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Lecture 5

Crim 320 Week 5.docx

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Simon Fraser University
CRIM 320
Patrick Lussier

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: 3 - Statistical testing takes into account the types of hypothesis selected o Non-directional hypothesis o Directional hypothesis Non Directional Hypothesis - Statement about the differences/association existing in the population without the direction of the differences/association - Exploratory analyses o H1: informal social control in a neighborhood is associated with the number of arrests made in neighborhood  Low informal control could lead to high number of arrests (less surveillance , more crime opportunity)  Low informal control could lead to a low number of arrests (less likely to be caught) - Does not matter what differences may exist in the population - If u1=low informal control and u2=high informal control o H1: µ1=/= µ 2 (i.e., µ 1> µ 2 or µ 1< µ 2) o H0: µ 1= µ 2 So we are actually testing two sub hypothesis because we are not stating a direction. Typically we make directional hypothesis if we have a pretty good idea about the relationship between IV and DV Directional Hypothesis - Statement about the differences existing in the populations - Explanatory analyses/evaluative studies - For example: o H1: cognitive-behavioral treatment programs lower the risk of recidivism following prison release - If µ=unrelated offenders, and µ2=treated offenders - Accepting the research hypothesis requires that µ1> µ2, or that untreated offenders have a higher recidivism rate than treated offenders o H1= µ1> µ2 o H0: µ1< µ2, (i.e., µ1< µ2 or µ1= µ2) Decision-making about the bull hypothesis Testing the Null Hypothesis - Can’t be 100% sure o Empirical analysis conducted on sample statistics,
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