90
# 1st Qu.:1.000 1st Qu.:22.55
# Median :2.000 Median :24.90
# Mean :1.967 Mean :24.61
# 3rd Qu.:3.000 3rd Qu.:26.40
# Max. :3.000 Max. :32.40
dataset<-transform(dataset, GROUP=factor(GROUP, labels=c("STUDY", "CONTROL")), GENDER=factor(GENDER, labels=c("MALE", "FEMALE")), SMOKING_STATUS=factor(SMOKING_STATUS, labels=c("NEVER SMOKER", "CURRENT SMOKER", "EX-SMOKER")))
summary(dataset)
# GROUP GENDER AGE PREOP_CCT POSTOP_CCT_1M
# STUDY :45 MALE :52 Min. :21.00 Min. :378.0 Min. :493.0
# CONTROL:45 FEMALE:38 1st Qu.:27.00 1st Qu.:397.0 1st Qu.:509.0
# Median :33.50 Median :470.0 Median :518.0
# Mean :33.14 Mean :459.3 Mean :518.1
# 3rd Qu.:39.00 3rd Qu.:518.0 3rd Qu.:527.0
# Max. :45.00 Max. :541.0 Max. :541.0
# SMOKING_STATUS BMI
# NEVER SMOKER :32 Min. :18.90
# CURRENT SMOKER:29 1st Qu.:22.55
# EX-SMOKER :29 Median :24.90
# Mean :24.61
# 3rd Qu.:26.40
# Max. :32.40
#####################################################
###GROUP VS GENDER
GROUP.GENDER<-table(GROUP, GENDER)
GROUP.GENDER
# GENDER
#GROUP 1 2
# 1 32 13
# 2 20 25
prop.table(GROUP.GENDER, 1)
# GENDER
#GROUP 1 2
# 1 0.7111111 0.2888889
# 2 0.4444444 0.5555556
chisq.test(GROUP.GENDER)
# Pearson's Chi-squared test with Yates' continuity correction
#data: GROUP.GENDER
#X-squared = 5.5111, df = 1, p-value = 0.0189
fisher.test(GROUP.GENDER)
# Fisher's Exact Test for Count Data
#data: GROUP.GENDER
#p-value = 0.01835
#alternative hypothesis: true odds ratio is not equal to 1
#95 percent confidence interval:
# 1.183925 8.107478
#sample estimates:
#odds ratio
3.0371
###GROUP VS SMOKING_STATUS
GROUP.SMOKING_STATUS<-table(GROUP, SMOKING_STATUS)
GROUP.SMOKING_STATUS
# SMOKING_STATUS
#GROUP 1 2 3
# 1 16 15 14
# 2 16 14 15
#Frequency
prop.table(GROUP.SMOKING_STATUS, 1)
# SMOKING_STATUS
#GROUP 1 2 3
# 1 0.3555556 0.3333333 0.3111111
# 2 0.3555556 0.3111111 0.3333333
chisq.test(GROUP.SMOKING_STATUS)
# Pearson's Chi-squared test
#data: GROUP.SMOKING_STATUS
#X-squared = 0.068966, df = 2, p-value = 0.9661
###GENDER VS SMOKING_STATUS
GENDER.SMOKING_STATUS<-table(GENDER,SMOKING_STATUS)
GENDER.SMOKING_STATUS
# SMOKING_STATUS
#GENDER 1 2 3
# 1 21 12 19
# 2 11 17 10
#Frequency
prop.table(GENDER.SMOKING_STATUS, 1)
# SMOKING_STATUS
#GENDER 1 2 3
# 1 0.4038462 0.2307692 0.3653846
# 2 0.2894737 0.4473684 0.2631579
chisq.test(GENDER.SMOKING_STATUS)
# Pearson's Chi-squared test
#data: GENDER.SMOKING_STATUS
#X-squared = 4.7165, df = 2, p-value = 0.09458
###Normality Test
# tapply(AGE, GROUP, shapiro.test)
#$`1`
# Shapiro-Wilk normality test
#data: X[[i]]
#W = 0.93537, p-value = 0.01459
#$`2`
# Shapiro-Wilk normality test
#data: X[[i]]
#W = 0.93621, p-value = 0.01565
##Wilcoxon rank test
wilcox.test(AGE~GROUP)
# Wilcoxon rank sum test with continuity correction
#data: AGE by GROUP
#W = 990.5, p-value = 0.8621
