Soc%20005%20-%20Lecture%203_1

Soc%20005%20-%20Lecture%203_1 - SOCIOLOGY 005 Lecture 3...

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SOCIOLOGY 005 Lecture 3 Inferential Statistics Often times we are interested in estimating values within the population based upon a sample We usually do this because we do not have a census of a population and because it is more cost effective But in order for us to “infer” a population value, we need to engage in employ some kind of random sample
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Inferential Statistics Before discussing more about inference, we need know how sample statistics correspond to population parameters s Y 2 ! Y 2 Mean Variance Std. Dev. s Y Y Y μ Y Sample Population Inferential Statistics When we are looking at particular observations or outcomes within a population, we can talk about them in terms of what was the probability of a particular observation occurring We refer to the distribution of probabilities of observing an outcome as a probability distribution
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Inferential Statistics Continuous probability distributions Since the underlying distribution is continuous, we look at areas between two outcomes when assessing the probability of an a particular outcome We call the probability of observing a score in between these two points (alpha) ! Inferential Statistics p ( a ! Y ! b ) = " Alpha
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Inferential Statistics A normal distribution has several unique characteristics It is unimodal Its mean, median, and mode equal one another We can calculate probabilities of observing a score based upon the symmetric nature of the curve based upon Z-scores The Normal Distribution The Normal Distribution !" + ! 68% ! Z " Z ! 95% ! 2 Z 2 Z 99.7% ! 3 Z 3 Z μ = 0 100% = .68
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The Normal Distribution We can also look at the probability that a score is observed μ = 0 1.67 The Normal Distribution ...or the area of a tail of a normal distribution which is cut off by a given z-score (alpha area) = 0 1.67 p ( Z ! Z " ) =
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The Normal Distribution μ = 0 1.67 What is the probability we’ll observe a score higher than 1.67 from the population mean? Z-Score Area from 0 to Z Area from Z to InFnity 1.66 0.4515 0.0485 1.67 0.4525 0.0475 { For these numbers, we need to consult a table Critical Value: Minimum value to designate an alpha area Central Limit Theorem Now that we know something about normal distributions, we can use this knowledge to infer values of a sample to a population. The central limit theorem states: “If all possible random samples of N observations are drawn from any population with a mean and variance , then as N grows larger, these sample means approach a normal distribution, with mean and variance . ! Y 2 Y Y Y 2 N
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Say we have a population of college students. .. And we ask them how many times have they have been intoxicated over the last two months. .. Central Limit Theorem want to take a sample.
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Soc%20005%20-%20Lecture%203_1 - SOCIOLOGY 005 Lecture 3...

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