frbd3fact: Analysis of Factorial Randomized Block Design for 3 factors
In doebioresearch: Analysis of Design of Experiments for Biological Research
Description
Usage
Arguments
Value
Examples
Description
The function gives ANOVA, R-square of the model, normality testing of residuals, SEm (standard error of mean), SEd (standard error of difference), interpretation of ANOVA results and multiple comparison test for means.
Usage
1
2
3
4
5
6
7
8
Arguments
data
dependent variables
replicationvector
vector containing replications
fact.A
vector containing levels of first factor
fact.B
vector containing levels of second factor
fact.C
vector containing levels of third factor
Multiple.comparison.test
0 for no test, 1 for LSD test, 2 for Duncan test and 3 for HSD test
Value
ANOVA, interpretation of ANOVA, R-square, normality test result, SEm, SEd and multiple comparison test result for the factors as well as the interaction.
Examples
1
2
3
4
data(factorialdata)
#FRBD analysis along with dunccan test for two dependent var.
frbd3fact(factorialdata[5:6],factorialdata$Replication,factorialdata$Nitrogen,
factorialdata$Phosphorus,factorialdata$Potassium,2)
Example output
$Yield
$Yield[[1]]
Analysis of Variance Table
Response: dependent.var
Df Sum Sq Mean Sq F value Pr(>F)
replicationvector 2 700.08 350.04 2.5605 0.1128
fact.A 1 24.00 24.00 0.1756 0.6816
fact.B 1 112.67 112.67 0.8241 0.3793
fact.C 1 0.17 0.17 0.0012 0.9726
fact.A:fact.B 1 42.67 42.67 0.3121 0.5852
fact.A:fact.C 1 620.17 620.17 4.5364 0.0514 .
fact.B:fact.C 1 48.17 48.17 0.3523 0.5623
fact.A:fact.B:fact.C 1 181.50 181.50 1.3276 0.2685
Residuals 14 1913.92 136.71
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
$Yield[[2]]
[1] "R Square 0.475"
$Yield[[3]]
[1] "SEm of A: 3.375 , SEd of A: 4.773 , SEm of B: 3.375 , SEd of B 4.773 , SEm of C: 3.375 , SEd of C: 4.773 , SEm of AB: 4.773 , SEd of AB: 6.751 , SEm of AC: 4.773 , SEd of AC: 6.751 , SEm of BC: 4.773 , SEd of BC: 6.751 , SEm of ABC: 6.751 , SEd of ABC: 9.547"
$Yield[[4]]
Shapiro-Wilk normality test
data: model$residuals
W = 0.94679, p-value = 0.2306
$Yield[[5]]
[1] "Normality assumption is not violated"
$Yield[[6]]
[1] "All the factor A level means are same so dont go for any multiple comparison test"
$Yield[[7]]
$Yield[[7]][[1]]
MSerror Df Mean CV
136.7083 14 122.6667 9.531712
$Yield[[7]][[2]]
Table CriticalRange
2 3.033186 10.23778
$Yield[[7]][[3]]
dependent.var groups
n1 123.6667 a
n0 121.6667 a
$Yield[[8]]
[1] "All the factor B level means are same so dont go for any multiple comparison test"
$Yield[[9]]
$Yield[[9]][[1]]
MSerror Df Mean CV
136.7083 14 122.6667 9.531712
$Yield[[9]][[2]]
Table CriticalRange
2 3.033186 10.23778
$Yield[[9]][[3]]
