Thursday, February 7, 2019

Basic of R- Session Hypothesis testing

# Data set MBAper, location of the dataset
data1<-read.csv("file:///C:/Users/LENOVO/Desktop/MBAdata.csv")

summary and descriptive statistics

descriptive statistics

t-test

str(data1$Gender)
##  Factor w/ 2 levels "Female","Male": 1 1 1 2 2 2 2 1 2 2 ...
# one sample t-test

# t.test(y,mu=50) # Ho: mu=50

t.test(data1$Percentage_in_10_Class, mu=80)
## 
##  One Sample t-test
## 
## data:  data1$Percentage_in_10_Class
## t = 6.5793, df = 272, p-value = 2.417e-10
## alternative hypothesis: true mean is not equal to 80
## 95 percent confidence interval:
##  82.32584 84.31211
## sample estimates:
## mean of x 
##  83.31897

independent 2-group t-test

# t.test(y~x) # where y is numeric and x is a binary factor

t.test(data1$Age_in_years_completed~data1$Gender)
## 
##  Welch Two Sample t-test
## 
## data:  data1$Age_in_years_completed by data1$Gender
## t = -2.0978, df = 246.26, p-value = 0.03694
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.83004766 -0.02616149
## sample estimates:
## mean in group Female   mean in group Male 
##             22.16667             22.59477
t.test(data1$Percentage_in_10_Class~data1$Gender)
## 
##  Welch Two Sample t-test
## 
## data:  data1$Percentage_in_10_Class by data1$Gender
## t = 3.5962, df = 266.85, p-value = 0.0003846
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  1.596708 5.460344
## sample estimates:
## mean in group Female   mean in group Male 
##             85.29650             81.76797
t.test(data1$Percentage_in_12_Class~data1$Gender)
## 
##  Welch Two Sample t-test
## 
## data:  data1$Percentage_in_12_Class by data1$Gender
## t = 4.7554, df = 264.43, p-value = 3.259e-06
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  3.114591 7.516383
## sample estimates:
## mean in group Female   mean in group Male 
##             83.54483             78.22935
t.test(data1$Percentage_in_Under_Graduate~data1$Gender)
## 
##  Welch Two Sample t-test
## 
## data:  data1$Percentage_in_Under_Graduate by data1$Gender
## t = 5.0318, df = 246.04, p-value = 9.381e-07
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  2.735661 6.254914
## sample estimates:
## mean in group Female   mean in group Male 
##             75.86800             71.37271
#-----------------------------------------------#

t.test(data1$Age_in_years_completed~data1$Gender, alternative=c("two.sided"))
## 
##  Welch Two Sample t-test
## 
## data:  data1$Age_in_years_completed by data1$Gender
## t = -2.0978, df = 246.26, p-value = 0.03694
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.83004766 -0.02616149
## sample estimates:
## mean in group Female   mean in group Male 
##             22.16667             22.59477
t.test(data1$Age_in_years_completed~data1$Gender, alternative=c("less"))
## 
##  Welch Two Sample t-test
## 
## data:  data1$Age_in_years_completed by data1$Gender
## t = -2.0978, df = 246.26, p-value = 0.01847
## alternative hypothesis: true difference in means is less than 0
## 95 percent confidence interval:
##         -Inf -0.09117358
## sample estimates:
## mean in group Female   mean in group Male 
##             22.16667             22.59477
t.test(data1$Age_in_years_completed~data1$Gender, alternative=c("greater"))
## 
##  Welch Two Sample t-test
## 
## data:  data1$Age_in_years_completed by data1$Gender
## t = -2.0978, df = 246.26, p-value = 0.9815
## alternative hypothesis: true difference in means is greater than 0
## 95 percent confidence interval:
##  -0.7650356        Inf
## sample estimates:
## mean in group Female   mean in group Male 
##             22.16667             22.59477

