Chapter 7 - Chapter 7 Sample Variability Finally getting to...

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Chapter 7 Sample Variability
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Finally getting to the exciting stuff So far… collecting data simple descriptions of sample data basic concepts of probability Now: final steps to turn data into useful information – making population statements based on sample data!
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4 Key Concepts Random Sampling Sampling Error Sampling Distribution of Sample Means Central Limit Theorem
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Key Concept #1: Random Sampling Already discussed way back when…. Key point – when I say a sample was collected randomly, implication is: all experimental units equally likely to be selected sample represent the entire population experimental units are independently selected experimental units selected without bias
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Key Concept #2: Sampling Error In this statistical context ‘Error’ is not a mistake The sampling error is an estimate of how much the sample value is different from the population value When you collect a sample from a population, do you expect μ = x ? No! But that doesn’t mean the sample is bad just means chance influences the experimental units actually selected
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Sampling Error Populations are large with a sample, you only look at a small subset of population Theoretically – an infinite number of samples could be collected Think about it for a moment – taking sample after sample after sample from same population…. Population Sample
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Population μ Sample 1 Sample 2 Sample 3 Sample 4 Sample 5 Sample 6 x 1 Many more samples x 2 x 3 x 4 x 5 x 6 Could take an infinite number of samples from a population Theoretically Will the sample means be identical? NO!
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Population μ = 23.4 22.6 23.4 19.9 26.2 23.5 23.8 Many more samples and many more sample means sample mean
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Sampling Error So samples from the same population can have different sample means These differences are due to chance (since you sampled RANDOMLY) Sampling Error is the difference between a sample statistic and a population parameter due to chance
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Remember… Probably take 1 sample Never really know the true population value Don’t know the exact sampling error for you study BUT – we can make a guess by thinking about all possible samples that could be taken from a population
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Key Concept #3: The Sampling Distribution of Sample Means The Sampling Distribution of Sample Means occurs when you DO take every possible sample from a population, calculate the mean of each sample and plot all the means Remember: we are theoretical here…
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Theoretical Example Example: Consider the data set {1, 2, 3, 4}: 1) Make a list of all samples of size 2 that can be drawn from this set (Sample with replacement) 2) Construct the sampling distribution of sample means
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{1, 1} 1.0 1/16
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This document was uploaded on 11/04/2011 for the course BIOM 301 at Maryland.

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Chapter 7 - Chapter 7 Sample Variability Finally getting to...

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