Introducing Statistics: A Graphic Guide
Genres: Mathematics
Book Preface
Drowning by Numbers
We are drowning in statistics. And they are not just numbers. For the media, statistics are routinely “damningâ€, “horrifyingâ€, “deadlyâ€, “troublesome†– or, on occasion, “encouragingâ€. The press constantly suggest that statistical information about crime, disease, poverty and transport delays is not only the source of the problem, but that it represents real entities or real people instead of one point on a graph.
Averages or Variation?
Much of the shock-horror statistical information used by the media is based on statistical averages. Despite the often misleading preoccupation with averages, the most important statistical concept neglected by journalists and news reporters is variation. This concept is essential to modern mathematical statistics and plays a pivotal role in biological, medical, educational and industrial statistics.
Why Study Statistics?
Statistics are used by scientists, economists, government officials, industry and manufacturers. Statistical decisions are made constantly and affect our daily lives – from the medicine we take, the treatments we receive, the aptitude and psychometric tests employers give routinely, the cars we drive, the clothes we wear (wool manufacturers use statistical tests to determine the thread weave for our comfort) to the food we eat and even the beer we drink.
What are Statistics?
Yet for all their ubiquity, we don’t really know what to make of statistics. As one columnist put it, “cigarettes are the biggest single cause of statisticsâ€. People express a wish to avoid bad things by saying, “I don’t want to be another statisticâ€. Do statisticians really think that all of humanity is reducible to a few numbers?
Although some people think that statistical results are irrefutable, others believe that all statistical information is deceptive
What Does Statistics Mean?
The word “statistics†is derived from the Latin status, which led to the Italian word statista, first used in the 16th century, referring to a statist or statesman – someone concerned with matters of the state. The Germans used Statistik around 1750, the French introduced statistique in 1785 and the Dutch adopted statistiek in 1807.
Early statistics was a quantitative system for describing matters of state – a form of “political arithmeticâ€.
The system was first used in 17th-century England by the London merchant John Graunt (1620–74) and the Irish natural philosopher William Petty (1623–87).
In the 18th century, many statists were jurists; their background was often in public law (the branch of law concerned with the state itself).
It was the Scottish landowner and first president of the Board of Agriculture, Sir John Sinclair (1754–1834), who introduced the word “statistics†into the English language in 1798 in his Statistical Account of Scotland.
I wanted to measure the “quantum of happiness†of the Scots. The What?
Sinclair used statistics for social phenomena rather than for political matters. This led eventually to the development of vital statistics in the mid-19th century.
Vital Statistics vs. Mathematical Statistics
Not all statistics are the same. There are two types: vital statistics and mathematical statistics.
Vital statistics is what most people understand by statistics. It is used as a plural noun and refers to an aggregate set of data.
It refers to the description and enumeration used in census counts or in the tabulation of official statistics such as marriage, divorce and crime statistics. We also have insurance statistics and even cricket and baseball statistics.
This process is primarily concerned with average values, and uses life tables, percentages, proportions and ratios: probability is most commonly used for actuarial (i.e. life-insurance) purposes. It was not until the 20th century that the singular form “statisticâ€, signifying an individual fact, came into use.
Mathematical statistics is used as a singular noun, and it arose out of the mathematical theory of probability in the late 18th century from the work of such continental mathematicians as Jacob Bernoulli, Abraham DeMoivre, Pierre-Simon Laplace and Carl Friedrich Gauss.
In the late 19th century, mathematical statistics began to take shape as a fully-fledged academic discipline in the work of Francis Ysidro Edgeworth (1845–1926), John Venn (1834–1923), Francis Galton (1822–1911), W.F.R. Weldon (1860–1906) and Karl Pearson (1857–1936).
We three began to apply Charles Darwin’s ideas to the measurement of biological variation, which required a new statistical methodology.
Mathematical statistics encompasses a scientific discipline that analyses variation, and is often underpinned by matrix algebra. It deals with the collection, classification, description and interpretation of data from social surveys, scientific experiments and clinical trials. Probability is used for statistical tests of significance.
Mathematical statistics is analytical and can be used to make statistical predictions or inferences about the population. Furthermore, it capitalizes on all the individual differences in a group by examining the spread of this statistical variation through such methods as the range and standard deviation, which we’ll look at later. Vital statistics is concerned with averages, whereas mathematical statistics deals with variation.
Used in this sense, statistics is a technical discipline, and while it is mathematical, it is essential to understand the statistical concepts underlying the mathematical procedures.
Contents
Cover
Title Page
Copyright
Drowning by Numbers
Averages or Variation?
Why Study Statistics?
What are Statistics?
What Does Statistics Mean?
Vital Statistics vs. Mathematical Statistics
The Philosophy of Statistics
Darwin and Statistical Populations
Victorian Values
Where Did it All Begin?
Parish Registers
The London Bills of Mortality
Halley’s Mortality Tables
Malthusian Populations
Demography – the Science of Populations
The Statistical Society of London
Edwin Chadwick and Sanitary Reforms
William Farr and Vital Statistics
Florence Nightingale: the Passionate Statistician
The Statistics of the Crimean War
Mortality Statistics in the Crimea
Polar Area Graphs
Probability
Variables
Games of Chance
De Moivre and Gambling in Soho
The Mathematical Theory of Probability
Relative Frequency
The Bayesian Approach
Probability Distributions
The Poisson Distribution
The Normal Distribution
Astronomical Observations
The Central Limit Theorem
The Gaussian Curve and the Principle of Least Squares
What’s Normal?
The Naming of the Normal
So What is the Normal Distribution?
Quetelismus
Galton’s Pantograph
How to Summarise the Data?
Quetelet and the Arithmetical Mean
The Mean
The Median
How to Locate or Calculate the Median
Does it Matter Which Statistical Average is Used?
Misleading With Statistics
Data Management Procedures
Standardized Frequency Distributions
Samples vs. Populations
The Histogram
Frequency Distributions
The Method of Moments
Natural Selection: the Changing Shapes of Darwinian Distributions
The Peppered Moth
The Pearsonian Family of Curves
The Interquartile Range
The Standard Deviation
Coefficient of Variation
Comparing Variation of Variables
Practical Applications
Pearson’s Scales of Measurement
Nominal and Ordinal Variables
Ratio and Interval
Early Uses of Correlation
Causation and Spurious Correlation
Path Analysis and Causation
Scatter Diagrams
Weldon and Negative Correlation
Curvilinear Relationships
Galton and Biological Regression
Regression to the Mean
Galton’s Two Regression Lines
George Udny Yule and the Method of Least Squares
Correlation vs. Regression
Galton’s Dilemma
Pearson’s Product-Moment Correlation
Simple Correlation and Multiple Correlation
Statistical Control
Discrete 2 × 2 Relationships
Biserial Correlations
Egon Pearson and Polychoric Correlations
Factor Analysis
Maurice Kendall’s Tau Coefficient
Correlation vs. Association
Curve-Fitting for Asymmetrical Distributions
Interpreting Results with Degrees of Freedom
The Chi-Square Probability Table
A Statistical Test for the Guinness Brewery
Quantifying Brewery Material
Agricultural Variation
Small Samples vs. Large Samples
Testing Statistical Differences Between Two Means
Statistical Results for Guinness
Student’s t-test
A New Statistical Era: Rothamsted’s Broadbalk Agricultural Data
Fisher’s Statistical Analysis of Variance
The Analysis of Agricultural Variation
The Analysis of Variance and Small Samples
Inferential Statistics
The Sampling Distribution
Conclusion
Bibliography
About the Author
Index
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