dependent.var groups
p0 124.8333 a
p1 120.5000 a
$Yield[[10]]
[1] "All the factor C level means are same so dont go for any multiple comparison test"
$Yield[[11]]
$Yield[[11]][[1]]
MSerror Df Mean CV
136.7083 14 122.6667 9.531712
$Yield[[11]][[2]]
Table CriticalRange
2 3.033186 10.23778
$Yield[[11]][[3]]
dependent.var groups
k0 122.7500 a
k1 122.5833 a
$Yield[[12]]
[1] "The means of levels of interaction between A and B factors are same so dont go for any multiple comparison test"
$Yield[[13]]
$Yield[[13]][[1]]
MSerror Df Mean CV
136.7083 14 122.6667 9.531712
$Yield[[13]][[2]]
Table CriticalRange
2 3.033186 14.47841
3 3.178300 15.17109
4 3.267858 15.59858
$Yield[[13]][[3]]
dependent.var groups
n1:p0 127.1667 a
n0:p0 122.5000 a
n0:p1 120.8333 a
n1:p1 120.1667 a
$Yield[[14]]
[1] "The means of levels of interaction between B and C factors are same so dont go for any multiple comparison test"
$Yield[[15]]
$Yield[[15]][[1]]
MSerror Df Mean CV
136.7083 14 122.6667 9.531712
$Yield[[15]][[2]]
Table CriticalRange
2 3.033186 14.47841
3 3.178300 15.17109
4 3.267858 15.59858
$Yield[[15]][[3]]
dependent.var groups
p0:k1 126.1667 a
p0:k0 123.5000 a
p1:k0 122.0000 a
p1:k1 119.0000 a
$Yield[[16]]
[1] "The means of levels of interaction between A and C factors are same so dont go for any multiple comparison test"
$Yield[[17]]
$Yield[[17]][[1]]
MSerror Df Mean CV
136.7083 14 122.6667 9.531712
$Yield[[17]][[2]]
Table CriticalRange
2 3.033186 14.47841
3 3.178300 15.17109
4 3.267858 15.59858
$Yield[[17]][[3]]
dependent.var groups
n1:k0 128.8333 a
n0:k1 126.6667 a
n1:k1 118.5000 a
n0:k0 116.6667 a
$Yield[[18]]
[1] "The means of levels of interaction between all the three factors ABC are same so dont go for any multiple comparison test"
$Yield[[19]]
$Yield[[19]][[1]]
MSerror Df Mean CV
136.7083 14 122.6667 9.531712
$Yield[[19]][[2]]
Table CriticalRange
2 3.033186 20.47557
3 3.178300 21.45516
4 3.267858 22.05972
5 3.328395 22.46838
6 3.371424 22.75885
7 3.402925 22.97149
8 3.426373 23.12978
$Yield[[19]][[3]]
dependent.var groups
n1:p0:k0 133.6667 a
n0:p0:k1 131.6667 a
n1:p1:k0 124.0000 a
n0:p1:k1 121.6667 a
n1:p0:k1 120.6667 a
n0:p1:k0 120.0000 a
n1:p1:k1 116.3333 a
n0:p0:k0 113.3333 a
$Plant_Height
$Plant_Height[[1]]
Analysis of Variance Table
Response: dependent.var
Df Sum Sq Mean Sq F value Pr(>F)
replicationvector 2 92.333 46.167 19.5859 8.773e-05 ***
fact.A 1 10.667 10.667 4.5253 0.051656 .
fact.B 1 2.667 2.667 1.1313 0.305498
fact.C 1 24.000 24.000 10.1818 0.006538 **
fact.A:fact.B 1 28.167 28.167 11.9495 0.003852 **
fact.A:fact.C 1 8.167 8.167 3.4646 0.083821 .
fact.B:fact.C 1 0.167 0.167 0.0707 0.794186
fact.A:fact.B:fact.C 1 10.667 10.667 4.5253 0.051656 .
