sampling & estimation. normal distribution normal sample
Post on 19-Dec-2015
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Sampling & Estimation
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Normal Distribution
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Normal Sample
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Binomial Distribution
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Estimation
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Sampling
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Sampling of the Mean
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The more observations the better!
Surprice!!!!!
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Sampling of the Variance
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Sampling of the proportion
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How accurate are these estimates?
Can we use that to report the uncertainty
in a clever way?
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Rule of
A random variable is very seldom more than two standard deviations away from the expected value.
A random variable is very seldom more than two standard deviations away from the expected value.
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… Ehh, we don’t know that one!
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Confidence Interval for the Mean when the variance is not know
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Confidence intervals for the variance
It looks like …..
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A 95% approximate interval for a proportion
Assume normality
BUT WHAT IF THIS INTERVAL
CONTAINS 0 OR 1?This would be possible if n is small, if p is nearly zero or if p is nearly one.
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Log-Transformation
Believe me!Assume normality
Use the expontial transformation, and write
But what if the interval contains
one?
This could happen if n is relatively small and p is nearly one.
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Logit-transformation
and it also looks like log(1-p), for p approx one.
Looks like the
log-transformation, for p small
To go the other way
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The function logit(p) The function expit(p)
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Logit-transformation
Assume normality
To get a 95% CI for p, we use the expit-transformation
Now we are happy!
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Why didn’t I just tell you about the logit-transformation in the first place?Because, when comparing proportions (risks), you may consider
To get 95% CI here, you’ll need all three approaches.
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How to calculate CI’s in SPSS
• It is easy (sort of) in the case of normally distributed variables
• More or less impossible in case of binomial (Use Excel)
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Assume we have a dataset with a variable called: Alcohol
Hmmmm
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Choose
• Analyze
• General Linear Model
• Univariate
Choose
• Analyze
• General Linear Model
• Univariate
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• Drag the variable Alcohol into Dependent Variable
• Click Options
• Choose Parameter estimates
• Drag the variable Alcohol into Dependent Variable
• Click Options
• Choose Parameter estimates
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… And now we get