# Reading the Hand-Short Data
DataHandShort<-read.csv("na9hczuHU5k9kTLJymhs.csv")
# Reading the Hand-Long Data
DataHandLong<-read.csv("UOxgyJUMDtgQtfYwFl5s.csv")

# Now we will calculate the Distal error as the distance error away from the center of the arm Formula mentioned below:
# Pre_Dominant_error= (Experimenter's Estimate of Arm Length/2) - Hand-short Dominant PreTrain Average
# Post_Dominant_error= (Experimenter's Estimate of Arm Length/2) - Hand-short Dominant PostTrain Average
# Pre_NonDominant_error= (Experimenter's Estimate of Arm Length/2) - Hand-short NonDominant PreTrain Average
# Post_NonDominant_error= (Experimenter's Estimate of Arm Length/2) - Hand-short NonDominant PostTrain Average

DataHandShort$Pre_Dominant_error<-(DataHandShort$DOMINANT..Experimenter.s.Estimate.of.Arm.Length/2)-DataHandShort$Hand.short.Dominant.PreTrain.Average
DataHandShort$Post_Dominant_error<-(DataHandShort$DOMINANT..Experimenter.s.Estimate.of.Arm.Length/2)-DataHandShort$Hand.short.Dominant.PostTrain.Average
DataHandShort$Pre_NonDominant_error<-(DataHandShort$NONDOMINANT..Experimenter.s.Estimate.of.Arm.Length/2)-DataHandShort$Hand.short.Non.Dominant.PreTrain.Average
DataHandShort$Post_NonDominant_error<-(DataHandShort$NONDOMINANT..Experimenter.s.Estimate.of.Arm.Length/2)-DataHandShort$Hand.short.Non.Dominant.PostTrain.Average

# now we will prepare the data for the ANOVA
DataHandShortNew<-data.frame(Gender=rep(DataHandShort$Gender,2),Group=rep(DataHandShort$Group,2),Dominance=c(rep("Pre",nrow(DataHandShort)),rep("Post",nrow(DataHandShort))),Dominant_Error=c(DataHandShort$Pre_Dominant_error,DataHandShort$Post_Dominant_error),NonDominant_Error=c(DataHandShort$Pre_NonDominant_error,DataHandShort$Post_NonDominant_error))

# Now we will apply the ANOVA for Dominant
# 1) For Hand-short with time variable (Pre_Dominant and Post_Dominant), Gender and training bisection (results of error so calculated above)
AnovaShortDominant<-aov(Dominant_Error~Gender*Group*Dominance,data=DataHandShortNew)
AnovaShortDominant
## Call:
## aov(formula = Dominant_Error ~ Gender * Group * Dominance, data = DataHandShortNew)
##
## Terms:
##                Gender Group Dominance Gender:Group Gender:Dominance
## Sum of Squares 13.355 19.102 35.054    13.048          4.839
## Deg. of Freedom    1    1       1          1             1
##             Group:Dominance Gender:Group:Dominance Residuals
## Sum of Squares          6.923                4.053 4242.546
## Deg. of Freedom             1                   1    200
##
## Residual standard error: 4.605728
## Estimated effects may be unbalanced
summary(AnovaShortDominant)
##                      Df Sum Sq Mean Sq F value Pr(>F)
## Gender                1 13 13.35 0.630 0.428
## Group                1 19 19.10 0.900 0.344
## Dominance             1 35 35.05 1.653 0.200
## Gender:Group          1 13 13.05 0.615 0.434
## Gender:Dominance       1    5 4.84 0.228 0.633
## Group:Dominance       1    7 6.92 0.326 0.568
## Gender:Group:Dominance 1    4 4.05 0.191 0.663
## Residuals          200 4243 21.21
# Now we will apply the ANOVA for Dominant
# 2) For Hand-short with time variable (Pre_NonDominant and Post_NonDominant), Gender and training bisection (results of error so calculated above)
AnovaShortNonDominant<-aov(NonDominant_Error~Gender*Group*Dominance,data=DataHandShortNew)
AnovaShortNonDominant
## Call:
## aov(formula = NonDominant_Error ~ Gender * Group * Dominance,
## data = DataHandShortNew)
##
## Terms:
##                Gender Group Dominance Gender:Group
## Sum of Squares 7.4468 26.8566 10.3359    3.0213
## Deg. of Freedom       1       1       1          1
##             Gender:Dominance Group:Dominance Gender:Group:Dominance
## Sum of Squares          0.8926       7.1449             0.0458
## Deg. of Freedom             1             1                   1
##             Residuals
## Sum of Squares 3120.4376
## Deg. of Freedom    200
##
## Residual standard error: 3

Write a program to generate a result. Suppose we are tossing a coin...