Residuals 14 33.000 2.357
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
$Plant_Height[[2]]
[1] "R Square 0.843"
$Plant_Height[[3]]
[1] "SEm of A: 0.443 , SEd of A: 0.627 , SEm of B: 0.443 , SEd of B 0.627 , SEm of C: 0.443 , SEd of C: 0.627 , SEm of AB: 0.627 , SEd of AB: 0.886 , SEm of AC: 0.627 , SEd of AC: 0.886 , SEm of BC: 0.627 , SEd of BC: 0.886 , SEm of ABC: 0.886 , SEd of ABC: 1.254"
$Plant_Height[[4]]
Shapiro-Wilk normality test
data: model$residuals
W = 0.95689, p-value = 0.3793
$Plant_Height[[5]]
[1] "Normality assumption is not violated"
$Plant_Height[[6]]
[1] "All the factor A level means are same so dont go for any multiple comparison test"
$Plant_Height[[7]]
$Plant_Height[[7]][[1]]
MSerror Df Mean CV
2.357143 14 12.41667 12.36482
$Plant_Height[[7]][[2]]
Table CriticalRange
2 3.033186 1.344316
$Plant_Height[[7]][[3]]
dependent.var groups
n1 13.08333 a
n0 11.75000 a
$Plant_Height[[8]]
[1] "All the factor B level means are same so dont go for any multiple comparison test"
$Plant_Height[[9]]
$Plant_Height[[9]][[1]]
MSerror Df Mean CV
2.357143 14 12.41667 12.36482
$Plant_Height[[9]][[2]]
Table CriticalRange
2 3.033186 1.344316
$Plant_Height[[9]][[3]]
dependent.var groups
p0 12.75000 a
p1 12.08333 a
$Plant_Height[[10]]
[1] "The means of one or more levels of factor C are not same, so go for multiple comparison test"
$Plant_Height[[11]]
$Plant_Height[[11]][[1]]
MSerror Df Mean CV
2.357143 14 12.41667 12.36482
$Plant_Height[[11]][[2]]
Table CriticalRange
2 3.033186 1.344316
$Plant_Height[[11]][[3]]
dependent.var groups
k1 13.41667 a
k0 11.41667 b
$Plant_Height[[12]]
[1] "The means of levels of interaction between A and B factors are not same, so go for multiple comparison test"
$Plant_Height[[13]]
$Plant_Height[[13]][[1]]
MSerror Df Mean CV
2.357143 14 12.41667 12.36482
$Plant_Height[[13]][[2]]
Table CriticalRange
2 3.033186 1.901150
3 3.178300 1.992105
4 3.267858 2.048239
$Plant_Height[[13]][[3]]
dependent.var groups
n1:p0 14.50000 a
n0:p1 12.50000 b
n1:p1 11.66667 b
n0:p0 11.00000 b
$Plant_Height[[14]]
[1] "The means of levels of interaction between B and C factors are same so dont go for any multiple comparison test"
$Plant_Height[[15]]
$Plant_Height[[15]][[1]]
MSerror Df Mean CV
2.357143 14 12.41667 12.36482
$Plant_Height[[15]][[2]]
Table CriticalRange
2 3.033186 1.901150
3 3.178300 1.992105
4 3.267858 2.048239
$Plant_Height[[15]][[3]]
dependent.var groups
p0:k1 13.83333 a
p1:k1 13.00000 ab
p0:k0 11.66667 b
p1:k0 11.16667 b
$Plant_Height[[16]]
[1] "The means of levels of interaction between A and C factors are same so dont go for any multiple comparison test"
$Plant_Height[[17]]
$Plant_Height[[17]][[1]]
MSerror Df Mean CV
2.357143 14 12.41667 12.36482
$Plant_Height[[17]][[2]]
Table CriticalRange
2 3.033186 1.901150
3 3.178300 1.992105
4 3.267858 2.048239
$Plant_Height[[17]][[3]]
dependent.var groups
n1:k1 13.50000 a
n0:k1 13.33333 a
n1:k0 12.66667 a
n0:k0 10.16667 b
$Plant_Height[[18]]
[1] "The means of levels of interaction between all the three factors ABC are same so dont go for any multiple comparison test"
$Plant_Height[[19]]
$Plant_Height[[19]][[1]]
MSerror Df Mean CV
2.357143 14 12.41667 12.36482
$Plant_Height[[19]][[2]]
Table CriticalRange
2 3.033186 2.688632
3 3.178300 2.817262
4 3.267858 2.896647
5 3.328395 2.950307
6 3.371424 2.988448
7 3.402925 3.016370
8 3.426373 3.037155
$Plant_Height[[19]][[3]]
dependent.var groups
n1:p0:k1 15.66667 a
n0:p1:k1 14.66667 ab
n1:p0:k0 13.33333 abc
n0:p0:k1 12.00000 bcd
n1:p1:k0 12.00000 bcd
n1:p1:k1 11.33333 cd
n0:p1:k0 10.33333 d
n0:p0:k0 10.00000 d
doebioresearch documentation built on July 8, 2020, 7:18 p.m.
