Lecture 9_sampling distributions

Lecture 9_sampling distributions - 9/22/2010 Sampling...

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9/22/2010 1 Sampling Distributions 1 Overview • Up to this point we have been concerned with describing characteristics of a set of scores (e.g., central tendency, variability, distributional shape) • In contrast, inferential statistics concerns the characteristics of a set of samples – How does a particular sample compare to others that could be drawn from the population? 2 3
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9/22/2010 2 4 Example • A local school district wants to know how their standardized test scores compare to national norms. Are the district‟s scores significantly higher, lower, or about the same as the national average? 5 Example • The Metropolitan Achievement Test (MAT) tests a range of abilities from foundation skills to critical thinking processes and strategies in K-12 th graders • Different versions of tests for different grades • The test has a mean of 50 and standard deviation ( sd ) of 21.06 in the population. • The average MAT score for the district is 56.47 ( n = 100 ). 6
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9/22/2010 3 Theoretical Procedure • In order to address the district‟s question about the school‟s performance we need information about other samples that could have been drawn from the population. • Theoretically we could go out and draw a large number of samples from other districts and use this information as a baseline for comparison 7 Theoretical Procedure • Taking 1000 different samples of n = 100 in other school districts we might get the following mean MAT scores: = 51.06 = 58.76 = 46.33 ….. = 49.49 1 M 2 M 3 M 1000 M 8 Distribution of Sample Means • We could make a histogram of the 1000 sample means that we collected – Instead of having a distribution of scores, we would have a distribution of sample means, or a sampling distribution because two samples from the same population will never be exactly the same (e.g., have the same mean, variability, etc.) 9
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9/22/2010 4 Sampling Distribution • A sampling distribution is a graph of all sample statistics, not scores, that could be drawn from a population for a specific sample size – i.e., the probability distribution, under repeated sampling of the population, of a given statistic for a specific sample size – A sampling distribution is important because it shows where a single sample falls in the distribution of all possible samples 10 Characteristics of a Sampling Distribution • Before we can draw any inferences from our sample, we need to know three pieces of information about the sampling distribution 1. The overall average of the sample means 2. How spread out, or variable, the samples are (i.e., the sampling fluctuation) 3. The shape of the sampling distribution 11 Overall Average of the Sample Means • We could take the 1000 sample means and get an overall average • In other words, we could determine the mean for a „typical‟ sample • With this information, we could compare the district‟s performance to a „typical‟ sample from the population of all possible school districts 12
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This note was uploaded on 02/17/2011 for the course PYSC 227 taught by Professor Fairchild during the Spring '10 term at South Carolina.

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Lecture 9_sampling distributions - 9/22/2010 Sampling...

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