#alternative hypothesis: true location shift is not equal to 0
#Warning message:
#In wilcox.test.default(x = c(24L, 29L, 40L, 26L, 33L, 37L, 22L, :
cannot compute exact p-value with ties
##Summary
tapply(AGE,GROUP,mean)
# 1 2
#33.00000 33.28889
tapply(AGE,GROUP,sd)
# 1 2
#7.019453 7.111521
xbarA<-tapply(AGE,GROUP,mean)
sA<-tapply(AGE,GROUP,sd)
nA<-tapply(AGE,GROUP,length)
mA<-tapply(AGE,GROUP, min)
maA<-tapply(AGE,GROUP, max)
cbind(mean=xbarA, std.dev=sA, n=nA, min=mA, max=maA)
# mean std.dev n min max
#1 33.00000 7.019453 45 21 44
#2 33.28889 7.111521 45 21 45
######################################################
###Normality Test
tapply(BMI, GROUP, shapiro.test)
#$`1`
# Shapiro-Wilk normality test
#data: X[[i]]
#W = 0.96637, p-value = 0.2128
#$`2`
# Shapiro-Wilk normality test
#data: X[[i]]
#W = 0.96988, p-value = 0.2868
#Varyans Test
var.test(BMI~GROUP)
# F test to compare two variances
#data: BMI by GROUP
#F = 0.71165, num df = 44, denom df = 44, p-value = 0.2631
#alternative hypothesis: true ratio of variances is not equal to 1
#95 percent confidence interval:
# 0.3910805 1.2949979
#sample estimates:
#ratio of variances
# 0.7116519
#Independent T Test
t.test(BMI~GROUP, var.equal=T)
# Two Sample t-test
#data: BMI by GROUP
#t = -0.015689, df = 88, p-value = 0.9875
#alternative hypothesis: true difference in means is not equal to 0
#95 percent confidence interval:
# -1.134835 1.117057
#sample estimates:
#mean in group 1 mean in group 2
# 24.60444 24.61333
#Summary
tapply(BMI,GROUP,mean)
# 1 2
#24.60444 24.61333
tapply(BMI,GROUP,sd)
# 1 2
#2.450692 2.905058
xbarBm<-tapply(BMI,GROUP,mean)
sBm<-tapply(BMI,GROUP,sd)
nBm<-tapply(BMI,GROUP,length)
mBm<-tapply(BMI,GROUP, min)
maBm<-tapply(BMI,GROUP, max)
cbind(mean=xbarBm, std.dev=sBm, n=nBm, min=mBm, max=maBm)
# mean std.dev n min max
#1 24.60444 2.450692 45 19.4 32.4
#2 24.61333 2.905058 45 18.9 30.2
######################################################
###PAIRED T TEST
shapiro.test(dataset$PREOP_CCT)
# Shapiro-Wilk normality test
#data: dataset$PREOP_CCT
#W = 0.80609, p-value = 1.578e-09
shapiro.test(dataset$POSTOP_CCT_1M)
# Shapiro-Wilk normality test
#data: dataset$POSTOP_CCT_1M
#W = 0.97366, p-value = 0.0642
wilcox.test(PREOP_CCT, POSTOP_CCT_1M, paired=T)
# Wilcoxon signed rank test with continuity correction
#data: PREOP_CCT and POSTOP_CCT_1M
#V = 1, p-value = 3.863e-09
#alternative hypothesis: true location shift is not equal to 0
#Warning messages:
#1: In wilcox.test.default(PREOP_CCT, POSTOP_CCT_1M, paired = T) :
# cannot compute exact p-value with ties
#2: In wilcox.test.default(PREOP_CCT, POSTOP_CCT_1M, paired = T) :
# cannot compute exact p-value with zeroes
summary(PREOP_CCT)
# Min. 1st Qu. Median Mean 3rd Qu. Max.
# 378.0 397.0 470.0 459.3 518.0 541.0
summary(POSTOP_CCT_1M)
