R Console Page 1
> #Anova
> #Assumptions:
> #1.Normality
> #2.homogeneity
> #3.independece of observations
> dt<-read.csv("anova1.csv")
> dt
marks sec
1 18 1
2 19 1
3 20 1
4 17 1
5 18 1
6 15 2
7 16 2
8 17 2
9 19 2
10 18 2
11 5 3
12 4 3
13 6 3
14 7 3
15 3 3
> str(dt)
'data.frame': 15 obs. of 2 variables:
$ marks: int 18 19 20 17 18 15 16 17 19 18 ...
$ sec : int 1 1 1 1 1 2 2 2 2 2 ...
> attach(dt)
The following object is masked _by_ .GlobalEnv:
marks
> section<-as.factor(sec)
> section
[1] 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3
Levels: 1 2 3
> library(rstatix)
Attaching package: ‘rstatix’
R Console Page 2
The following object is masked from ‘package:stats’:
filter
Warning message:
package ‘rstatix’ was built under R version 4.1.3
> install.packages('rstatix')
Warning: package ‘rstatix’ is in use and will not be
installed
> dt %>% group_by(sec) %>% shapiro_test(marks)
# A tibble: 3 x 4
sec variable statistic p
<int> <chr> <dbl> <dbl>
1 1 marks 0.961 0.814
2 2 marks 0.987 0.967
3 3 marks 0.987 0.967
>
> #2.for homoginity
> bartlett.test(marks~as.factor(sec),data=dt)
Bartlett test of homogeneity of variances
data: marks by as.factor(sec)
Bartlett's K-squared = 0.47112, df = 2, p-value = 0.
7901
> #using anova
> res<-aov(marks~sec,data=dt)
> res
Call:
aov(formula = marks ~ sec, data = dt)
Terms:
sec Residuals
Sum of Squares 448.9000 118.8333
Deg. of Freedom 1 13
Residual standard error: 3.023413
R Console Page 3
Estimated effects may be unbalanced
> summary(res)
Df Sum Sq Mean Sq F value Pr(>F)
sec 1 448.9 448.9 49.11 9.23e-06 ***
Residuals 13 118.8 9.1
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’
0.1 ‘ ’ 1
> res<-aov(marks~as,factor(sec),data=dt)
Error in model.frame.default(formula = marks ~ as, d
ata = dt, drop.unused.levels = TRUE) :
invalid type (closure) for variable 'as'
In addition: Warning message:
In if (projections) qr <- lmcall$qr <- TRUE :
the condition has length > 1 and only the first el
ement will be used
> res<-aov(marks~as.factor(sec),data=dt)
> summary(res)
Df Sum Sq Mean Sq F value Pr(>F)
as.factor(sec) 2 542.5 271.3 129.2 7.65e-09 **
*
Residuals 12 25.2 2.1
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’
0.1 ‘ ’ 1
>
> #NH: Avg(s1)=Avg(s2)=Avg(s3) there is no significe
nt diff in sections
> #AH: Avg(s1)#Avg(s2)=Avg(s3) there is atleast one
significent diff in sections
> #AH: Avg(s1)=Avg(s2)#Avg(s3) there is atleast one
significent diff in sections
> #AH: Avg(s1)#Avg(s2)#Avg(s3) there is atleast one
significent diff in sections
> # {any e power(stars) thing leads to reaject null
hypo}
>
R Console Page 4
> #post-hoc tests when equal variances assumed is do
ne
> #post-hoc tests when equal variances assumed is no
t done
> #post-hoc tests when equal variances assumed is do
ne
> #Scheffe,Tuskey....
> #post-hoc can only be done when homiginity is sati
sfied
> TuskeyHSD(res)
Error in TuskeyHSD(res) : could not find function "T
uskeyHSD"
> TukeyHSD(res)
Tukey multiple comparisons of means
95% family-wise confidence level
Fit: aov(formula = marks ~ as.factor(sec), data = dt
)
$`as.factor(sec)`
diff lwr upr p adj
2-1 -1.4 -3.845137 1.045137 0.3132778
3-1 -13.4 -15.845137 -10.954863 0.0000000
3-2 -12.0 -14.445137 -9.554863 0.0000001
> aggregate(marks,by=list(sec),FUN=mean)
Error in aggregate.data.frame(as.data.frame(x), ...)
:
arguments must have same length
> with(dt,aggregate(marks,by=list(sec),FUN=mean))
Group.1 x
1 1 18.4
2 2 17.0
3 3 5.0
> dt1<-read.csv("anova1loc.csv")
> dt1
marks sec loc
1 18 1 1
2 19 1 2
R Console Page 5
3 20 1 3
4 17 1 4
5 18 1 5
6 15 2 1
7 16 2 2
8 17 2 3
9 19 2 4
10 18 2 5
11 5 3 1
12 4 3 2
13 6 3 3
14 7 3 4
15 3 3 5
> bartlett.test(marks~as.factor(loc),data=dt)
Error in is.factor(x) : object 'loc' not found
> res1<-aov(marks~as.factor(loc),data=dt)
Error in is.factor(x) : object 'loc' not found
> bartlett.test(marks~as.factor(loc),data=dt1)
Bartlett test of homogeneity of variances
data: marks by as.factor(loc)
Bartlett's K-squared = 0.18911, df = 4, p-value = 0.
9958
> res1<-aov(marks~as.factor(loc),data=dt1)
> res1
Call:
aov(formula = marks ~ as.factor(loc), data = dt1)
Terms:
as.factor(loc) Residuals
Sum of Squares 7.7333 560.0000
Deg. of Freedom 4 10
Residual standard error: 7.483315
Estimated effects may be unbalanced
> save.image("C:\\Users\\kvs Ramana\\Documents\\R pr
ogram\\anova")
R Console Page 6
> res1<-aov(marks~as.factor(loc),data=dt1)
