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University of Toronto St. George
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Sociology
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SOC202H1
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Scott Schieman
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Sociology

SOC202H1

Scott Schieman

Winter

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Soc202 Readings notes 2
Chapter 7 － Using Probability Theory to Produce Sampling Distributions
(Focus on pages 206 - 215 (up to "Nominal Variables"); pages 219 – 222 )
Point Estimates
Sampling error – the difference between the calculated value of a sample
statistic and the true value of a population parameter (unknown)
Point estimate – a statistic provided without indicating a range of error.
(mean of a population)
o There’s a variability in statistical outcomes from sample to sample
Predicting Sampling Error
Repeated sampling – drawing a sample and computing its statistics and then
drawing a second sample, a third, a fourth, and so on. (learned that sampling
is only a estimate)
Symbols to represent population parameter for interval/ratio variables
o UX = the mean of a population
o OX = the standard deviation of a population
Sampling error = Xbar – UX
Sampling error is patterned and systematic and therefore is predictable
o 1) The resulting sample means were similar in value and tended to
cluster around a particular value.
o 2) sampling variability was mathematically predictable form
probability curves
Sampling distribution
From repeated sampling, a mathematical description of all possible sampling
outcomes and the probability of each one
A raw score distribution is scores of each person in your sample
Sampling distribution for interval/ratio variables
Example: Physicians
o 48 years = mean of sample means
o UX = mean of a sampling distribution of means, will always equal to
population mean
o As with any normal curve, standard deviation is the distance to the
point of inflection of the curve
o Sampling distribution of means (X bar) describes all possible
sampling outcomes and the probability of each outcome.
Standard Error
Standard error – the standard deviation of a sampling distribution. The
standard error measures the spread of sampling error that occurs when a
population is sampled repeatedly
o Measures the spread
o Equation – the standard error of a sampling distribution of means is
the samples standard deviation divided by the square root of the
sample size (S(xbar) = sx/square root of N) Law of large numbers
The larger the samples size, the smaller the standard error
Replacing n with higher number, sample error decreases
The central limit Theorem
Regardless of the shape of a raw score distribution of an interval/ratio
variable, its sampling distribution will be normal when the sample size, n, is
greater than 121 cases and will center on the true population mans.
Sampling distribution has a small range than the raw score distribution (not
a normal curve)
Distributions are rectangular in shape when the raw scores have equal
chances of getting picked
Bean Counting as a Way of Grasping the Statistical Imagination
Sampling distribution is a probability distribution, it tells us how frequently
to expect any and all sampling out comes when we draw random samples
The central limit theorem essentially states that random sampling results in
normal curves: symmetrical distributions that bunch in the middle and tail
out to the sides
As long as sample size is sufficiently large, the sample distribution of
proportions takes the bell shape of a normal curve
Distinguishing Among Populations, Samples, and Sampling Distributions
Sample = Statistics, Population = Parameter, Sampling distribution =
Hypothetical distribution of an infinite number of samples of size N.
Statistical Follies and Fallacies: Treating a point estimate as though it were
absolutely true
No single statistics is the last word on estimating a parameter of the
population Chapter 8: Parameter Estimation Using Confidence Intervals
Focus on pages 237 - 256 (up to "choosing sample size"); also, skip "confidence
intervals of the mean for small samples" paragraph on page 251
The statistics of a sample are estimates.
In this chapter we learn to say confidently just how close this single point
estimate is to the true parameter within a range of error.
Confidence Interval – a range of possible values of a parameter expressed
with a specific degree of confidence ( draw only one sample and compute
point estimate)
o With this, we take a point estimate and couple it with a knowledge
about sampling distribution
o The objective is to estimate a population parameter within a specific
span or “interval” of values
o Frequently used in exploratory studies
o The level of confidence – a calculated degree of confidence that a
statistical procedure conducted with sample data will produce a
correct result for the sampled population (success rate)
Confidence Interval if a Population Mean
Sample statistics are the tools to answer what is the value of UX?
The level of expected error – the difference between the stated level of
confidence and “perfect confidence” of 100 percent.
Calculation: the level of confidence and the level of significance
o a symbolize the level of expected error/ level of significance
o Level of confidence = 100% - a
o a = 100% - level of confidence
Calculation: the standard error for a confidence interval of population
mean
o Because the

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