[RE-POSTED]Week 11 - Data analysis-Part II.ppt

Data Analysis Part II: Testing Relationships Among VariablesTake home questions from last weekMeasures of central tendencyParole board question

The concept of chance and significance tests

Categorical variablesContingency tables and the chi-square statistic

Continuous variablesCorrelationsT-tests independent groupspaired samples

Controlling for a third variable with categorical data [If Time]Contingency tables again

Take Home QuestionImagine people rated, on a scale of 1 to 5 whether they believed crime in Canada had declined, stayed the same, or increased in the last 10 years:1 = large decline2 = small decline3 = no change4 = small increase5 = large increase

What measure of central tendency (mean and standard deviation, mode or median) would you use for each of the following purposes?1) For describing the most common response.Mode

2) For purposes of dividing the people into two groups of equal size: those who believed crime had generally declined and those who believed that crime had generally increased.Median

3) For describing the average response.Mean and Standard Deviation

Take Home QuestionA parole board is trying to figure out how bad offenders were seen to be by the judge who sentenced them for robbery.

Offender A got a sentence of 36 months from Judge A who sentences robbers to a mean of 30 months and a standard deviation of 3 months.

Offender B got a sentence of 71 months from Judge B who sentences robbers to a mean of 32 months and a standard deviation of 26 months.

Which offender, A or B, should the parole board consider to be the worse of the two?

Offender A = 36 (mean 30, sd 3)Offender B = 71 (mean 32, sd 26)

CalculationOffender A = 36 (mean 30, sd 3)Offender B = 71 (mean 32, sd 26)

Z-score = (score mean) / sd

Offender A = (36 30) / 3=6 / 3= 2

Offender B = (71 32) / 26= 39 / 26= 1.5

A: 21 24 27 30 33 36 39 B: 6 32 58 71 84 110

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AnswerThe parole board should consider offender A the worse offence. Offenders A sentence was 2 standard deviations above the average sentence. Thus, only roughly 3% of offenders receive a more severe sentence. Offender B was 1 a standard deviation above the average so about 10% of offenders receive more severe sentences

Imagine you were a witness to a crime. All you can remember about the offender is that he was rather good looking. The police then arrest someone whom they think committed the crime and place him in a line-up. Imagine you are shown this line-up and asked by the police to identify the guilty person. The police seem certain that they have the right person, but they need your identification. You try your best to pick out the guilty man. In the picture below, whom would you pick:

Type I and Type II Errors

Actual State of Affairs in the WorldNull hypothesis is trueExperimental hypothesis is trueYour DecisionAccept experimental hypothesisType I error(false positive)Correct decisionAccept the null hypothesisCorrect decisionType II error(false negative)

Hypothesis: Women are less likely then men to feel safe from crime walking alone in their neighbourhood after dark.

How safe do you feel from crime walking alone in your neighbourhood after dark? Do you feel:___ very safe___ reasonably safe___ somewhat unsafe___ very unsafe___ do not walk alone___ dont know

Please indicate your gender___ male___ female

Are those who think sentences are "not severe enough" more or less likely to have a fair bit of confidence in the justice system than those who think sentences are too severe / about right"?

Is the relationship significant?

Positive CorrelationFrom text: pg 359Negative CorrelationCorrelations

Ratings of the Police and CourtsNote: Police = scale from 1 to 50 / Courts = scale from 1 to 40

Ratings of the Police and Courts

Correlation between Time (Years: 1961 to 2012) and Homicide Rates

Plotting Time (Years) and Homicide Rates

T-testsPair SamplesGroup 1 score 1 score 2

Independent GroupsGroup 1 scoreGroup 2 score

Example 1: T-Test Independent Groups

Example 2: T-Test Independent Groups

Example 1: T-Test Paired Samples

Example 2: T-Test Paired Samples

Which Statistical Test Would be Most Appropriate?Chi-squareCorrelationT-test (independent groups)T-test (paired samples)

Looking at prisoners, do those serving time for assault have more previous convictions than those serving time for break and enter?

Is there a significant linear relationship between the number of previous convictions a person has the number of months sentenced to prison?

A sample of men are asked in prison to list all of the offences they committed in the year prior to going to prison. These same men are found a year after being released and are asked, again, to list all the offences they committed in the year following release. Are they committing significantly fewer offences after being released compared to before they went into prison?

Do women score significantly higher than men in a research methods class?

Is there a significant linear relationship between number of years working at a company and salary?

Which Statistical Test Would be Most Appropriate?1. Looking at prisoners, do those serving time for assault have more previous convictions than those serving time for break and enter? T-test for independent groups Or chi-square if previous convictions are recoded into something like: 1, 2, 3 or more

2. Is there a significant linear relationship between the number of previous convictions a person has the number of months sentenced to prison? Correlation

3. A sample of men are asked in prison to list all of the offences they committed in the year prior to going to prison. These same men are found a year after being released and are asked, again, to list all the offences they committed in the year following release. Are they committing significantly fewer offences after being released compared to before they went into prison? T-test (paired samples)Or chi-square if previous convictions are recoded into something like: 1, 2, 3 or more

4. Do women score significantly higher than men in a research methods class? T-test for independent groups if ratio scale (e.g. percents)Or chi-square if letter grades (A, B, C, D)

5. Is there a significant linear relationship between number of years working at a company and salary? Correlation

Controlling for a 3rd VariableWhere you live (urban/rural) relates to whether or not you experience a victimizationWhere you live also relates to the number of times you go out in the eveningGoing out in the evening relates to whether or not youre victimized

So if you control for going out, does where you live still relate to victimization?

