1. 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 Center for Aging and Population Health Dept. of Epidemiology, GSPH Dept. of Epidemiology, GSPH

2. Data Types Two basic types: [1] Qualitative (Categorical) Variables  Has values that are intrinsically non-numerical (i.e. without a specific order) (i.e. without a specific order) Sex of participants in a clinical trial Sex of participants in a clinical trial Type of mouse (e.g. wild, flavors of knock-out) Type of mouse (e.g. wild, flavors of knock-out) Types of adverse events Types of adverse events Type of RA treatment: MTX, MTN+ETN, … Type of RA treatment: MTX, MTN+ETN, …

3. Data Types (cont’d) [2] Quantitative (numeric)  Has values that are intrinsically numerical (i.e. have a scale or at least a specific order) (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) IL12 pg/ml cytokine levels (Th1 cell line) in children with active LS (continuous) DAS28 joint count (discrete) DAS28 joint count (discrete) BMI(continuous) BMI(continuous)

4. Quantitative Data Types (cont’d ) Ordinal Subtype Clear ordering Clear ordering Each step indicates an increase (or decrease) Each step indicates an increase (or decrease) vs previous level, but don’t necessarily reflect equal steps Level of education attained Elementary school, high school, some college, college graduate. Elementary school, high school, some college, college graduate.

5. Ordinal Data Type (cont’d ) How much pain did you have in your right knee on most days during the last month? How much pain did you have in your right knee on most days during the last month? 1, None 1, None 2, Mild 2, Mild 3, Moderate 3, Moderate 4, Severe 4, Severe 5, Extreme 5, Extreme 7, Refused 7, Refused 8, Don't know 8, Don't know

6. Ordinal Data Type (cont’d ) How willing are you to have a hip replacement in the next year? How willing are you to have a hip replacement in the next year? 1, Definitely not willing 1, Definitely not willing 2, Probably not willing 2, Probably not willing 3, Unsure 3, Unsure 4, Definitely willing 4, Definitely willing 5, Probably willing 5, Probably willing 7, Refused 7, Refused 8, Don't know 8, Don't know

7. Descriptive Statistics for Continuous Variables Aflatoxin levels of raw peanut kernels (n=15). 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.

8. Aflatoxin levels of raw peanut kernels Stem-and-leaf plot (can be done by hand) Stem (tens)Leaf (Units) 16 16 26 6 2 7 3 8 26 6 2 7 3 8 30 6 1 5 7 30 6 1 5 7 48 48 50 2 50 2

9. Aflatoxin levels of raw peanut kernels Stem-and-leaf plot (can be done by hand) Stem (tens)Leaf (Units) 16 16 22 3 6 6 7 8 22 3 6 6 7 8 30 1 5 6 7 30 1 5 6 7 48 48 50 2 50 2 Range= max-min= 52-16=36 Mode = 26 (highest frequency)

10. Aflatoxin levels of raw peanut kernels 30, 26, 26, 36, 48, 50, 16, 31, 22, 27, 23, 35, 52, 28, 37 Q1 median Q3 Q1 median Q3 16, 22, 23 26, 26, 27, 28, 30, 31, 35, 36, 37, 48, 50, 52 1st Quartile: 25%) (3rd Quartile: 75%) (1st Quartile: 25%) (3rd Quartile: 75%) IQR= Q3-Q1= 37-26= 11

11. Aflatoxin levels of raw peanut kernels

12. Box-and-Whisker Plot (skeletal)

14. Box-and-Whisker Plot (full Bell-labs version with outliers)

17. 25 flights randomly sampled each day during Xmas week 1988