# Min. 1st Qu. Median Mean 3rd Qu. Max.
# 493.0 509.0 518.0 518.1 527.0 541.0
###ANOVA
tapply(BMI, SMOKING_STATUS, shapiro.test)
#$`1`
# Shapiro-Wilk normality test
#data: X[[i]]
#W = 0.97169, p-value = 0.5473
#$`2`
# Shapiro-Wilk normality test
#data: X[[i]]
#W = 0.94353, p-value = 0.1241
#$`3`
# Shapiro-Wilk normality test
#data: X[[i]]
#W = 0.97065, p-value = 0.5775
anova(lm(BMI~SMOKING_STATUS))
#Analysis of Variance Table
#Response: BMI
# Df Sum Sq Mean Sq F value Pr(>F)
#SMOKING_STATUS 1 0.00 0.0003 0 0.9952
#Residuals 88 635.59 7.2226
aov(formula = lm(BMI~SMOKING_STATUS))
#Call:
#aov(formula = lm(BMI ~ SMOKING_STATUS))
#Terms:
# SMOKING_STATUS Residuals
#Sum of Squares 0.0003 635.5926
#Deg. of Freedom 1 88
#Residual standard error: 2.687498
#Estimated effects may be unbalanced
##Coefficients
lm(formula = BMI~SMOKING_STATUS)
#Call:
#lm(formula = BMI ~ SMOKING_STATUS)
#Coefficients:
# (Intercept) SMOKING_STATUS
# 24.60480 0.00208
##Homogeneity of Variances(Bartlett test or Levene test )
bartlett.test(BMI~SMOKING_STATUS)
# Bartlett test of homogeneity of variances
#data: BMI by SMOKING_STATUS
#Bartlett's K-squared = 1.0775, df = 2, p-value = 0.5835
##Post hoc Test
pairwise.t.test(dataset$BMI, dataset$SMOKING_STATUS, p.adjust.method = "bonferroni")
# Pairwise comparisons using t tests with pooled SD
#data: dataset$BMI and dataset$SMOKING_STATUS
# NEVER SMOKER CURRENT SMOKER
#CURRENT SMOKER 1 -
#EX-SMOKER 1 1
#P value adjustment method: bonferroni
##Summary
tapply(BMI, SMOKING_STATUS, sd)
# 1 2 3
#2.412835 2.808739 2.891780
tapply(BMI, SMOKING_STATUS, mean)
# 1 2 3
#24.58750 24.65172 24.58966
xbarBS<-tapply(BMI, SMOKING_STATUS,mean)
sBS<-tapply(BMI, SMOKING_STATUS,sd)
nBS<-tapply(BMI, SMOKING_STATUS,length)
mBS<-tapply(BMI, SMOKING_STATUS, min)
maBS<-tapply(BMI, SMOKING_STATUS, max)
cbind(mean=xbarBS, std.dev=sBS, n=nBS, min=mBS, max=maBS)
# mean std.dev n min max
#1 24.58750 2.412835 32 20.2 30.2
#2 24.65172 2.808739 29 19.4 32.4
#3 24.58966 2.891780 29 18.9 30.1
########################################################
#CORRELATION & SIMPLE LINEAR REGRESSION
shapiro.test(dataset$AGE)
# Shapiro-Wilk normality test
#data: dataset$AGE
#W = 0.93759, p-value = 0.0003098
shapiro.test(dataset$BMI)
# Shapiro-Wilk normality test
#data: dataset$BMI
#W = 0.98085, p-value = 0.207
##Correlation
cor.test(BMI,AGE,method="spearman")
# Spearman's rank correlation rho
#data: BMI and AGE
#S = 26463, p-value < 2.2e-16
#alternative hypothesis: true rho is not equal to 0
#sample estimates:
# rho
#0.7821707
#Warning message:
#In cor.test.default(BMI, AGE, method = "spearman") :
# Cannot compute exact p-value with ties
##Simple Linear Regression
lm(BMI~AGE)
#Call:
#lm(formula = BMI ~ AGE)
#Coefficients:
#(Intercept) AGE
# 15.1810 0.2844
summary(lm(BMI~AGE))
#Call:
#lm(formula = BMI ~ AGE)
#Residuals:
# Min 1Q Median 3Q Max
#-4.8145 -1.0200 -0.2934 0.9077 5.8456
#Coefficients:
# Estimate Std. Error t value Pr(>|t|)
#(Intercept) 15.18101 0.91136 16.66 <2e-16 ***
#AGE 0.28445 0.02691 10.57 <2e-16 ***
#---
#Signif. codes: 0 �***� 0.001 �**� 0.01 �*� 0.05 �.� 0.1 � � 1
