#New Statistics Short Course
#Exercise 3
#CIs, Effect Sizes, 
#CIs for Effect Sizes

dat<-read.csv(file.choose()) #mta_church
names(dat)

#### Part a (One-Sample)
#80%
t.test(dat$mot_apol[dat$group=="church"],
       conf.level=.80)$conf.int
#95%
t.test(dat$mot_apol[dat$group=="church"],
       conf.level=.95)$conf.int

#The 95% CI is wider; if we need 95% of 
#intervals to contain the population 
#parameter, instead of just 80%, then 
#the interval must be wider.
#This is a function of the larger 
#critical value at alpha=.05 than 
#at alpha=.20


#### Part b (Two-Sample)
#Let's reduce the sample size
#Original (N=1000)
t.test(dat$mot_apol ~ dat$group, conf.level=.90)$conf.int
#N=100
library(dplyr)
dat2<-sample_n(dat,100)
t.test(dat2$mot_apol ~ dat2$group, conf.level=.90)$conf.int

#Smaller n means a larger standard 
#error and a larger critical value,
#both of these mean a wider interval


#### Part c
#If we conducted the study over and 
#over again, 90% of the CIs would 
#contain the true population parameter
#(in this case mu1-mu2)

#Even more important for a researcher
#is to interpret the width of the CI
#and how that affects the conclusions


#### Part d
#raw mean difference
mean(dat$mot_apol[dat$group=="church"])-mean(dat$mot_apol[dat$group=="nochurch"])
#standardized mean difference
library(psych)
cohen.d(dat,"group",alpha=.1)
#percent of variance explained
library(lsr)
mod<-aov(mot_apol ~ group, data=dat)
etaSquared(mod)[1]
#r (or % of SD explained)
library(psych)
d2r(.2)
cohen.d(dat,"group")$r


#### Part e
cohen.d.ci(d=.2,n=1000,alpha=.1)
library(MBESS)
#need the F value (and df)
summary(mod)
ci.pvaf(F.value=10.28,df.1=1,df.2=998,conf.level=.9,N=1000)
#by simuation
library(dplyr)
etasq<-numeric(1000)
for (i in 1:1000) {
  newdat<-sample_n(dat,size=1000,replace=TRUE)
  newmod<-aov(mot_apol~group,data=newdat)
  etasq[i]<-etaSquared(newmod)[1]
}
quantile(etasq,c(.05,.95))


#### Part f
library(canprot)
CLES(dat$mot_apol[dat$group=="church"],dat$mot_apol[dat$group=="nochurch"])

#The probability of the score being 
#higher for a subject from the 
#"nochurch" group, if one subject was 
#randomly selected from each group