Descriptive Statistics Descriptive Statistics

Examining Your DataExamining Your Data

Robert Boudreau, PhDRobert Boudreau, PhD

Co-Director of Methodology CoreCo-Director of Methodology Core

PITT-Multidisciplinary Clinical Research Center PITT-Multidisciplinary Clinical Research Center

for Rheumatic and Musculoskeletal Diseasesfor Rheumatic and Musculoskeletal Diseases

Core Director for BiostatisticsCore Director for Biostatistics

Center for Aging and Population Health Center for Aging and Population Health

Dept. of Epidemiology, GSPH Dept. of Epidemiology, GSPH

Data TypesData TypesTwo basic types:Two basic types:

[1] [1] QualitativeQualitative (Categorical) Variables (Categorical) Variables Has values that are intrinsically non-numerical 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 trialSex 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 eventsTypes of adverse events Type of RA treatment: MTX, MTN+ETN, …Type of RA treatment: MTX, MTN+ETN, …

Data Types (cont’d)Data Types (cont’d)

[2] [2] QuantitativeQuantitative (numeric) (numeric) Has values that are intrinsically numerical 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 IL12 pg/ml cytokine levels (Th1 cell line) in children with active LS children with active LS (continuous)(continuous)

DAS28 joint count DAS28 joint count (discrete)(discrete) BMIBMI (continuous)(continuous)

Quantitative Data Types (cont’dQuantitative Data Types (cont’d))

Ordinal Subtype Ordinal Subtype Clear orderingClear ordering Each step indicates an increase (or decrease) Each step indicates an increase (or decrease)

vs previous level, but don’t necessarily reflect vs previous level, but don’t necessarily reflect equal stepsequal steps

Level of education attainedLevel of education attained

Elementary school, high school, Elementary school, high school, some college, college graduate.some college, college graduate.

Ordinal Data Type (cont’dOrdinal Data Type (cont’d))

How much pain did you have in your right knee on How much pain did you have in your right knee on most days during the last month?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 know8, Don't know

Ordinal Data Type (cont’dOrdinal Data Type (cont’d))

How willing are you to have a hip replacement in How willing are you to have a hip replacement in the next year?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

Descriptive Statistics Descriptive Statistics for Continuous Variablesfor Continuous Variables

Aflatoxin levels of raw peanut kernels (n=15).Aflatoxin levels of raw peanut kernels (n=15).

30, 26, 26, 36, 48, 50, 16, 31, 22, 27, 23, 35, 52, 30, 26, 26, 36, 48, 50, 16, 31, 22, 27, 23, 35, 52, 28, 37 28, 37

Aflatoxin, a natural toxin produced by certain Aflatoxin, a natural toxin produced by certain strains of the mold strains of the mold Aspergillus flavusAspergillus flavus and and A. A. parasiticusparasiticus that grow on peanuts stored in warm, that grow on peanuts stored in warm, humid silos. Peanuts aren't the only affected crops. humid silos. Peanuts aren't the only affected crops. Aflatoxins have been found in pecans, pistachios and Aflatoxins have been found in pecans, pistachios and walnuts, as well as milk, grains, soybeans and walnuts, as well as milk, grains, soybeans and spices. Aflatoxin is a potent carcinogen, known to spices. Aflatoxin is a potent carcinogen, known to cause liver cancer in laboratory animals and may cause liver cancer in laboratory animals and may contribute to liver cancer in Africa where peanuts contribute to liver cancer in Africa where peanuts are a dietary staple.are a dietary staple.

Aflatoxin levels of raw peanut kernelsAflatoxin levels of raw peanut kernels

Stem-and-leaf plot Stem-and-leaf plot (can be done by hand)(can be done by hand)

Stem (tens)Stem (tens) Leaf (Units)Leaf (Units)

11 66

22 6 6 2 7 3 86 6 2 7 3 8

33 0 6 1 5 70 6 1 5 7

44 88

55 0 20 2

Aflatoxin levels of raw peanut kernelsAflatoxin levels of raw peanut kernels

Stem-and-leaf plot Stem-and-leaf plot (can be done by hand)(can be done by hand)

Stem (tens)Stem (tens) Leaf (Units)Leaf (Units) 11 66 22 2 3 6 6 7 82 3 6 6 7 8 33 0 1 5 6 70 1 5 6 7 44 88 55 0 20 2

Range= max-min= 52-16=36Range= max-min= 52-16=36Mode = 26 (highest frequency)Mode = 26 (highest frequency)

Aflatoxin levels of raw peanut kernelsAflatoxin levels of raw peanut kernels

30, 26, 26, 36, 48, 50, 16, 31, 22, 27, 23, 35, 52, 28, 3730, 26, 26, 36, 48, 50, 16, 31, 22, 27, 23, 35, 52, 28, 37 Q1Q1 median Q3median Q316, 22, 23 16, 22, 23 2626, 26, 27, 28, , 26, 27, 28, 3030, 31, 35, 36, , 31, 35, 36, 3737, 48, 50, 52, 48, 50, 52 (1st Quartile: 25%) (3rd Quartile: 75%)1st Quartile: 25%) (3rd Quartile: 75%)

IQR= Q3-Q1= 37-26= 11

Aflatoxin levels of raw peanut kernelsAflatoxin levels of raw peanut kernels

Box-and-Whisker Plot (skeletal)Box-and-Whisker Plot (skeletal)

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

25 flights randomlysampled each dayduring Xmas week 1988