Class_8 - The Chi-Square Distributions(Statistical...

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The Chi-Square Distributions (Statistical Inference)
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Two Statistical Tasks 1. Description 2. Inference
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Thus far, we have completed: 1. Descriptive Statistics a. Central tendency i. discrete variables ii. continuous variables b. Variation i. discrete variables ii. continuous variables c. Association i. discrete variables
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Now we begin: 2. Inferential Statistics a. Estimation b. Hypothesis testing
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Inferential statistics are based on random sampling . A sample is a subset of some universe (or population [set]). If (and only if ) the sample is selected according to the laws of probability , we can make inferences about the universe from known (statistical) characteristics of the sample.
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“Random” means selected so that each element in the universe has exactly the same chance of being picked for the sample (sometimes called an equi-probability sample).
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Put differently, the only difference between elements selected into the sample and those not selected is pure chance (i.e., “the luck of the draw”).
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All inferential statistics evaluate the probability that unlucky selection in creating a random sample (the “luck of the draw,” technically called “sampling error”) explains the statistical outcomes obtained from random samples.
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Sample 1: 75% cardinal (n 1 = 4)
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Sample 2: 0% cardinal (n 2 = 4)
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Sample 3: 25% cardinal (n 3 = 4)
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Percent cardinal f 0 lowest 25 medium 50 highest 75 medium 100 lowest
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0% 25% 50% 75% 100% Percent cardinal in random samples
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All statistics calculated on variables from a random sample have a (known) sampling distribution . Sampling distributions are the theoretically possible distributions of statistical outcomes from an infinite number of random samples of the same size.
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Knowing this, we do not actually need to draw an infinite number of random samples.
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