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Lecture

# October 2.docx

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University of Guelph

Sociology and Anthropology

SOAN 2120

David Walters

Fall

Description

Height (Males)
October 2, 2012 – SOAN 2120
99%
Height (Males) 95%
Any individual value
cinto a z-scored
99%
Any individual value 95%
can be converted
into a z-score
5 0’!5 ’! Mean 6 2’6 4’!
5 8’
-2.6 -2 Std Dev = 3 inche+2 +2.6
St dev St dev St devSt dev
Standard Deviation Scale
5 0’!5 ’! Mean 6 2’6 4’!
5 8’
-2.6 -2 Std Dev = 3 inche+2 +2.6
St dev St dev St devSt dev
Standard Deviation Scale
Walters
Commonly used cut-offs (alpha levels – ! )
SOAN 2120 99%
I n t r o d u c t o r y R e 95% a r c h M e t h o d s
Commonly used cut-offs (alpha levels – ! )
99%
95%
Lecture: Statistical Inference’!
1-.95 5 6’
•!1/20 = .05
1-.99
Mean
•1-.950 = .01 4 5’5 0’! 5 6’ 6 ’!6 ’!
•!1/20 = .05
1-.99
1 in 100 would be the outliers (really short or really tall)
•!1/100 = .01
Calculating p-values
•!Statistics Tables
•!How do we know that a z-score of plus or
minus 2 translates to a p-value of .05
•!Calculus
http://bcs.whfreeman.com/bps3e/
http://bcs.whfreeman.com/bps3e/
z’s converted to p’s
2
2 Commonly used cut-offs (alpha levels – ! )
99%
z’s converted to p’s95%
1-.95 4 ’!5 ’! 5 6’ 6 ’6 ’!
•!1/20 = .05
1-.99
•!1/100 = .01
-2 2
integrate that function from -2 to +2 and you end up with .95 – that’s the area b/w
those two points
.05 versus .01
1
Implications
Hypothesis testing
http://bcs.whfreeman.com/bps3e/
2.576 = above the mean
-2.576 = below the mean
^^^^^^ use that website that’s on the slide– it will HELP YOU
What have we been doing?
•Summarizing distributions 2
–!Normal distribution
•!Probabilities
•!Is a particular value different from the
mean?
New Topic
•Statistical inference
•!Using sample information to estimate population
values
•!Normal distribution
•!Just as variables have distributions, sample
statistics have distributions as well
3 sample – first slide we saw today of
male heights
population-
sampling – “from all possible samples” – abstract concept – take multiple samples,
we can calculate a mean and plot those means in a histogram (just like the height) –
sampling distribution based on calculating a statistic over and over again from
samples of the same size – most abstract but the most powerful •!
•!
•!
This is the sampling distribution over repeated samples.
randomly take 10 people from that population then calculate the mean of their
height
How do we know that the mean of a
tadistribution of samples is the same as the
take third randpopulation mean?an of a
distribution of samples is the same as the
•!Statistical theory
•!Simulationse know that the mean of a
•!distribution of samples is the same as the
–!Take a sample (Income of 40,000 people)
•!Sim•!Populationulation mean?
•!Statistical theorythe mean 40,000 people)
•!Pop»!1000 random samples
•!Simul–!C»!Calculate the mean
–!Take »!1000 random samples0,000 people)
•!Population
–!Calculate the meanan
»!1000 random samples
»!Calculate the mean
Statistics are Variable
Statistics are Variable
•! The fact that statistics from random
samples have definite sampling
•!distStatistics are Variable carefulom
sestimate of how trustworthy a statistic
dis as an estimate of a parameterul
•estimate of how trustworthy a statistic
•!samples have definite samplinghe spread
idistributions allows a more careful
•!estimate of how trustworthy a statistic
of its sampling distribution
is as an estimate of a parameter
•! Variability is described by the spread
of its sampling distribution
–!Larger samples give smaller spread
5
5
5 Statistics and Bias
•! The bias of a statistic is the difference between
its average value (obtained from the sampling
distribution) and the true value of the parameter
•! A statStatistics and Biasf the mean of its sampling
distribution is equal to the parameter being estimated
–!An unbiased statistic will sometimes give an
•!

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