Statistics ' ' ' A Crash Course

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Statistics . . . A Crash Course

• (Dr.) Jason Brotherton

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Managing Expectations

• Im not a statistician
• I dont even play one on TV
• What this is NOT
• A thorough course on statistics
• (you WILL be dangerous!)
• What we hope to achieve
• A brief sampling of what you can do
• A practical foundation for doing it

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Overview

• Principles of Testing
• Populations and samples
• Generating a hypothesis
• The Tests (focusing on Excel, not Statistics)
• Describing a population
• Comparing two populations
• t-Test
• Paired t-Test
• Looking for correlations
• Regression
• ?2 test (chi-squared)

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Before we begin

• Which method is better, A or B?
• How to prove it?

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Works for Questionnaires Too!

• Are students who answer A,B for Q1 more likely
  to answer D,E for Q2?
• How to prove it?

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Populations and Samples
We want to know about these
We have this to work with
Random Selection
Population
Sample
Inference
µ
?
Parameter
Statistic
(Population mean)
(Sample mean)
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Generating a Hypothesis

• Research Hypothesis
• Students at Tech perform differently than
  students at Georgia
• (tech ! georgia)
• (or could be one direction)
• tech gt georgia
• Null Hypothesis
• They perform the same
• (tech georgia)
• Easy enough, but ... How do you prove it?

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Tasks We Can Do

• Describe a population
• Compare one population to another
• T-test
• Compare one population to itself (before and
  after effects)
• Paired t-test
• Validate trends, correlations
• Regression
• CHI-Square

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Describing a Population

• We look for the central tendency of the data set
• Mean
• Median
• Mode
• Save the math, use Excel, but understand the
  influencing factors

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Variance and Standard Deviation

• Mean, median, mode not enough!
• Variance is the sum of each samples distance
  from the mean.
• Standard Deviation is the square root of the
  variance.
• Standard Deviation measures the variability in
  the data.

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More about Standard Deviation

• What does it really mean?

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Comparing Two Populations

• T-test
• What is it good for?
• How to report results?

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Comparing Before and After

• Paired t-test
• What is it good for?
• How to report results?

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Looking for a trend / correlation

• Regression Analysis
• Continuous data
• What is it good for?
• How to report results?

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Looking for a trend / correlation

• CHI-Squared
• Discrete data
• What is it good for?
• How to report results?

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What You Should Take Away

• Be able to identify which test is useful for
  which task.
• T-test, Paired t-test, Regression, ?2
• Be able to do each test in Excel and know how to
  write up the results.