Statistics for Scientists

Material for Session 2: Describing Data

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General Principles:

• All numbers you measure, or obtain from samples, contain scatter (random variability).
• The job of statistical analysis is to deal with the randomness.
• A collection of numbers form a distribution that reflects the shape of the parent population.

What is the distribution of the set of numbers you've obtained?

Make a histogram!

• All statistics packages can make histograms
• Excel can tabulate and graph histograms, but it's tricky
• Go to the Descriptive Statistics section of StatPages.net

Other graphical representations of the shape of a distribution

• Box & Whiskers Diagram
• Dot-Plot

Where are the numbers "centered"? (central tendency)

• Arithmetic Mean (average)
• Other Means (geometric, root-mean-square, harmonic)
• Median
• Mode

How much do they spread away from the center? (dispersion)

• Average Deviation (quaint)
• Standard Deviation
• Coefficient of Variation (SD / mean)
• Range
• Semi-interquartile Range (quaint)

How do they differ from the usual "bell shape"?

• Skewness (asymmetric tails)
• Kurtosis (pointy or flat peak)

Fitting a distribution to your data

• Normal
• Log-normal