# Exercise Corsican Blue tip



### 1)
CorsBT<-read.csv("Corsican_blue_tit.csv")
CorsBT[,1:2]<-apply(CorsBT[,1:2],2,function(x){x<-as.Date(x, format = "%d %B %Y")})
CorsBT$Building=as.Date(CorsBT$Building,origin='1970-01-01')
CorsBT$Laying=as.Date(CorsBT$Laying,origin='1970-01-01')


BuildLayGap<-CorsBT$Laying-CorsBT$Building
BuildLayGap<-as.numeric(BuildLayGap)

### first test for normality
shapiro.test(BuildLayGap[1:6])

#	Shapiro-Wilk normality test
#
#data:  BuildLayGap[1:6]
#W = 0.87257, p-value = 0.2367
#

shapiro.test(BuildLayGap[7:12])

#	Shapiro-Wilk normality test
#
#data:  BuildLayGap[7:12]
#W = 0.94146, p-value = 0.671

##### Conclusion: Neither set of durations departs significantly from normal

### Now test for equal variance
fligner.test(BuildLayGap~Location,data=CorsBT)

#	Fligner-Killeen test of homogeneity of variances
#
#data:  BuildLayGap by Location
#Fligner-Killeen:med chi-squared = 0.63518, df = 1, p-value = 0.4255


### Both ok so we can apply a t-test

CorsBT<-cbind(CorsBT,BuildLayGap)
t.test(BuildLayGap[1:6],BuildLayGap[7:12],data=CorsBT)


#	Welch Two Sample t-test
#
#data:  BuildLayGap[1:6] and BuildLayGap[7:12]
#t = 4.8415, df = 8.9563, p-value = 0.000932
#alternative hypothesis: true difference in means is not equal to 0
#95 percent confidence interval:
# 10.20454 28.12880
#sample estimates:
#mean of x mean of y 
# 30.33333  11.16667 

#### Conclusion: highly significant difference

### 2)
D<-as.numeric(CorsBT$Laying-CorsBT$Building)
a<-glm(D ~ CorsBT$Building*CorsBT$Location)
summary(a)

#Call:
#glm(formula = D ~ CorsBT$Building * CorsBT$Location)
#
#Deviance Residuals: 
#   Min      1Q  Median      3Q     Max  
#-8.569  -4.981  -1.873   4.923  10.402  
#
#Coefficients:
#                                          Estimate Std. Error t value Pr(>|t|)
#(Intercept)                              2.487e+01  7.312e+01   0.340    0.743
#CorsBT$Building                         -2.124e-03  1.132e-02  -0.188    0.856
#CorsBT$Locationmainland                  1.845e+01  1.036e+02   0.178    0.863
#CorsBT$Building:CorsBT$Locationmainland  9.984e-05  1.609e-02   0.006    0.995
#
#(Dispersion parameter for gaussian family taken to be 58.28636)
#
#    Null deviance: 1572.25  on 11  degrees of freedom
#Residual deviance:  466.29  on  8  degrees of freedom
#AIC: 87.973
#
#Number of Fisher Scoring iterations: 2
#


#### conclusion: No interaction