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Description Usage Arguments Value Examples
Description
The function gives ANOVA, R-square of the model, normality testing of residuals, SEm (standard error of mean), SEd (standard error of difference), interpretation of ANOVA results and multiple comparison test for means.
Usage
1 2 3 4 5 6 7 8 |
Arguments
data |
dependent variables |
replicationvector |
vector containing replications |
fact.A |
vector containing levels of first factor |
fact.B |
vector containing levels of second factor |
fact.C |
vector containing levels of third factor |
Multiple.comparison.test |
0 for no test, 1 for LSD test, 2 for Duncan test and 3 for HSD test |
Value
ANOVA, interpretation of ANOVA, R-square, normality test result, SEm, SEd and multiple comparison test result for the factors as well as the interaction.
Examples
1 2 3 4 | data(factorialdata)
#FRBD analysis along with dunccan test for two dependent var.
frbd3fact(factorialdata[5:6],factorialdata$Replication,factorialdata$Nitrogen,
factorialdata$Phosphorus,factorialdata$Potassium,2)
|
Example output
$Yield
$Yield[[1]]
Analysis of Variance Table
Response: dependent.var
Df Sum Sq Mean Sq F value Pr(>F)
replicationvector 2 700.08 350.04 2.5605 0.1128
fact.A 1 24.00 24.00 0.1756 0.6816
fact.B 1 112.67 112.67 0.8241 0.3793
fact.C 1 0.17 0.17 0.0012 0.9726
fact.A:fact.B 1 42.67 42.67 0.3121 0.5852
fact.A:fact.C 1 620.17 620.17 4.5364 0.0514 .
fact.B:fact.C 1 48.17 48.17 0.3523 0.5623
fact.A:fact.B:fact.C 1 181.50 181.50 1.3276 0.2685
Residuals 14 1913.92 136.71
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
$Yield[[2]]
[1] "R Square 0.475"
$Yield[[3]]
[1] "SEm of A: 3.375 , SEd of A: 4.773 , SEm of B: 3.375 , SEd of B 4.773 , SEm of C: 3.375 , SEd of C: 4.773 , SEm of AB: 4.773 , SEd of AB: 6.751 , SEm of AC: 4.773 , SEd of AC: 6.751 , SEm of BC: 4.773 , SEd of BC: 6.751 , SEm of ABC: 6.751 , SEd of ABC: 9.547"
$Yield[[4]]
Shapiro-Wilk normality test
data: model$residuals
W = 0.94679, p-value = 0.2306
$Yield[[5]]
[1] "Normality assumption is not violated"
$Yield[[6]]
[1] "All the factor A level means are same so dont go for any multiple comparison test"
$Yield[[7]]
$Yield[[7]][[1]]
MSerror Df Mean CV
136.7083 14 122.6667 9.531712
$Yield[[7]][[2]]
Table CriticalRange
2 3.033186 10.23778
$Yield[[7]][[3]]
dependent.var groups
n1 123.6667 a
n0 121.6667 a
$Yield[[8]]
[1] "All the factor B level means are same so dont go for any multiple comparison test"
$Yield[[9]]
$Yield[[9]][[1]]
MSerror Df Mean CV
136.7083 14 122.6667 9.531712
$Yield[[9]][[2]]
Table CriticalRange
2 3.033186 10.23778
$Yield[[9]][[3]]
dependent.var groups