Take Home Question #1Look at the cross-tab on the next slide and answer the following questions:

Are people who are very satisfied with their personal safety more or less likely than those who are somewhat/very dissatisfied with their safety to believe that sentences are not severe enough?

What proportion of those who are very satisfied with their personal safety believe that sentences are not severe enough?

What proportion of those who are somewhat/very dissatisfied with their personal safety believe that sentences are not severe enough?

What proportion of those who feel that sentences are too severe/ about right feel somewhat/very dissatisfied with their personal safety?

What proportion of those who feel that sentences are not severe enough feel somewhat/very dissatisfied with their personal safety?

If Im interested in how those who believe sentencing is about right/not severe enough vary with respect to their views on personal safety, would I want to look at row or column percents?

Is the relationship between perceptions of sentencing and safety from crime significant?

Perceptions of sentence severity and personal safety

Take Home Question #2People were asked to rate, on a 10 point scale, how good of a job they thought the police and courts are doing (1=poor job, 10 = great job). Given the output below, what can you say about how people view the police vs. courts?

Take Home Question #3Which Statistical Test Would be Most Appropriate?Looking at kids in youth court, are those who have more 2 or more court appearances more negative (on a scale from 1 to 100) in their ratings of the courts than those who only have one court appearance?

Is there a linear relationship between number of hours of free time in a month and number of crimes committed during that month?

Is there a relationship between believing that crime has increased (yes/no) and whether one feels sentences are about right or too lenient?

Which do people feel more confident will reduce crime increasing sentences or providing more social supports for people. (Confidence is rated on a scale that runs from 1/not at all confident to 10/very confident).

Study OneRegression to the mean: Surprisingly large increase in reports of graffiti in Colton. Suggests that Sept and Oct were odd months graffiti likely to come back down naturally.

Selection bias: Choice of Colton and Appelton not equivalent groups. Only matched on age but whole host of other issues might make those two neighbourhoods very different from one another (SES, crime, social issues, etc). The fact that there was no graffiti problems in Appelton, while Colton experienced a surprisingly large increase suggests the two neighbourhoods are different.

Diffusion of treatment: The intervention consisted of three aspects: 1) more patrolling; 2) greater vigilance in dispersing youths and 3) cleaning up the graffiti. But one of those elements appeared to spread into the control neighbourhood specifically, Appelton got the clean-up part of the intervention. The control group should not receive any of the intervention if comparisons are to be made.

Testing (sensitizing people to the goals of the study): Police chief told officers to think carefully about filling in occurrence reports because he wanted to compare the number of incidents before and after the intervention to see whether his program in Colton had worked. That might have led officers to under-report graffiti incidents in Colton since officers knew what the Police Chief was hoping to find.

History: Seasonal change Sept/Oct vs. Dec/Jan. Maybe less graffiti because its cold and miserable out.

Study TwoSelection bias: An officer re-assigned some of the youths out of the experimental group and into the control group because he felt it wasnt in the public interest to divert the case. The two groups are now different from one another the worst offenders were likely screened out of the experimental group.Mortality: 100 kids ended up in the experimental group, but only 80 completed the program. Theyve likely lost the worst offenders so will over-estimate the impact of the program (i.e. will see less crime).

Instrumentation: The experimental group was asked about offending in the last month while the control group was asked about offending in the last two months. Obviously the control group might have more offending since the time frame was longer.Compensatory equalization of treatment: Defense counsel and youths demanded some sort of diversion program and got it. Some of the kids from the control group (the court kids) likely ended up diverted into some sort of similar program as what the experimental group received.

Selection bias: The first 80 youths that the researcher found charge data on were used to measure recidivism for the control group. Who knows why they were the first ones found (more serious charges? worse charges?) but its not a random sample of who was in that control group so likely not representative of that group.

Common ProblemsExplaining the problem under different headings. Doing that suggests that you actually dont know what the threat is and are simply covering your bases with all possible labels. E.g. from study two, listing the subject loss of 20 from the experimental group as a mortality problem, but then listing it again as a selection bias problem.

Arguing a Maturation effect. Given the short time-frame of both studies, its not realistic to argue that people are aging out of crime. Also, the argument needs to fit the findings so it would have to involve one group systemically aging faster out of crime than the other group.

Describing Selection Bias problems as predominately a problem of having unequal Ns or low Ns. If that was the main focus of the description of the selection bias problem you likely did not get any marks because it suggested that if the researcher had an equal or higher N, there would be no selection bias problem and thats wrong. An answer focusing on the Ns suggests little understanding of what the problem actually is. To get full marks you needed to be very clear that the method used to create the group (or groups) was problematic.

Common ProblemsQuoting something from the study and not explaining WHY it is a problem. Just highlighting that something happened does not demonstrate that you understand WHY it is a problem (e.g. from Study 2, simply noting the Mortality problem by saying that 100 were assigned, but only 80 completed the program is insufficient. For full marks, you needed to explain why thats a problem (e.g. Theyve likely lost the worst offenders so may over-estimate the impact of the program (i.e. will see less crime)).

Listing a threat and making up scenarios for how it might have happened. You must draw from the experiment just like we did in class to show that you can identify the threat, rather then simply making up scenarios for how random threats might apply. If you dont engage with the study, its not clear if you really understand the threats.E.g. from study one, saying that maybe the police also cracked down on vandalism in Appelton so maybe the entire intervention spread to that neighbhourhood.

Note: If you come to see me about your assignment you should bring your answers to all the studies that were assigned (in class or as homework) so I can see how misunderstandings developed.

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[RE-POSTED]Week 11 - Data analysis-Part II.ppt

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