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

35 views7 pages

13 Apr 2012

School

Department

Course

Professor

1

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)

2

- 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: