Source: Handout 01, Principles of Statistics I (Texas A&M University) | Textbook: Ott & Longnecker, 7th Ed.
Tags: applications of statistics, acid rain, clinical trial, Salk vaccine, forensic science, bowhead whale, ozone exposure, public opinion polls, FDA, epidemiology, courtroom statistics
Statistics is applied across an enormous range of fields: environmental science (acid rain, ozone monitoring), medicine (clinical trials for vaccines and drugs), law (forensic evidence, salary discrimination suits), wildlife conservation (whale population estimation), and public opinion (polling). These examples show that every application follows the same core process of planning, collecting, analysing, and reporting.
Clinical trial
A controlled experiment with human participants, typically involving random assignment to treatment and placebo groups, used to establish the effectiveness of a drug or medical device.
Placebo
A solution or tablet that does not contain the active medication, given to a control group so that any observed effect can be attributed to the treatment rather than the act of receiving care.
Epidemiology
The study of how diseases are distributed in populations and the factors that influence that distribution. Epidemiologists use statistical methods to identify associations between exposures and health outcomes.
Statistical association
A measured relationship between two variables in data. An association does not, by itself, imply causation.
Spatial-temporal model
A statistical model that accounts for variation across both geographic location and time. Used in environmental monitoring (e.g., ozone concentration mapping).
Acid rain is caused by sulfuric and nitric acids released from burning hydrocarbon fuels. Its effects include:
Preventing fish reproduction in contaminated spring snow melts
Weakening trees, making them vulnerable to insects and disease
Leaching nutrients from soil near affected water bodies
Causing an estimated $15 billion in structural damage in the U.S. by the early 2000s
The National Science Foundation recommended a 50% reduction in sulfur-oxide emissions. Statisticians play a role in monitoring atmospheric conditions, testing emission control devices, and evaluating alternative energy sources.
The Salk vaccine trial (begun 1954) is a landmark example of statistics in medicine.
Polio incidence was extremely low (fewer than 50 cases per 100,000 children), so detecting a difference between vaccine and placebo required a very large sample
Statisticians determined that 400,000 children were needed
Participants were randomly assigned to vaccine or placebo groups through a public school inoculation programme
Fewer than 200 polio cases were reported among the 400,000, but more than three times as many appeared in the placebo group
These results, combined with statistical calculations, confirmed the vaccine's effectiveness
The key lesson: sample size must be large enough relative to the rarity of the event you are trying to detect. Without statistical planning, this conclusion would not have been possible.
The FDA now requires pharmaceutical firms to provide rigorous statistical evidence of effectiveness before approving new drugs and devices.
Statistical evidence appears in courtrooms in several ways:
Epidemiological testimony: determining whether a statistical association exists between an exposure (e.g., silicone breast implant leakage) and a disease (e.g., autoimmune condition), and whether the association reflects causation or random variation
Salary discrimination suits: statistical models are built to explain salary differences based on work experience, education, and performance. Adjusted salaries are then compared across demographic groups to see whether significant differences persist after controlling for relevant factors
Forensic science: many traditional forensic methods (bite marks, hair analysis, footwear comparison, firearms matching) have been criticised for lacking rigorous statistical validation. A 2016 report from the President's Council of Advisors on Science and Technology called for more study of error rates in these methods
Bowhead whales were the first great whale species for which commercial whaling was stopped.
Researchers conducted a visual and acoustic census at Point Barrow, Alaska
Statistical models and estimation techniques were applied to the census data
Results showed the population was increasing at a healthy rate after the hunting ban
The International Whaling Commission uses these estimates to set aboriginal subsistence whaling quotas
This is an example of statistics informing conservation and policy decisions.
Houston's ozone levels were rated second only to Los Angeles for exceeding national air quality standards.
Hourly ozone measurements from 9–12 monitoring stations were collected from 1980 to 1993, along with temperature, wind speed, and wind direction
Three statistical goals: assess data quality and missing data patterns; build a spatial-temporal model to predict ozone at any location and time; estimate population exposure indices using census data
Key findings: highest ozone levels occurred at locations with relatively small populations of young children; exposure of young children to ozone decreased by roughly 20% over the period; the placement of monitors was not ideal for assessing population exposure
This project used all four components of the learning-from-data process: planning, graphing, modelling, and reporting.
Polls are a highly visible application of statistics. Common topics include consumer confidence, candidate preferences, product preferences, policy attitudes, and social issues.
Critical questions to ask about any poll:
What was the population of interest?
Was the sample selected from that population?
What questions were asked, and how were they phrased?
Was each respondent asked the same question?
Could the phrasing have biased the responses?
These issues are covered in detail in Handout 2.
⚠️ The Salk vaccine trial illustrates why sample size must be matched to the rarity of the event being studied. This concept recurs in hypothesis testing.
⚠️ Understand the difference between statistical association and causation, especially in the courtroom/epidemiology context.
⚠️ Know that forensic "feature comparison" methods (bite marks, hair, footwear) have been challenged for lacking statistical reliability.
⚠️ The ozone study is a good example of spatial-temporal modelling and the practical policy implications of statistical analysis.
⚠️ For polls: be able to identify potential sources of bias (population definition, sampling method, question phrasing).
Q: Why did the Salk vaccine trial require 400,000 participants?
A: Because the incidence rate of polio was extremely low (fewer than 50 per 100,000 children). A very large sample was needed to detect a statistically significant difference between the vaccinated and placebo groups.
Q: In a salary discrimination case, why do statisticians build models that include variables like work experience and education?
A: To control for legitimate factors that explain salary differences. Only after adjusting for these factors can the analysis determine whether significant salary differences remain that might be attributable to age, ethnicity, or sex.
Q: What was the key finding of the Houston ozone study regarding monitor placement?
A: The current placement of monitors was not ideal for assessing population exposure to ozone. The highest ozone levels occurred in locations with relatively small populations of young children.
Q: Name three critical questions you should ask when evaluating any opinion poll.
A: (1) What was the population of interest? (2) Was the sample selected from that population? (3) How were the questions phrased, and could the phrasing have biased responses?
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