sampling & estimation
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Sampling & Estimation. Normal Distribution. Normal Sample. Binomial Distribution. Estimation. Sampling. Sampling of the Mean. The more observations the better!. Surprice!!!!!. Sampling of the Variance. Sampling of the proportion. How accurate are these estimates?. - PowerPoint PPT PresentationTRANSCRIPT
Sampling & Estimation
Normal Distribution
Normal Sample
Binomial Distribution
Estimation
Sampling
Sampling of the Mean
The more observations the better!
Surprice!!!!!
Sampling of the Variance
Sampling of the proportion
How accurate are these estimates?
Can we use that to report the uncertainty
in a clever way?
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.
… Ehh, we don’t know that one!
Confidence Interval for the Mean when the variance is not know
Confidence intervals for the variance
It looks like …..
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.
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.
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
The function logit(p) The function expit(p)
Logit-transformation
Assume normality
To get a 95% CI for p, we use the expit-transformation
Now we are happy!
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.
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)
Assume we have a dataset with a variable called: Alcohol
Hmmmm
Choose
• Analyze
• General Linear Model
• Univariate
Choose
• Analyze
• General Linear Model
• Univariate
• Drag the variable Alcohol into Dependent Variable
• Click Options
• Choose Parameter estimates
• Drag the variable Alcohol into Dependent Variable
• Click Options
• Choose Parameter estimates
… And now we get