genderexperiment.Rmd

---
title: "Gender Experiment - w241 Final Project"
author: "Daniel Alvarez"
date: "3/13/2020"
output: html_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```


```{r,include=FALSE, results='hide'}
# clear out environment variables
rm(list=ls())

# set seed for randomization
set.seed(1)
```


Load packages
```{r, include=FALSE}
# load packages 
library(foreign)
library(data.table)
library(knitr)
library(dplyr)
library(foreign)
library(zoo)
library(lmtest) # robust standard errors
library(sandwich) # robust standard errors
library(stargazer) # reporting formatted results
library(magrittr) # printing document
library(pwr) # estimating power
```


## Gender experiment 

Here we load the pre-treatment survey data. Then block on gender and age, by peaking at the distribution. Then, assign subjects randomly to the pilot study and treatment, placebo and control groups.

```{r read data}
d <- fread('./pretreatmentresponses1.csv')
d
```

Peak at the dataset

```{r}
str(d)
summary(d)
dim(d)
```

Set an `id` variable (ordinal) useful for randomization assignment

```{r}
d[,'id'] <- c(1:nrow(d))
```


Rename long variable names

```{r}
colnames(d)[1:5] <-c("timestamp","gender_string","age","email","consent")
str(d)
```

Check for any "No" consents. These would be excluded from the study.

```{r}
table(d$consent)
```


### Modify dataset

Look at gender distribution.
```{r}
table(d$gender_string)
```

Look at age distribution
```{r}
hist(d$age,main="Age distribution", xlab="Counts for age",ylab = "Frequency", breaks=50)
```

```{r}
# summary statistics on age
summary(d$age)
```


Codify gender as a binary variable. Female is 0, Male is 1.

```{r}
d[, gender:=ifelse(gender_string=='Female',0,1)]

# check through a cross-tab
# table(d$gender_string,d$gender)
```

### Randomly assign subjects to pilot study

Assume 10 people assigned to pilot.

```{r pressure, echo=FALSE}

# Assume 10 people assigned to the pilot
n_pilot <- 10
x_prob <- n_pilot/nrow(d)
x_prob <- round(x_prob,digits=2)
x_prob

d[,'is_pilot':= sample(c(0:1),size=.N, replace=TRUE, prob=c(1-x_prob,x_prob))]

# check number of people assigned to pilot is ~10
table(d$is_pilot)
```

### Blocking 

Block on gender.

```{r}
# Assign variables
N = nrow(d)
n_female <- length(d$age[d$gender==0])
n_female

n_male = length(d$age[d$gender==1])
n_male

#randomly assign subjects to either treatment or control groups blocking by state
randomize_blockbygender <- function(){
  ifelse(d$gender==1,sample(c(rep(0,n_female/2),rep(1,n_female/2))),sample(c(rep(0,n_male/2),rep(1,n_male/2))) )
}

d[,'treatment'] <- randomize_blockbygender()

```

Check cross-tab of treatment and gender to observe if more or less equal proportions of gender in each block.

```{r}
table(d$gender,d$treatment)
```



### Introduce two treatment groups: female voice `TF` and male voice `TM`

Split treatment group further into two treatment groups

```{r}
n_treatment = length(d$age[d$treatment==1])
n_treatment

#randomly assign subjects to either two treatment groups (TF and TM) for those with treatment==1
randomize_treatment <- function(){
  ifelse(d$treatment==1,sample(c(rep(0,n_treatment/2),rep(1,n_treatment/2))),0)
}

d[,'is_treatedmalevoice'] <- randomize_treatment()
```

Check cross-tab of treatment and is_treatedmalevoice to observe if more or less equal proportions of treatment of male and female voice when treatment ==1.

```{r}
table(d$is_treatedmalevoice,d$treatment)
```

For dataset readability purposes, include a string variable for each subjects assignment: control `C`, treatment with male voice `TM`, and treatment with female voice `TF`.

```{r}
# create a string assignment variable for readability purposes
d[treatment==0, assignment:='C']
d[treatment==1 & is_treatedmalevoice==1, assignment:='TM']
d[treatment==1 & is_treatedmalevoice==0, assignment:='TF']

# check cross-tab
table(d$assignment)
```

Peak at resulting dataset.

```{r}
head(d)
```

```{r}
d
```


##Examine covariate balance across assignment groups

Due to blocking, the distribution of experimental subject's gender is roughly balanced across assignment groups.
```{r}
# check cross-tab of assignment and subject gender
table(d$assignment, d$gender_string)

assignment.labs <- c("Control", "Treatment-Female Voice", "Treatment-Male Voice")
names(assignment.labs) <- c("C", "TF", "TM")

ggplot(d,aes(x=gender_string))+stat_count(width = 0.5)+ 
  facet_grid(~assignment, labeller = labeller(assignment = assignment.labs)) + labs(title = 'Histograms of gender distribution by assignment group')+theme_bw()
```


```{r}
# check cross-tab of assignment and age
table(d$assignment, d$age)

# examine age distributions across assignment groups

assignment.labs <- c("Control", "Treatment-Female Voice", "Treatment-Male Voice")
names(assignment.labs) <- c("C", "TF", "TM")

ggplot(d,aes(x=age))+geom_histogram(bins=30)+ 
  facet_grid(~assignment, labeller = labeller(assignment = assignment.labs)) + labs(title = 'Histograms of age distribution by assignment group')+theme_bw()
```