CRIM 320 Lecture Notes - Lecture 5: Statistical Parameter, Confidence Interval, Standard Deviation

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Week 5 Crim 320
February 6, 2012
Hypothesis testing
The logic of hypothesis testing
Testing Research hypothesis
We suspect a relationship between two or more variables in a given population
Possible research hypotheses
- H1: the number of crimes committed by males and females is different
- H2: drug-users and non-drug users differ as to number of violent crimes committed
- H3: the frequency of crime is different in inner-city neighborhoods that in suburban
neighborhoods
Making statement about the effect of an IV (e.g., gender, drug use, location) on the DV (e.g., number of
crime)
- Hypothesis are explicitly states as:
o H1
o H2
o etc
Hypothesized effect of an IV on a DV that we believe true in the population:
- Association between two variables
o Ex: lower parental supervision is associated with a higher # of problem beh committed
by children
- Group differences on one variable
o Ex: adolescent gang members are more likely to continue offending in adulthood than
non gang members
- In statistics, however, we test for the null hypothesis
Null Hypothesis
- Statement of no difference or no association between a IV and a DV
- Null hypothesis is states as:
o H0
- Research Hypotheses need to be reformulated as null hypotheses
o H1: the number of crimes committed by males and females is different (research
hypothesis)
o H0: there are no gender differences in terms of the number of crimes committed (null
hypothesis)
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- Example two
o H1: drug users and non drug users differ as to number of violent crimes committed
(research hypo)
o H0: there is no difference in the number of violent crime committed (null hypo)
- Statistical theory involves testing the assumption of no difference or no association from a
sample of observations
o Two possible conclusions
We reject the null hypothesis
We accept the null hypothesis
Once you have conducted your statistical analysis, you have to interpret the findings, and once you have
the findings you make the call of whether you reject the null hypothesis or accept it.
- Rejecting the null hypothesis
o Sample statistics: Drug-users =/= non-drug users
o We accept the research hypothesis and conclude that the differences in our sample are
the result of actual differences in the population
- Accepting the null hypothesis
o Sample statistics: drug-users == Non drug-users
o We can’t accept the research hypothesis
o Conclude that the lack of differences with our sample statistics indicate no differences in
the population
The goal is always to generalize to the population
Goal of Inferential statistics
- Determine whether the differences observed in the sample data are the results of sampling
error or reflect actual differences in the population
- Sample statistics: (number of violent crimes)
o Drug-users: X=3.4 (s=3.2) vs. Non drug-users: X= 2.6 (x=2.9)
o Sampling error or actual differences in the population
- If differences due to sampling error, then we are unable to reject the null hypothesis
o The differences found do not reflect actual differences in the population
o We expect some differences due to sampling error
o But are those differences more important than what is expected from chance alone?
- If differences are attributed to population differences, then we reject the null hypothesis of no
difference and accept the research hypothesis
Non-directional & directional hypothesis
Two types of hypothesis:
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