short report 1 luke webb joe white

---
title: "Studying the Effect of Cloud Seeding on Rainfall"
author: "Joe White and Luke Webb"
date: "4/14/2018"
output: pdf_document
---


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


Introduction

This paper is a statistical analysis of a case study conducted in Southern Florida between 1968 and 1972, measuring the rainfall of cumulus clouds that were "seeded" with a massive injection of silver iodine against a control group of clouds that were "unseeded," or normal.

During this time period, there were 52 days of research when it was deemed "appropriate" for cloud seeding. The experimenters randomly decided to either seed or not seed the clouds on these days, and measured the corresponding amounts of rainfall in acres-feet.

For our analysis, we will use a boxplot and a bootstrap to determine if there is a statistically relevant difference between the rainfall amounts of seeded and unseeded clouds.

Results


``` {r}
clouds <- read.csv("http://people.carleton.edu/~apoppick/ClassData/rainfall.csv", header=TRUE)
boxplot(Rainfall ~ Treatment, data = clouds, main = "Rainfall of Seeded and Unseeded Clouds", xlab = "Treatment of Cloud", ylab = "Rainfall (acres-feet)")
```

As shown by the boxplots, the median of the seeded clouds (221.6) is higher than the unseeded clouds (44.2). The interquartile ranges overlap; the unseeded data is much more concentrated, as shown by the smaller interquartile range and smaller spread. There are four outliers for seeded and three for unseeded, all greater than the maximums.


The bootstrap of the dataset is symmetric and bellshaped. Therefore, we can be 95% confident that the average difference in rainfall between seeded and unseeded clouds (Seeded-Unseeded) is between 30.82 and 563.09 acres-feet. The average difference in mean (Seeded-Unseeded).

The mean of the difference between the two groups is 278.50, and the standard error is 135.64.

Discussion

While it appears that seeded clouds produced a statistically relevant higher amount of rainfall, there is still uncertainty. For instance, some bootstrap mean differences were negative, meaning that some bootstraps produced bootstrap samples where the mean rainfall for unseeded clouds was higher that mean rainfall for seeded clouds. Therefore while we believe that seeding increases rainfall of clouds, we cannot be sure. In addition, there are limitations to the original experiment. There were only 52 total samples collected, and weather is very complicated and multifaceted. There could be confounding variables that this study does not account for. A larger, more comprehensive study is needed to truly determine the effect of seeding clouds.

Appendix of R Commands

Boxplot

clouds <- read.csv("http://people.carleton.edu/~apoppick/ClassData/rainfall.csv", header=TRUE)
boxplot(Rainfall ~ Treatment, data = clouds, main = "Rainfall of Seeded and Unseeded Clouds", xlab = "Treatment of Cloud", ylab = "Rainfall (acres-feet)")

Bootstrap

library(CarletonStats)
tapply(clouds$Rainfall, clouds$Treatment, mean)
boot(Rainfall ~ Treatment, data = clouds)