Moral statistics

Moral statistics most narrowly refers to numerical data generally considered to be indicative of social pathology in groups of people. Examples include statistics on crimes (against persons and property), illiteracy, suicide, illegitimacy, abortion, divorce, prostitution, and the economic situation sometimes called pauperism in the 19th century.

The gathering of anything that might be called social statistics is often dated from John Graunt’s (1662)^[1] analysis of the London Bills of Mortality, which tabulated birth and death data collected by London parishes. The beginnings of the systematic collection of population statistics (now called demography) occurred in the mid-18th century, often attributed to Johann Peter Süssmilch in 1741. Data on moral variables began to be collected and disseminated by various state agencies (most notably in France and Britain) in the early 19th century, and were widely used in debates about social reform.

The first major work on this topic was the Essay on moral statistics of France by André-Michel Guerry in 1833.^[2] In this book, Guerry presented thematic maps of the departments of France, shaded according to illiteracy, crimes against persons and against property, illegitimacy, donations to the poor and so forth, and used these to ask questions about how such moral variables were related.

In Britain this theme was taken up beginning in 1847 by Joseph Fletcher who published several articles on the topic Moral and educational statistics of England and Wales.^[3]^[4]

References

↑ Graunt, J. (1662) Natural and Political Observations on the Bills of Mortality., London: John Martyn and James Allestry.
↑ Guerry, A.-M. (1833) Essai sur la statistique morale de la France. Crochard, Paris.
↑ Fletcher, J. (1847). Moral and educational statistics of England and Wales. Journal of the Statistical Society of London, 10, 193–221. JSTOR 2338048
↑ Fletcher, J. (1849). Moral and educational statistics of England and Wales. Journal of the Statistical Society of London, 12, 151–176, 189–335. JSTOR 2338222

Study design	Effect size Standard error Statistical power Sample size determination

Survey methodology	Sampling stratified cluster Opinion poll Questionnaire

Controlled experiments	Design control optimal Controlled trial Randomized Random assignment Replication Blocking Factorial experiment

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Statistical inference

Statistical theory

Frequentist inference

Confidence interval Testing hypotheses Power

Unbiased estimators	Mean unbiased minimum-variance Median unbiased

Biased estimators	Maximum likelihood Method of moments Minimum distance Density estimation

Parametric tests	Likelihood-ratio Wald Score

Specific tests

Z (normal) Student's t-test F Shapiro–Wilk Kolmogorov–Smirnov

Goodness of fit	Chi-squared G Sample source (Anderson–Darling) Sample normality (Shapiro–Wilk) Skewness / kurtosis normality (Jarque-Bera) Model comparison (Likelihood-ratio) Model quality (Akaike criterion)

Signed-rank	1-sample (Wilcoxon) 2-sample (Mann–Whitney U) 1-way anova (Kruskal–Wallis)

Bayesian inference

Correlation	Pearson product–moment Partial correlation Confounding variable Coefficient of determination

Regression analysis	Errors and residuals Regression model validation Mixed effects models Simultaneous equations models Multivariate adaptive regression splines (MARS)

Linear regression	Simple linear regression Ordinary least squares General linear model Bayesian regression

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Partition of variance	Analysis of variance (ANOVA, anova) Analysis of covariance Multivariate ANOVA Degrees of freedom

Categorical / Multivariate / Time-series / Survival analysis

Categorical

Multivariate

Time-series

General	Decomposition Trend Stationarity Seasonal adjustment Exponential smoothing Cointegration Structural break Granger causality

Specific tests	Dickey–Fuller Johansen Q-statistic (Ljung–Box) Durbin–Watson Breusch–Godfrey

Time domain	Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model (Box–Jenkins) Autoregressive conditional heteroskedasticity (ARCH) Vector autoregression (VAR)

Frequency domain	Spectral density estimation Fourier analysis Wavelet

Survival

Survival function	Kaplan–Meier estimator (product limit) Proportional hazards models Accelerated failure time (AFT) model First hitting time

Hazard function	Nelson–Aalen estimator

Test	Log-rank test

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Biostatistics	Bioinformatics Clinical trials / studies Epidemiology Medical statistics

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Moral statistics

References

Further reading