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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