CRIM 320 Lecture Notes - Lecture 4: Binomial Distribution, Statistical Significance, Sampling Distribution

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Crim 320 week 4 Distributions, the Normal Curve, and Hypothesis Testing
Housekeeping:
- Outline has been revised
- Office hours have been revised: please feel free to go to any or all
- All assignments will be handed in during lecture
- Must have both names, both std numbers, and tutorial in which it will be picked-up
Objectives
- Discuss the fundamentals of the binomial distribution
- Explain how sample size affects statistical significance
- Explain how hypothesis testing and testing and tests of statistical significance are related to the
standard normal distribution.
- Sample has stats
- When we can make inferences from sample |stats to a population| parameter, it’s significant if
it has an effect, real results
Hypothesis Testing
- Hypothesis testing is about evaluating sample results. It focuses on two closely related questions
- What can we say about a population based on the results observed in a sample?
- Are the sample results identical to the results we would observe from the entire
population?
The binomial distribution
- Is relevant for variables that can only have two possible outcomes
- Ex. For example, flipping a coin. Would expect % heads but might not
- How often would we get a result that differed from our expectation of five?
- A binomial distribution is a dist that can only have two possible outcomes
Ex: Flip a coin
Sampling dist a distribution of all possible sample outcomes for a statistic
Standard error the standard deviation of a sampling distribution
Ex: Recidivism
- First, select 10 parolees at random, and count number of times they “succeed” within five years
of release. Then, repeat this process 500 times.
- See graph. Add from “Number of Trials” colum: 66 + 24 + 4 _ 2 = 96/500= 19.2%
How Unusual?
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