SOC201H1 Lecture Notes - Central Limit Theorem, Statistic, Sampling Distribution

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Published on 15 Apr 2013
School
UTSG
Department
Sociology
Course
SOC201H1
Professor
Chapter 7
February-25-13
11:07 PM
INTRODUCTION
Sampling distributions allow us to refine the estimates provided by statistics calculated on a
sample
POINT ESTIMATES
Sampling error: difference between the calculated value of a sample statistic and the true value of
a population parameter
Point estimate: a statistic provided without indicating a range of error
There is a variability in statistical outcomes from sample to sample
PREDICTING SAMPLE ERRORS
Repeated sampling: drawing a sample and computing its statistics and then drawing a second
sample, a third, a fourth, and so on
English letters used for sample statistics. Greek used for population parameters.
Sampling error is patterned and systematic and therefore is predictable
The resulting sample means were similar in value and tended to cluster around a particular value
o Probability theorists suspected that this value was the true value of the population
parameter
o Sampling variability was mathematically predictable from probability curves
SAMPLING DISTRIBUTIONS
Sampling distribution: from repeated sampling, a mathematical description of all possible
sampling outcomes and the probability of each one
o Eg. The mean age of the population of all doctors is 48 years. Draw 10 000 samples out of
144 doctors. From each sample, calculate the mean age. Plot each value on a histogram and
they will take teh shape of a normal distribution
When the sample size, n, is greater than 121 cases, a sampling distribution of means is normal in
shape.
The mean of a sampling distribution of means will always equal the population mean
o Eg. Sum the values of all 10 000 sample means and divide by 10 000 = 48
A sampling distribution tells us how often a sample statistic is likely to miss the true population
parameter value and by how much
THE STANDARD ERROR
Standard error: the standard deviation of a sampling distribution
o It is a measure of predictable sampling errors
Measures the spread of sampling error that occurs when a population is sampled repeatedly
The standard error of a sampling distribution of means is the sample's standard deviation divided
by teh square root of the sample size n
(I copied and pasted this image from the internet. SEx = s
sfor the variable X
sx = the standard deviation of a sample
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Document Summary

Sampling distributions allow us to refine the estimates provided by statistics calculated on a sample. Sampling error: difference between the calculated value of a sample statistic and the true value of a population parameter. Point estimate: a statistic provided without indicating a range of error. There is a variability in statistical outcomes from sample to sample. Repeated sampling: drawing a sample and computing its statistics and then drawing a second sample, a third, a fourth, and so on. The resulting sample means were similar in value and tended to cluster around a particular value. Sampling error is patterned and systematic and therefore is predictable: probability theorists suspected that this value was the true value of the population parameter, sampling variability was mathematically predictable from probability curves. Sampling distribution: from repeated sampling, a mathematical description of all possible sampling outcomes and the probability of each one: eg. The mean age of the population of all doctors is 48 years.

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