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Lecture 6

# Lecture 6 - October 24

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University of Toronto St. George

Geography

GGR270H1

Damian Dupuy

Fall

Description

th
Date: October 24 , 2012
SAMPLING –SAMPLING DESIGNS
Number of different sampling designs exist:
-simple random (most basic, use some random generation method i.e. a random number
table
-systematic sampling (take a system approach and rather than randomly select people through
random number tables, a system says every 10 person we will choose, i.e. a phonebook)
-Stratified (organize sample based on organization of the population, the organization of the
sample represents the organization of the population)
Everything has an equal chance of being chosen
Can also have spatial sampling designs (looking at where things happen- i.e. the concentration
of lead on a site, involves applying some sort of physical grid)
-use Cartesian Coordinates (lines of latitude/longitude)
-simple
-stratified random (you have your whole map which is then divided into squares, and then
randomly select a set of points form those squaresensures coverage of the map –i.e. the
deposits of lead)
-transect (randomly select lines along a map, and you sample along the lines)
Sampling Distribution
Sample statistics will change or vary for each random sample selected
Probability distributions for statistics are called Sampling Distributions (if you take multiple
samples and calculate the mean, and plot the means and generate a distribution of those
statistics, what you have is a distribution of statistics which is the difference between a sample
distribution and a sampling distribution)
sample distribution-distribution of actual scores, drawn from one sample
sampling distribution- distribution of a statistics, drawn from multiple samples
often ask about this difference in EXAMS
A sampling distribution is the distribution of a statistic that is drawn from all possible samples
of a given size n
Can be developed for any statistics, not just the mean (but we tend to use the mean)
Central Limit Theorem
Sampling Distribution will have its own mean and standard deviation
But…the mean of a sampling distribution has important properties –summarized by Central
Limit Theorem
If all samples are randomly drawn, and are independent, then the mean of the sampling
distribution of sample means will be the population mean mu
-If our sample is large enough, we can use it to predict our population
The frequency distribution of sample means will be normally distributed What this means for us is that…
when the sample size is large, the sample mean is likely to be quite close to the population
mean
A large sample is more likely to be closer to the true population mean than a smaller sample
Theoretically the difference between a large sample and a small sample is n=30 (the minimum
number of observations to carry out a test)
Central Limit Theorem – Variability
Standard deviation of the sampling distribution is equal to the sample standard deviation
divided by the square root of the sample size
This is called the Standard Error of the Mean
Indicates how much a typical sample mean is likely to differ from the true population mean
Measures the amount of sampling error
The larger the n the smaller the amount of sampling error (smaller sampling error indicates less
variability)
the larger the n, the less variability there is= the more peaked the curve is (leptokurtic)
Standard Error
Standard error of the mean
Standard error of a proportion SEp= , Note: q=1-p
Central Limit Theorem III
How large is large???
If we have a normal population, it doesn’t matter what our size is, it’ll still be normal
When the population is skewed, the sample size must be large (n greater than 30) before
the sampling distribution will become normal
Sample Estimation
Statistical inference is concerned about making decisions or predictions about population
parameters, using samples
Two ways we do this:
-estimation
-hypothesis testing (make decisions of the parameter based on preconceived notions, draw
conclusions about the literature that might to our research scenario, statements about what we
think might be the case, and these hypothesis are then tested)
Estimators are calculated using information from samples
Usually expressed as a formula Two different types
-Point (use the info in our sample to select a value that predicts

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