Lab2.Rmd

---
title: "R Notebook"
output:
  html_document:
    df_print: paged
  pdf_document: default
---

This is an [R Markdown](http://rmarkdown.rstudio.com) Notebook. When you execute code within the notebook, the results appear beneath the code. 

Try executing this chunk by clicking the *Run* button within the chunk or by placing your cursor inside it and pressing *Ctrl+Shift+Enter*. 

```{r}
library(pacman)
p_load(dplyr,foreign,ggplot2,psych)
```

##Power and sample size for r
You plan to conduct a study to examine the association between IQ and
spatial ability in older adults. Based on your past research, you expect that the true (population)
correlation between these two variables is likely to be around .20.
```{r}
p_load(pwr)
pwr.r.test(r=0.2,power=0.8,sig.level = 0.05)
```
alpha=0.01
```{r}
pwr.r.test(r=0.2,power=0.8,sig.level = 0.01)
```
Post-hoc Power Analysis: You are planning a study to investigate the association between self-esteem and cortisol (a stress hormone) in response to a stressful speech task. Your theory
predicts that individuals with high self-esteem should show a lower cortisol response. You have a
small grant to pay for the biological assays, but your budget will cover only 25 subjects. If you
expect an effect size of about = -.30, how much statistical power would you have in your study
(assuming = .05, two-tailed)?
```{r}
pwr.r.test(n=25, r=-.30, sig.level = .05)
```

## Comparing two correlations
```{r}
df<-read.spss("Class_Survey.sav", to.data.frame = T)
```
```{r}
df.m <- df %>% filter(gender=="MALE") %>% select(HEIGHT,weight)
df.f <- df %>% filter(gender=="FEMALE") %>% select(HEIGHT,weight)
```
```{r}
describe(df.m)
```

```{r}
describe(df.f)
```
```{r}
hist(df.m$HEIGHT)
ggplot(df,aes(x=weight,fill=gender))+geom_histogram(color="white",alpha=.5,position = "identity",binwidth = 10)+ggtitle("Distribution of weight by gender") #position="identity":so that two plots are overlay, not stack.
```
```{r}
cor.test(df.f$HEIGHT,df.f$weight)
cor.test(df.m$HEIGHT,df.m$weight)
```
```{r}
r.test(n=52,r12=.296,n2=31,r34=.609)
```
The correlation of weight and height for men and women are not significantly different from each other.
```{r}
r.test(n=104,r12=.296,n2=62,r34=.609)
```

```{r}
r.test(n=nrow(na.omit(df.f)),r12=cor(df.f$weight,df.f$HEIGHT,use="complete.obs"), r34=cor(df.m$weight, df.m$HEIGHT), n2=nrow(df.m))

```
## Bivariate regression
```{r}
mod1<-lm(lifesat~friends1,data=df)
summary(mod1)
```
In R: intercept=intercept (estimate Std.); unstandardized slope (b): estimate std; standard error of b:error; t-statistic for b: t value; p-value for b: Pr; Standard error of estimate (or prediction): Residual standard error. 
```{r}
p_load(lm.beta)
lm.beta(mod1)
```
```{r}
summary(lm.beta(mod1))
```
**The result of summary(mod1) and summary(lm.beta(mod1)) is the same? **

```{r}
plot(df$friends1,df$lifesat)
abline(mod1,col="red")
```
```{r}
ggplot(df,aes(x=friends1,y=lifesat)) + geom_point() + geom_smooth(method = lm,fullrange=T) + xlim(c(0,7)) + theme_bw()
```