Two Sample Problems

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Two Sample Problems

• Lecture 4

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Examples of various hypotheses

• Average salary in Copenhagen is larger than in
  Bælum
• H0 µC µB. HA µC lt µB.
• Sodium content in Furresøen is equal to the
  content in Madamsø
• H0 µF µM. HA µF ? µM.
• Proportion of Turks in Århus is the same as in
  Aalborg
• H0 pÅ pA. HA pÅ ? pA.
• Average height of men in Sweden is the same as
  in Denmark
• H0 µS µD. HA µS ? µD.
• The average temperature is increasing over time
• H0 µtime 1 µtime 2. HA µtime 1 lt µtime 2 if
  time 1 time 2.

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Todays tests

• Compare means
• Independent samples (also called two samples in
  the book).
• Paired samples.
• Compare variances for independent samples.
• Compare proportions.

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An example
An embarasing Measurement
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Embarasing Measurement
It seems to be bigger after than before!!!
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NICE AND NORMAL !!!
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95 CI for mean before and after
The observations in living color
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Another look at the data
All the differences are bigger than zero
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Look at the differences
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How about testing if the mean difference is
significantly bigger than zero?
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Result of One Sample T-test on Differences
Mean bigger than 2 SE
Mean actually 6.113 SE, therefore p 0.000
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Equivalently
The Compare Means menu is sufficient for alot of
different tests
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Blah blah we want to see a TEST!
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Output
95 CI for difference
Mean difference
P-value
Test statistic
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Conclusion
If you want to test the difference between BEFORE
and AFTER (or similar designs)
Test if the DIFFERENCE is zero!
And do this with a PAIRED T-TEST!!
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Two-Sample T-test (unpaired)
Data normal ? Equal variances?
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Time Categorical variable
Age e.g. Age gt 40
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Two-Sample Output
P-value for equal means
Equal variances
95 CI
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K-Sample
Data normal (in each group) ? Equal variances?
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Equal variances?
If NOT!!!
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K-Sample Output
P-value
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A Small Trick (Post Hoc)
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OK OK, Ill use another data set
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RECIPE
Equal means or mean some value
Formulate the hypothesis
Normal, binomial ect.
Formulate the model
Paired, unpaired, more groups
Recognize the design
Normal ? Equal variances?
Check the assumptions
Run the SPSS procedure
Get your p-value