independent 2-group t-test

t.test(y1,y2) # where y1 and y2 are numeric

t.test(data1$Percentage_in_10_Class,data1$Percentage_in_12_Class)
## 
##  Welch Two Sample t-test
## 
## data:  data1$Percentage_in_10_Class and data1$Percentage_in_12_Class
## t = 3.5745, df = 533.24, p-value = 0.0003827
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  1.240114 4.266186
## sample estimates:
## mean of x mean of y 
##  83.31897  80.56582
#-------------------
t.test(data1$Percentage_in_10_Class,data1$Percentage_in_12_Class, var.equal = TRUE)
## 
##  Two Sample t-test
## 
## data:  data1$Percentage_in_10_Class and data1$Percentage_in_12_Class
## t = 3.5745, df = 544, p-value = 0.0003821
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  1.240182 4.266118
## sample estimates:
## mean of x mean of y 
##  83.31897  80.56582
t.test(data1$Percentage_in_10_Class,data1$Percentage_in_12_Class, var.equal = FALSE)
## 
##  Welch Two Sample t-test
## 
## data:  data1$Percentage_in_10_Class and data1$Percentage_in_12_Class
## t = 3.5745, df = 533.24, p-value = 0.0003827
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  1.240114 4.266186
## sample estimates:
## mean of x mean of y 
##  83.31897  80.56582
#---------------------
t.test(data1$Percentage_in_10_Class,data1$Percentage_in_12_Class, conf.level = 0.95)
## 
##  Welch Two Sample t-test
## 
## data:  data1$Percentage_in_10_Class and data1$Percentage_in_12_Class
## t = 3.5745, df = 533.24, p-value = 0.0003827
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  1.240114 4.266186
## sample estimates:
## mean of x mean of y 
##  83.31897  80.56582

paired t-test

t.test(y1,y2,paired=TRUE) # where y1 & y2 are numeric

t.test(data1$Percentage_in_10_Class,data1$Percentage_in_12_Class, paired = TRUE)
## 
##  Paired t-test
## 
## data:  data1$Percentage_in_10_Class and data1$Percentage_in_12_Class
## t = 4.845, df = 272, p-value = 2.129e-06
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  1.634436 3.871864
## sample estimates:
## mean of the differences 
##                 2.75315

analysis of variance

library(psych)

describeBy(data1$Percentage_in_10_Class, data1$Previous_Degree)
## 
##  Descriptive statistics by group 
## group: Arts
##    vars n  mean   sd median trimmed  mad  min  max range  skew kurtosis
## X1    1 4 81.03 8.48   82.8   81.03 5.41 69.2 89.3  20.1 -0.44    -1.83
##      se
## X1 4.24
## -------------------------------------------------------- 
## group: Commerce
##    vars   n  mean   sd median trimmed  mad min  max range  skew kurtosis
## X1    1 101 81.28 8.79   81.7   81.52 9.93  61 96.4  35.4 -0.19    -0.85
##      se
## X1 0.87
## -------------------------------------------------------- 
## group: Engineering
##    vars   n mean   sd median trimmed  mad min  max range  skew kurtosis
## X1    1 108 85.5 6.91   86.1   85.83 7.56  68 97.2  29.2 -0.45    -0.49
##      se
## X1 0.67
## -------------------------------------------------------- 
## group: Journalism
##    vars n mean sd median trimmed mad min max range skew kurtosis se
## X1    1 1   65 NA     65      65   0  65  65     0   NA       NA NA
## -------------------------------------------------------- 
## group: Management
##    vars  n  mean   sd median trimmed  mad  min max range  skew kurtosis
## X1    1 36 81.84 8.47     83   82.29 8.45 58.9  94  35.1 -0.59    -0.34
##      se
## X1 1.41
## -------------------------------------------------------- 
## group: Science
##    vars  n  mean   sd median trimmed  mad min max range  skew kurtosis
## X1    1 23 85.53 9.16   88.6   87.09 6.23  56  95    39 -1.69     2.71
##      se
## X1 1.91
describeBy(data1$Percentage_in_10_Class, data1$Previous_Degree, mat = TRUE)
##     item      group1 vars   n     mean       sd median  trimmed     mad
## X11    1        Arts    1   4 81.02500 8.483071   82.8 81.02500 5.41149
## X12    2    Commerce    1 101 81.27931 8.787344   81.7 81.51617 9.93342
## X13    3 Engineering    1 108 85.50361 6.913155   86.1 85.82818 7.56126
## X14    4  Journalism    1   1 65.00000       NA   65.0 65.00000 0.00000
## X15    5  Management    1  36 81.83944 8.474893   83.0 82.29067 8.45082
## X16    6     Science    1  23 85.52870 9.164647   88.6 87.09263 6.22692
##      min  max range       skew   kurtosis        se
## X11 69.2 89.3  20.1 -0.4377254 -1.8275607 4.2415357
## X12 61.0 96.4  35.4 -0.1926382 -0.8546568 0.8743734
## X13 68.0 97.2  29.2 -0.4537738 -0.4903248 0.6652186
## X14 65.0 65.0   0.0         NA         NA        NA
## X15 58.9 94.0  35.1 -0.5920874 -0.3430281 1.4124822
## X16 56.0 95.0  39.0 -1.6928706  2.7076566 1.9109610
describeBy(data1$Percentage_in_10_Class, data1$Previous_Degree, mat = FALSE)
## 
##  Descriptive statistics by group 
## group: Arts
##    vars n  mean   sd median trimmed  mad  min  max range  skew kurtosis
## X1    1 4 81.03 8.48   82.8   81.03 5.41 69.2 89.3  20.1 -0.44    -1.83
##      se
## X1 4.24
## -------------------------------------------------------- 
## group: Commerce
##    vars   n  mean   sd median trimmed  mad min  max range  skew kurtosis
## X1    1 101 81.28 8.79   81.7   81.52 9.93  61 96.4  35.4 -0.19    -0.85
##      se
## X1 0.87
## -------------------------------------------------------- 
## group: Engineering
##    vars   n mean   sd median trimmed  mad min  max range  skew kurtosis
## X1    1 108 85.5 6.91   86.1   85.83 7.56  68 97.2  29.2 -0.45    -0.49
##      se
## X1 0.67
## -------------------------------------------------------- 
## group: Journalism
##    vars n mean sd median trimmed mad min max range skew kurtosis se
## X1    1 1   65 NA     65      65   0  65  65     0   NA       NA NA
## -------------------------------------------------------- 
## group: Management
##    vars  n  mean   sd median trimmed  mad  min max range  skew kurtosis
## X1    1 36 81.84 8.47     83   82.29 8.45 58.9  94  35.1 -0.59    -0.34
##      se
## X1 1.41
## -------------------------------------------------------- 
## group: Science
##    vars  n  mean   sd median trimmed  mad min max range  skew kurtosis
## X1    1 23 85.53 9.16   88.6   87.09 6.23  56  95    39 -1.69     2.71
##      se
## X1 1.91
library(ggplot2)
## 
## Attaching package: 'ggplot2'
## The following objects are masked from 'package:psych':
## 
##     %+%, alpha
ggplot(data1, aes(data1$Previous_Degree,data1$Percentage_in_10_Class))+geom_boxplot()
ggplot(data1, aes(data1$Previous_Degree,data1$Percentage_in_10_Class))+geom_boxplot(aes(color=Previous_Degree))
anova1<-aov(Percentage_in_10_Class~Previous_Degree, data=data1)
anova1
## Call:
##    aov(formula = Percentage_in_10_Class ~ Previous_Degree, data = data1)
## 
## Terms:
##                 Previous_Degree Residuals
## Sum of Squares         1483.374 17412.972
## Deg. of Freedom               5       267
## 
## Residual standard error: 8.075712
## Estimated effects may be unbalanced
print(anova1)
## Call:
##    aov(formula = Percentage_in_10_Class ~ Previous_Degree, data = data1)
## 
## Terms:
##                 Previous_Degree Residuals
## Sum of Squares         1483.374 17412.972
## Deg. of Freedom               5       267
## 
## Residual standard error: 8.075712
## Estimated effects may be unbalanced
summary(anova1)
##                  Df Sum Sq Mean Sq F value   Pr(>F)    
## Previous_Degree   5   1483  296.67   4.549 0.000535 ***
## Residuals       267  17413   65.22                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# post hoc test

