C: Context The influence of factors taken into account The - PDF document

Dec 2010 Statistical Literacy: Confounding Fall 2010 1 Fall 2010 2 Statistical Literacy: Statistical Literacy Confounding Statistical literacy is the ability to read and MILO SCHIELD, interpret summary statistics in everyday life. Augsburg College Statistical Literacy studies Director, W. M. Keck Statistical Literacy Project Vice President, National Numeracy Network (1) the relation between statistical associations and causation, and University of St. Thomas. December 2010 (2) the kinds of influence on a statistic or statistical association. [Take CARE] Slides at www.StatLit.org/pdf/ 2010-Schield-UST-Confounding-Slides.pdf Fall 2010 3 Fall 2010 4 Take CARE Take CARE C: Context C: Context The influence of factors taken into account The influence of related factors • by comparisons of counts, averages, ratios and (confounders) that were not taken into comparisons of averages and ratios; • by epidemiological models (cf., deaths attributable to account in the study and that were not obesity); blocked by the study design. • by regression models; and • by the study design (cf., controlled vs. uncontrolled; longitudinal vs. cross-sectional; experiment vs. Two continuous measures observational study) or by selection in tables and graphs. The influence of related factors (confounders) not taken into account in the study and not blocked by the study design. Fall 2010 5 Fall 2010 6 SEASON WINS vs. TOTAL PAYROLL Association vs. Causation Adjusting for Land Size US Major League Baseball 102 Indians . 92 House Prices (Average Acres = 1.6) Braves $450,000 1995 Season Wins Red Sox Reds 82 $350,000 Yankees Rangers Best-Fit Line 72 Mets Padres Orioles $250,000 Marlins Expos 62 $150,000 Tigers Pirates Twins BlueJays 52 $50,000 10 20 30 40 50 60 0 1 2 3 4 5 6 Total Payroll ($Millions) Land Size (Acres) 2004AssessMTB 2010-Schield-UST-Confounding-Slides.pdf 1

Dec 2010 Statistical Literacy: Confounding Fall 2010 7 Fall 2010 8 Adjusting for Land Size Income: US Families by Race & Structure Take CARE $65,000 White Families C: Context $60,000 $55,000 The influence of related factors $50,000 (confounders) that were not taken into $45,000 Mean Income account in the study and that were not $40,000 $35,000 blocked by the study design. $30,000 Population $25,000 Two-group averages $20,000 Black Families $15,000 48% 78% 82% $10,000 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Percentage who are headed by Married Couple Fall 2010 9 Fall 2010 10 Adjusting for Land Size Auto Deaths and Airbag Presence Take CARE Confounded by Seatbelt Use C: Context 125 Airbag The influence of related factors Death Rate per 10,00 98 (confounders) that were not taken into Accidents .. account in the study and that were not 70 blocked by the study design. Standardized No Airbag 43 Airbag Two-group rates or percentages 15 0% 20% 40% 60% 80% 100% All Percentage who wear Seatbelts None Fall 2010 11 Fall 2010 12 Subscription Renewal Rates by Month Adjusting for Land Size Conclusion Confounded by Change in Subscription Mix 80% Statistical literacy is an art Standardize 70% as well as a science. 60% Renewal Rate February January 50% 40% Seeing plausible confounders 30% as a major influence on statistics 20% 10% 40% 46% is a skill 10% 0% 20% 40% 60% 80% 100% that requires training. Percentage of Renewals which are Agent 2010-Schield-UST-Confounding-Slides.pdf 2

Fall 2010 1 Statistical Literacy: Confounding MILO SCHIELD, Augsburg College Director, W. M. Keck Statistical Literacy Project Vice President, National Numeracy Network University of St. Thomas. December 2010 Slides at www.StatLit.org/pdf/ 2010-Schield-UST-Confounding-Slides.pdf

Fall 2010 2 Statistical Literacy Statistical literacy is the ability to read and interpret summary statistics in everyday life. Statistical Literacy studies (1) the relation between statistical associations and causation, and (2) the kinds of influence on a statistic or statistical association. [Take CARE]

Fall 2010 3 Take CARE C: Context The influence of factors taken into account • by comparisons of counts, averages, ratios and comparisons of averages and ratios; • by epidemiological models (cf., deaths attributable to obesity); • by regression models; and • by the study design (cf., controlled vs. uncontrolled; longitudinal vs. cross-sectional; experiment vs. observational study) or by selection in tables and graphs. The influence of related factors (confounders) not taken into account in the study and not blocked by the study design.

Fall 2010 4 Take CARE C: Context The influence of related factors (confounders) that were not taken into account in the study and that were not blocked by the study design. Two continuous measures

Fall 2010 5 SEASON WINS vs. TOTAL PAYROLL Association vs. Causation US Major League Baseball 102 Indians . 92 Brav es 1995 Season Wins Red Sox Reds 82 Yankees Rangers 72 Mets Padres Orioles Marlins Expos 62 Tigers Pirates Twins BlueJays 52 10 20 30 40 50 60 Total Payroll ($Millions)

Fall 2010 6 Adjusting for Land Size House Prices (Average Acres = 1.6) $450,000 $350,000 Best-Fit Line $250,000 $150,000 $50,000 0 1 2 3 4 5 6 Land Size (Acres) 2004AssessMTB

Fall 2010 7 Take CARE C: Context The influence of related factors (confounders) that were not taken into account in the study and that were not blocked by the study design. Two-group averages

Fall 2010 8 Adjusting for Land Size Income: US Families by Race & Structure $65,000 White Families $60,000 $55,000 $50,000 $45,000 Mean Income $40,000 $35,000 $30,000 Population $25,000 Black Families $20,000 $15,000 48% 78% 82% $10,000 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Percentage who are headed by Married Couple

Fall 2010 9 Take CARE C: Context The influence of related factors (confounders) that were not taken into account in the study and that were not blocked by the study design. Two-group rates or percentages

Fall 2010 10 Adjusting for Land Size Auto Deaths and Airbag Presence Confounded by Seatbelt Use 125 Airbag Death Rate per 10,00 98 Accidents .. 70 Standardized No Airbag 43 Airbag 15 0% 20% 40% 60% 80% 100% All Percentage who wear Seatbelts None

Fall 2010 11 Subscription Renewal Rates by Month Adjusting for Land Size Confounded by Change in Subscription Mix 80% Standardize 70% 60% Renewal Rate February January 50% 40% 30% 20% 10% 40% 46% 10% 0% 20% 40% 60% 80% 100% Percentage of Renewals which are Agent

Fall 2010 12 Conclusion Statistical literacy is an art as well as a science. Seeing plausible confounders as a major influence on statistics is a skill that requires training.