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Lecture 4

Crim 320 Week 4.docx

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CRIM 320
Patrick Lussier

1 Crim 320 Week 4 January 30, 2012 Probability and Probability Distributions Sample and Population - Population (N) - The entire set of elements in which we are interested in - Need to define a target population by specifying: o Unit of analysis (situations, individuals, groups, institutions etc) o Geographical location & temporal boundaries - The distribution of scores represents the population distribution - Usually, we don’t know much about the characteristics of the population distribution We usually don’t know much about the population distribution because very rare do we know the data of the ENTIRE population Sample - Sample (n) - A subset of elements from the larger population - Importance of representativeness o Random sampling o i.e., all units of population have equal chance of being selected - The distribution of scores represents the sample distribution - Can analyze sample distribution through descriptive statistics Make sure it is representative of your sample, meaning must be a Random selection (everyone has an equal chance of being in the study). Inferential stats use the sample to infer something regarding the original population. Mean Std dev Characteristics of statistics Popn µ ∂ Popn Unknown One true distribution (mu) (sigma) parameters parameter Sample X s Sample Known Vary from distribution statistics sample to sample Your sample statistics may vary from one sample to another – that’s the tricky part. Although it varies between sample to sample, there is only ONE true parameter in population. i.e. prevalence of intimate partner violence in Canada, there can only be ONE number. 2 Fundamental Problem - Most studies are based on sample data - Sample statistics vary from study to another - We want to make statement about the characteristics of the population distribution, but have information only on the distribution of sample scores… - Example… o Survey of 5000 Canadian voters – we are not interested in those 5000 voters per se, but how all Canadians will vote on the next election Inferential Statistics - Mathematical techniques that provide the researcher with tools for making statements about popn on the basis of data about samples - Provide a systematic way to minimize risk of drawing false conclusions about the popn when using sample statistics - The foundation of inferential statistics is probability theory When you are reading studies, it’s important to look at where and how the sample was drawn because it allows us to think about to whom the sample statistics we can generalize, or infer the conclusions to.. Probability (P) - The # of times that a particular event or outcome can occur divided by the number of times any events or outcome can occur - This will be the guide to making conclusions about POPn parameters Divergence between popn and sample statistics - Popn of federally convicted sex offenders in Quebec (1994-2000) N = 553 o Rate of general re-offending for a popn of sex offenders: 22.5% o Six randomly selected samples of 25 sex offenders… - From the 553 ppl, made 6 random samples consisting of of 25 ppl in each, each of the sample will differ in their percentages, but they will be around the 22.5% Central limit theorem - If repeated independent random samples of size n are drawn from a population, then as n grows large, the sampling distribution of sample means will be approximately normal - If you increase your sample size and the distribution will get closer to a normal distribution, the
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