Chapter 7

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!
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
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
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
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
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
{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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