p0 124.8333 a
p1 120.5000 a
$Yield[[10]]
[1] "All the factor C level means are same so dont go for any multiple comparison test"
$Yield[[11]]
$Yield[[11]][[1]]
MSerror Df Mean CV
136.7083 14 122.6667 9.531712
$Yield[[11]][[2]]
Table CriticalRange
2 3.033186 10.23778
$Yield[[11]][[3]]
dependent.var groups
k0 122.7500 a
k1 122.5833 a
$Yield[[12]]
[1] "The means of levels of interaction between A and B factors are same so dont go for any multiple comparison test"
$Yield[[13]]
$Yield[[13]][[1]]
MSerror Df Mean CV
136.7083 14 122.6667 9.531712
$Yield[[13]][[2]]
Table CriticalRange
2 3.033186 14.47841
3 3.178300 15.17109
4 3.267858 15.59858
$Yield[[13]][[3]]
dependent.var groups
n1:p0 127.1667 a
n0:p0 122.5000 a
n0:p1 120.8333 a
n1:p1 120.1667 a
$Yield[[14]]
[1] "The means of levels of interaction between B and C factors are same so dont go for any multiple comparison test"
$Yield[[15]]
$Yield[[15]][[1]]
MSerror Df Mean CV
136.7083 14 122.6667 9.531712
$Yield[[15]][[2]]
Table CriticalRange
2 3.033186 14.47841
3 3.178300 15.17109
4 3.267858 15.59858
$Yield[[15]][[3]]
dependent.var groups
p0:k1 126.1667 a
p0:k0 123.5000 a
p1:k0 122.0000 a
p1:k1 119.0000 a
$Yield[[16]]
[1] "The means of levels of interaction between A and C factors are same so dont go for any multiple comparison test"
$Yield[[17]]
$Yield[[17]][[1]]
MSerror Df Mean CV
136.7083 14 122.6667 9.531712
$Yield[[17]][[2]]
Table CriticalRange
2 3.033186 14.47841
3 3.178300 15.17109
4 3.267858 15.59858
$Yield[[17]][[3]]
dependent.var groups
n1:k0 128.8333 a
n0:k1 126.6667 a
n1:k1 118.5000 a
n0:k0 116.6667 a
$Yield[[18]]
[1] "The means of levels of interaction between all the three factors ABC are same so dont go for any multiple comparison test"
$Yield[[19]]
$Yield[[19]][[1]]
MSerror Df Mean CV
136.7083 14 122.6667 9.531712
$Yield[[19]][[2]]
Table CriticalRange
2 3.033186 20.47557
3 3.178300 21.45516
4 3.267858 22.05972
5 3.328395 22.46838
6 3.371424 22.75885
7 3.402925 22.97149
8 3.426373 23.12978
$Yield[[19]][[3]]
dependent.var groups
n1:p0:k0 133.6667 a
n0:p0:k1 131.6667 a
n1:p1:k0 124.0000 a
n0:p1:k1 121.6667 a
n1:p0:k1 120.6667 a
n0:p1:k0 120.0000 a
n1:p1:k1 116.3333 a
n0:p0:k0 113.3333 a
$Plant_Height
$Plant_Height[[1]]
Analysis of Variance Table
Response: dependent.var
Df Sum Sq Mean Sq F value Pr(>F)
replicationvector 2 92.333 46.167 19.5859 8.773e-05 ***
fact.A 1 10.667 10.667 4.5253 0.051656 .
fact.B 1 2.667 2.667 1.1313 0.305498
fact.C 1 24.000 24.000 10.1818 0.006538 **
fact.A:fact.B 1 28.167 28.167 11.9495 0.003852 **
fact.A:fact.C 1 8.167 8.167 3.4646 0.083821 .
fact.B:fact.C 1 0.167 0.167 0.0707 0.794186
fact.A:fact.B:fact.C 1 10.667 10.667 4.5253 0.051656 .