TukeyHSD(anova1)
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = Percentage_in_10_Class ~ Previous_Degree, data = data1)
## 
## $Previous_Degree
##                                diff        lwr        upr     p adj
## Commerce-Arts            0.25430693 -11.563795 12.0724093 0.9999999
## Engineering-Arts         4.47861111  -7.324892 16.2821142 0.8854315
## Journalism-Arts        -16.02500000 -41.942839  9.8928389 0.4837954
## Management-Arts          0.81444444 -11.403342 13.0322309 0.9999643
## Science-Arts             4.50369565  -8.054630 17.0620215 0.9077213
## Engineering-Commerce     4.22430418   1.015492  7.4331168 0.0026482
## Journalism-Commerce    -16.27930693 -39.575405  7.0167907 0.3416660
## Management-Commerce      0.56013751  -3.939651  5.0599263 0.9992302
## Science-Commerce         4.24938872  -1.106481  9.6052586 0.2069561
## Journalism-Engineering -20.50361111 -43.792306  2.7850837 0.1199175
## Management-Engineering  -3.66416667  -8.125471  0.7971381 0.1752232
## Science-Engineering      0.02508454  -5.298494  5.3486627 1.0000000
## Management-Journalism   16.83944444  -6.661937 40.3408258 0.3133739
## Science-Journalism      20.52869565  -3.151511 44.2089020 0.1311848
## Science-Management       3.68925121  -2.498810  9.8773126 0.5254607
Two way anova
anova2<-aov(Percentage_in_10_Class~Previous_Degree+Gender, data=data1)
anova2
Interaction Effect
anova3<-aov(Percentage_in_10_Class~Previous_Degree+Gender+Previous_Degree:Gender, data=data1)
anova3

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