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Lecture 4

Crim 320 - week 4.docx

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CRIM 320
Rebecca Carleton

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? - In the social sciences, we tend to use the 5 percent rule - If the chance of a given outcome is less than five in 100, we say that it is unusual - A claim of statistical significance suggests that the result would happen in fewer than 5 percent of trials - Something actual is going on The effects of Sample size – n=10 - LESS than 0.05, results are statistically significant - GREATER than 0.05, results are not statistically significant - Since 0.344 is greater than 0.05, the results are not significant. - If Greater, then possibly due to chance The effects of Sample size – n=40 - All that has changed is the sample size - But the impact of
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