---
title: "Optional Tutorial Week 6"  
author:   
  - Siqi Zheng  
institute:   
  - Department of Statistical Science   
  - University of Toronto
date: Academic year 2020-2021  
output:   
  beamer_presentation:
    theme: "Boadilla"
    keep_tex: yes
header-includes:
  - \usepackage{multicol}
  - \AtBeginSubsection{}   
---

## Possible Topics for Today

- Q & A Session 
- Hypothesis Testing vs Bootstrap Sampling

# Q & A Session


## Course Materials?

- Assignments
- Project Procedure
- ...

# Hypothesis Testing vs Bootstrap Sampling

## Similarities

- Both bootstrapping and traditional methods use samples to draw inferences about populations. 

## Characteristics of Hypothesis Testing

- Traditional hypothesis testing procedures require equations that estimate sampling distributions using the properties of the sample data, the experimental design, and a test statistic. 

- Requires proper test statistic and certain __assumptions__. 

- For example, t-test requires the assumption that the population follows a normal distribution.

## Characteristics of Bootstrap Sampling

- This method takes the sample data that a study obtains, and then resamples it over and over to create many simulated samples. 

- Each of these simulated samples has its own properties. When you graph the distribution of these means on a histogram, you can observe the sampling distribution of the mean. 

- Don’t need to worry about test statistics, formulas, and assumptions.

- No new data are created in this process.

## Bootstrap Sampling Method

1. The bootstrap method has an equal probability of randomly drawing each original data point for inclusion in the resampled datasets.

2. The procedure can select a data point more than once for a resampled dataset. This property is the “with replacement” aspect of the process.

## Assumptions for Bootstrap?

__Representative Sample__: This method treats the original sample as a proxy for the real population and then draws random samples from it. Consequently, the central assumption for bootstrapping is that the original sample accurately represents the actual population.

## Why Bootstrap?

- When it is not feasible to obtain other samples from a population.

- When we do not want to make assumptions about the population distribution.

## Reference

Frost, J. (2020, June 12). Introduction to Bootstrapping in Statistics with an Example. Retrieved October 22, 2020, from https://statisticsbyjim.com/hypothesis-testing/bootstrapping/
