Power_Analysis.Rmd

---
title: "Power Analysis"
author: "Danielle Robinson"
date: "May 31, 2016"
output: html_document
---



##What are the variables in a power analysis?
n, d, sig.level, and power are dependent on each other. If you have three, you can calculate the fourth.

  n = number of samples in each group
  d =  Cohen's d, or "effect size"
  sig.level = 0.05
  power = 0.75 (0.2 is low power, 0.5 is medium, 0.8 is high power)
  alternative = two.sided (default)
  
##Calculating Cohen's d
d = effect size calculated with help from http://www.socscistatistics.com/effectsize/Default3.aspx
  Cohen's d = (M2 - M1) ⁄ SDpooled
  SDpooled = √((SD12 + SD22) ⁄ 2)
  
##For my predicted data:  
Cohen's d = (40.47 - 33.05) ⁄ 5.458416 = 1.359369.

##Running the code:
```{r}
library(pwr)
pwr.t.test(n = NULL, d = 1.359369, power = 0.75, sig.level = 0.05, type = "two.sample", alternative = "two.sided")
```

It is possible that I could see an effect with an n=9. If I drop the power to 0.5...

```{r}
pwr.t.test(n = NULL, d = 1.359369, power = 0.5, sig.level = 0.05, type = "two.sample", alternative = "two.sided")
```

##Conclusion: It is possible to see a moderate to large effect with  n= ~8