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Quantitative Data Analysis:  Statistics – Part 2
Overview ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
The Normal Distribution
The Normal Distribution ,[object Object],[object Object]
Abraham de Moivre ,[object Object],[object Object],[object Object],[object Object],[object Object]
Carl Friedrich Gauss ,[object Object],[object Object],[object Object],[object Object]
 
 
The Normal Distribution
The Normal Distribution ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
The Normal Distribution
The Normal Distribution
 
Density Curves:  Properties
The Normal Distribution ,[object Object],[object Object],[object Object],[object Object]
Characterization ,[object Object],[object Object],[object Object]
Same Mean,  Different Standard Deviation 10 1
Different Mean,  Different Standard Deviation 10 1
Different Mean,  Same Standard Deviation 10 1
 
 
 
 
 
 
 
 
 
The Normal Distribution ,[object Object],[object Object],[object Object],[object Object]
The Normal Distribution
Why? ,[object Object]
Why? ,[object Object]
So what? ,[object Object],[object Object],[object Object]
So what? Before = 6.4 After = 9.2 0 10
So what? Is this a significant difference? Before = 6.4 After = 9.2 10 0
So what? or is it  more likely a sampling variation? Before = 6.4 After = 9.2 10 0
So what? Before = 6.4 After = 9.2 10 0
So what? Before = 6.4 After = 9.2 10 0
So what? Before = 6.4 After = 9.2 How many standard devaitions from the  mean is this? 10 0
So what? Before = 6.4 After = 9.2 How many standard devaitions from the  mean is this? 10 0 and is it statistically significant?
So what? Before = 6.4 After = 9.2 10 0 σ σ σ
One Tail / Two Tail ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
STANDARD NORMAL DISTRIBUTION ,[object Object],[object Object],[object Object],[object Object]
STANDARD NORMAL DISTRIBUTION ,[object Object],[object Object]
Exercise ,[object Object]
Answer ,[object Object],[object Object],[object Object],[object Object],[object Object]
Trends in Statistical Tests used in Research Papers Historically Currently Testing Estimation Hypothesis Tests Quoting P-Values Confidence Intervals Results in: Accept/Reject Results in: p-Value Results in: Approx. Mean
Confidence Intervals   ,[object Object]
Confidence Intervals  
[object Object],[object Object],[object Object],[object Object],[object Object],Jerzy Neyman
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Egon Pearson
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Confidence Intervals   ,[object Object]
Confidence Intervals   ,[object Object]
Confidence Intervals   ,[object Object]
Example 1
Example 1 ,[object Object],[object Object],[object Object],[object Object],[object Object]
Example 1 - Solution ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Example 2
Example 2 ,[object Object],[object Object],[object Object],[object Object],[object Object]
Example 2 – 95% CI ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Example 2 – 99% CI ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Example 2 – 99.99% CI ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
T-Tests
William Sealy Gosset ,[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object]
T-Tests ,[object Object]
T-Tests ,[object Object]
T-Tests ,[object Object],[object Object],[object Object]
 
[object Object],[object Object],[object Object],[object Object]
T-Tests ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
T-Tests ,[object Object],[object Object],[object Object],[object Object]
Two Sample T-Test:  Unpaired Sample ,[object Object]
Two Sample T-Test:  Paired Sample ,[object Object]
Choosing the right test
Choosing a statistical test  http://www.graphpad.com/www/Book/Choose.htm
Choosing a statistical test  http://www.graphpad.com/www/Book/Choose.htm

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