#####Nested designs and Pseudoreplication


### import data - dataset 1


datum=read.csv(file.choose())
head(datum)


### model without random effect of field


results=lm(Biomass~Treatment,data=datum)


### model with random effect of field


library(nlme)
results2=lme(Biomass~Treatment,data=datum,random=(~1|Field))


###Is effect of field significant?


anova(results2,results)


###No, so can we remove it?


anova(results) ### model incorrectly assumes you have 18 samples for testing effect of treatment
anova(results2) ### model correctly assumes you have 6 samples for test effect of treatment
# Alternative - average within fields (don't include field in analysis)
# Field is sample, only need random effect if multiple samples from each field


### import data - dataset 2


datum=read.csv(file.choose())
head(datum)


###analyze data, plots nested within fields


results=lme(Biomass~Treatment,data=datum,random=~1|Field/Plot)
summary(results)


###analyze data, just plots (don't account for fields


results=lme(Biomass~Treatment,data=datum,random=~1|Plot)
summary(results)
#Note that number of plots is incorrect due to the way we numbered plots in data