Descriptive Statistics

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• Descriptive Statistics
• Examining Your Data
• Robert Boudreau, PhD
• Co-Director of Methodology Core
• PITT-Multidisciplinary Clinical Research Center
• for Rheumatic and Musculoskeletal Diseases
• Core Director for Biostatistics
• Center for Aging and Population Health
• Dept. of Epidemiology, GSPH

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Data Types

• Two basic types
• 1 Qualitative (Categorical) Variables
• ? Has values that are intrinsically non-numerical
  
• (i.e. without a specific order)
• Sex of participants in a clinical trial
• Type of mouse (e.g. wild, flavors of knock-out)
• Types of adverse events
• Type of RA treatment MTX, MTNETN,

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Data Types (contd)

• 2 Quantitative (numeric)
• ? Has values that are intrinsically numerical
• (i.e. have a scale or at least a specific
  order)
• IL12 pg/ml cytokine levels (Th1 cell line) in
  children with active LS (continuous)
• DAS28 joint count (discrete)
• BMI (continuous)

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Quantitative Data Types (contd)

• Ordinal Subtype
• Clear ordering
• Each step indicates an increase (or decrease)
• vs previous level, but dont necessarily reflect
  equal steps
• Level of education attained
• Elementary school, high school, some college,
  college graduate.

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Ordinal Data Type (contd)

• How much pain did you have in your right knee
  on most days during the last month?
• 1, None
• 2, Mild
• 3, Moderate
• 4, Severe
• 5, Extreme
• 7, Refused
• 8, Don't know

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Ordinal Data Type (contd)

• How willing are you to have a hip replacement
  in the next year?
• 1, Definitely not willing
• 2, Probably not willing
• 3, Unsure
• 4, Definitely willing
• 5, Probably willing
• 7, Refused
• 8, Don't know

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Descriptive Statistics for Continuous Variables

• Aflatoxin levels of raw peanut kernels (n15).
• 30, 26, 26, 36, 48, 50, 16, 31, 22, 27, 23, 35,
  52,
• 28, 37
• Aflatoxin, a natural toxin produced by certain
  strains of the mold Aspergillus flavus and A.
  parasiticus that grow on peanuts stored in warm,
  humid silos. Peanuts aren't the only affected
  crops. Aflatoxins have been found in pecans,
  pistachios and walnuts, as well as milk, grains,
  soybeans and spices. Aflatoxin is a potent
  carcinogen, known to cause liver cancer in
  laboratory animals and may contribute to liver
  cancer in Africa where peanuts are a dietary
  staple.

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Aflatoxin levels of raw peanut kernels

• Stem-and-leaf plot (can be done by hand)
• Stem (tens) Leaf (Units)
• 1 6
• 2 6 6 2 7 3 8
• 3 0 6 1 5 7
• 4 8
• 5 0 2

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Aflatoxin levels of raw peanut kernels

• Stem-and-leaf plot (can be done by hand)
• Stem (tens) Leaf (Units)
• 1 6
• 2 2 3 6 6 7 8
• 3 0 1 5 6 7
• 4 8
• 5 0 2
• Range max-min 52-1636
• Mode 26 (highest frequency)

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Aflatoxin levels of raw peanut kernels
30, 26, 26, 36, 48, 50, 16, 31, 22, 27, 23, 35,
52, 28, 37
Q1 median
Q3 16, 22, 23 26, 26, 27, 28, 30, 31, 35,
36, 37, 48, 50, 52 (1st
Quartile 25)
(3rd Quartile 75) IQR Q3-Q1 37-26
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Aflatoxin levels of raw peanut kernels
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Box-and-Whisker Plot (skeletal)
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Box-and-Whisker Plot (full Bell-labs version
with outliers)
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25 flights randomly sampled each day during Xmas
week 1988
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