Residuals 14 33.000 2.357
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
$Plant_Height[[2]]
[1] "R Square 0.843"
$Plant_Height[[3]]
[1] "SEm of A: 0.443 , SEd of A: 0.627 , SEm of B: 0.443 , SEd of B 0.627 , SEm of C: 0.443 , SEd of C: 0.627 , SEm of AB: 0.627 , SEd of AB: 0.886 , SEm of AC: 0.627 , SEd of AC: 0.886 , SEm of BC: 0.627 , SEd of BC: 0.886 , SEm of ABC: 0.886 , SEd of ABC: 1.254"
$Plant_Height[[4]]
Shapiro-Wilk normality test
data: model$residuals
W = 0.95689, p-value = 0.3793
$Plant_Height[[5]]
[1] "Normality assumption is not violated"
$Plant_Height[[6]]
[1] "All the factor A level means are same so dont go for any multiple comparison test"
$Plant_Height[[7]]
$Plant_Height[[7]][[1]]
MSerror Df Mean CV
2.357143 14 12.41667 12.36482
$Plant_Height[[7]][[2]]
Table CriticalRange
2 3.033186 1.344316
$Plant_Height[[7]][[3]]
dependent.var groups
n1 13.08333 a
n0 11.75000 a
$Plant_Height[[8]]
[1] "All the factor B level means are same so dont go for any multiple comparison test"
$Plant_Height[[9]]
$Plant_Height[[9]][[1]]
MSerror Df Mean CV
2.357143 14 12.41667 12.36482
$Plant_Height[[9]][[2]]
Table CriticalRange
2 3.033186 1.344316
$Plant_Height[[9]][[3]]
dependent.var groups
p0 12.75000 a
p1 12.08333 a
$Plant_Height[[10]]
[1] "The means of one or more levels of factor C are not same, so go for multiple comparison test"
$Plant_Height[[11]]
$Plant_Height[[11]][[1]]
MSerror Df Mean CV
2.357143 14 12.41667 12.36482
$Plant_Height[[11]][[2]]
Table CriticalRange
2 3.033186 1.344316
$Plant_Height[[11]][[3]]
dependent.var groups
k1 13.41667 a
k0 11.41667 b
$Plant_Height[[12]]
[1] "The means of levels of interaction between A and B factors are not same, so go for multiple comparison test"
$Plant_Height[[13]]
$Plant_Height[[13]][[1]]
MSerror Df Mean CV
2.357143 14 12.41667 12.36482
$Plant_Height[[13]][[2]]
Table CriticalRange
2 3.033186 1.901150
3 3.178300 1.992105
4 3.267858 2.048239
$Plant_Height[[13]][[3]]
dependent.var groups
n1:p0 14.50000 a
n0:p1 12.50000 b
n1:p1 11.66667 b
n0:p0 11.00000 b
$Plant_Height[[14]]
[1] "The means of levels of interaction between B and C factors are same so dont go for any multiple comparison test"
$Plant_Height[[15]]
$Plant_Height[[15]][[1]]
MSerror Df Mean CV
2.357143 14 12.41667 12.36482
$Plant_Height[[15]][[2]]
Table CriticalRange
2 3.033186 1.901150
3 3.178300 1.992105
4 3.267858 2.048239
$Plant_Height[[15]][[3]]
dependent.var groups
p0:k1 13.83333 a
p1:k1 13.00000 ab
p0:k0 11.66667 b
p1:k0 11.16667 b
$Plant_Height[[16]]
[1] "The means of levels of interaction between A and C factors are same so dont go for any multiple comparison test"
$Plant_Height[[17]]
$Plant_Height[[17]][[1]]
MSerror Df Mean CV
2.357143 14 12.41667 12.36482
$Plant_Height[[17]][[2]]
Table CriticalRange
2 3.033186 1.901150
3 3.178300 1.992105
4 3.267858 2.048239
$Plant_Height[[17]][[3]]
dependent.var groups
n1:k1 13.50000 a
n0:k1 13.33333 a
n1:k0 12.66667 a
n0:k0 10.16667 b
$Plant_Height[[18]]
[1] "The means of levels of interaction between all the three factors ABC are same so dont go for any multiple comparison test"
$Plant_Height[[19]]
$Plant_Height[[19]][[1]]
MSerror Df Mean CV
2.357143 14 12.41667 12.36482
$Plant_Height[[19]][[2]]
Table CriticalRange
2 3.033186 2.688632
3 3.178300 2.817262
4 3.267858 2.896647
5 3.328395 2.950307
6 3.371424 2.988448
7 3.402925 3.016370
8 3.426373 3.037155
$Plant_Height[[19]][[3]]
dependent.var groups
n1:p0:k1 15.66667 a
n0:p1:k1 14.66667 ab
n1:p0:k0 13.33333 abc
n0:p0:k1 12.00000 bcd
n1:p1:k0 12.00000 bcd
n1:p1:k1 11.33333 cd
n0:p1:k0 10.33333 d
n0:p0:k0 10.00000 d
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