#Residual standard error: 1.784 on 88 degrees of freedom
#Multiple R-squared: 0.5595, Adjusted R-squared: 0.5545
#F-statistic: 111.8 on 1 and 88 DF, p-value: < 2.2e-16
lm.velo <- lm(BMI~AGE)
lm.velo
#Call:
#lm(formula = BMI ~ AGE)
#Coefficients:
#(Intercept) AGE
# 15.1810 0.2844
###Fitted ValueS
predict(lm.velo,int="c")
# fit lwr upr
#1 22.00777 21.39240 22.62313
#2 23.43001 22.99559 23.86443
#3 26.55894 26.03551 27.08237
#4 22.57666 22.04231 23.11102
#5 24.56780 24.19407 24.94153
#6 25.70559 25.27885 26.13234
#7 21.43887 20.73554 22.14221
#8 24.85225 24.47581 25.22869
#9 27.69673 27.00643 28.38703
#10 22.57666 22.04231 23.11102
#11 26.55894 26.03551 27.08237
#12 25.42115 25.01751 25.82479
#13 24.56780 24.19407 24.94153
#14 25.99004 25.53505 26.44503
#15 22.86111 22.36357 23.35865
#16 27.69673 27.00643 28.38703
#17 23.14556 22.68159 23.60954
#18 23.14556 22.68159 23.60954
#19 26.27449 25.78701 26.76197
#20 22.00777 21.39240 22.62313
#21 26.55894 26.03551 27.08237
#22 22.86111 22.36357 23.35865
#23 26.27449 25.78701 26.76197
#24 23.43001 22.99559 23.86443
#25 25.13670 24.75010 25.52329
#26 25.70559 25.27885 26.13234
#27 22.57666 22.04231 23.11102
#28 21.15442 20.40525 21.90360
#29 22.00777 21.39240 22.62313
#30 25.42115 25.01751 25.82479
#31 27.12784 26.52467 27.73100
#32 23.14556 22.68159 23.60954
#33 24.56780 24.19407 24.94153
#34 25.99004 25.53505 26.44503
#35 23.71446 23.30473 24.12419
#36 25.13670 24.75010 25.52329
#37 21.72332 21.06467 22.38197
#38 23.14556 22.68159 23.60954
#39 22.57666 22.04231 23.11102
#40 27.12784 26.52467 27.73100
#41 22.29222 21.71842 22.86602
#42 27.69673 27.00643 28.38703
#43 27.69673 27.00643 28.38703
#44 26.84339 26.28122 27.40556
#45 26.55894 26.03551 27.08237
#46 27.12784 26.52467 27.73100
#47 25.99004 25.53505 26.44503
#48 22.86111 22.36357 23.35865
#49 24.56780 24.19407 24.94153
#50 25.13670 24.75010 25.52329
#51 26.27449 25.78701 26.76197
#52 22.00777 21.39240 22.62313
#53 25.99004 25.53505 26.44503
#54 26.84339 26.28122 27.40556
#55 22.00777 21.39240 22.62313
#56 22.00777 21.39240 22.62313
#57 26.84339 26.28122 27.40556
#58 26.84339 26.28122 27.40556
#59 23.99891 23.60806 24.38975
#60 25.42115 25.01751 25.82479
#61 27.41228 26.76629 28.05827
#62 21.43887 20.73554 22.14221
#63 27.12784 26.52467 27.73100
#64 25.99004 25.53505 26.44503
#65 24.28335 23.90473 24.66198
#66 26.27449 25.78701 26.76197
#67 25.99004 25.53505 26.44503
#68 22.86111 22.36357 23.35865
#69 21.15442 20.40525 21.90360
#70 25.70559 25.27885 26.13234
#71 25.13670 24.75010 25.52329
#72 21.72332 21.06467 22.38197
#73 24.85225 24.47581 25.22869
#74 26.27449 25.78701 26.76197
#75 22.00777 21.39240 22.62313
#76 23.71446 23.30473 24.12419
#77 22.29222 21.71842 22.86602
#78 23.14556 22.68159 23.60954
#79 23.43001 22.99559 23.86443
#80 22.57666 22.04231 23.11102
#81 27.69673 27.00643 28.38703
#82 27.98118 27.24535 28.71701
#83 23.99891 23.60806 24.38975
#84 22.00777 21.39240 22.62313
#85 23.99891 23.60806 24.38975
#86 26.27449 25.78701 26.76197
#87 26.55894 26.03551 27.08237
#88 27.41228 26.76629 28.05827
#89 23.43001 22.99559 23.86443
#90 22.57666 22.04231 23.11102