# New Statistics Short Course
# Exercise 2: Issues with NHST and p-values

# Open and inspect the dataset
dat<-read.csv(file.choose())
names(dat)
head(dat)

# Explore the means
tapply(dat$mot_apol,dat$group,mean)


# Question 1

# a) Ho: mu1 = mu2, Ha: mu1 != mu2

# b) It is highly unlikely that these populations would be 
#    exactly equal

# c) 
t.test(mot_apol ~ group, data=dat)

# It is expected that the p-value is this small given the 
# sample size

# d) The alpha level will depend on the nature of the research

# How exploratory vs confirmatory is the research? 

# Will the government force people to go to church if the
# effect is statistically significant?

# e) The magnitude of the p-value does not provide an estimate 
# of the probability that Ho is true


## f) Maybe a more informative research hypothesis is whether 
#    the church group is at least 2.5 points higher than the 
#    no_church group (about d = .5)

# A more informative hypothesis given the research question
t.test(mot_apol ~ group, mu=2.5, data=dat)

## g) Dichotomous vs magnitude of p-value? Neither is very good 
# in this setting given all that we have discussed.


# Question 2

# a) Sample of 50 cases
library(dplyr)
dat2<-sample_n(dat,50)
t.test(mot_apol ~ group, data=dat2)

# Sample of 25 cases
dat3<-sample_n(dat, 25)
t.test(mot_apol ~ group, data=dat3)

# b) Five samples of n = 50
s1<-sample_n(dat,50)
s2<-sample_n(dat,50)
s3<-sample_n(dat,50)
s4<-sample_n(dat,50)
s5<-sample_n(dat,50)

t.test(mot_apol ~ group, data=s1)
t.test(mot_apol ~ group, data=s2)
t.test(mot_apol ~ group, data=s3)
t.test(mot_apol ~ group, data=s4)
t.test(mot_apol ~ group, data=s5)

# c) No!!!