Conclusions
I. A curve has been found representing the frequency distribution of standard deviations of samples drawn from a normal population.
II. A curve has been found representing the frequency distribution of values of the means of such samples, when these values are measured from the mean of the population in terms of the standard deviation of the sample…
IV. Tables are given by which it can be judged whether a series of experiments, however short, have given a result which conforms to any required standard of accuracy or whether it is necessary to continue the investigation.

The Charms of Statistics.—It is difficult to understand why statisticians commonly limit their inquiries to Averages, and do not revel in more comprehensive views. Their souls seem as dull to the charm of variety as that of the native of one of our flat English counties, whose retrospect of Switzerland was that, if its mountains could be thrown into its lakes, two nuisances would be got rid of at once. An Average is but a solitary fact, whereas if a single other fact be added to it, an entire Normal Scheme, which nearly corresponds to the observed one, starts potentially into existence. Some people hate the very name of statistics, but I find them full of beauty and interest. Whenever they are not brutalised, but delicately handled by the higher methods, and are warily interpreted, their power of dealing with complicated phenomena is extraordinary. They are the only tools by which an opening can be cut through the formidable thicket of difficulties that bars the path of those who pursue the Science of man.

A single death is a tragedy, a million deaths is a statistic.

All statements are true, if you are free to redefine their terms.

Among the current discussions, the impact of new and sophisticated methods in the study of the past occupies an important place. The new 'scientific' or 'cliometric' history—born of the marriage contracted between historical problems and advanced statistical analysis, with economic theory as bridesmaid and the computer as best man—has made tremendous advances in the last generation.

Any experiment may be regarded as forming an individual of a 'population' of experiments which might be performed under the same conditions. A series of experiments is a sample drawn from this population.
Now any series of experiments is only of value in so far as it enables us to form a judgment as to the statistical constants of the population to which the experiments belong. In a great number of cases the question finally turns on the value of a mean, either directly, or as the mean difference between the two qualities.
If the number of experiments be very large, we may have precise information as to the value of the mean, but if our sample be small, we have two sources of uncertainty:— (I) owing to the 'error of random sampling' the mean of our series of experiments deviates more or less widely from the mean of the population, and (2) the sample is not sufficiently large to determine what is the law of distribution of individuals.

Any statistics can be extrapolated to the point where they show disaster.

Facts are stubborn, but statistics are more pliable.

Given a large mass of data, we can by judicious selection construct perfectly plausible unassailable theories—all of which, some of which, or none of which may be right.

He uses statistics as a drunken man uses lamp-posts—for support rather than illumination.

I fancy you give me credit for being a more systematic sort of cove than I really am in the matter of limits of significance. What would actually happen would be that I should make out Pt (normal) and say to myself that would be about 50:1; pretty good but as it may not be normal we'd best not be too certain, or 100:1; even allowing that it may not be normal it seems good enough and whether one would be content with that or would require further work would depend on the importance of the conclusion and the difficulty of obtaining suitable experience.

I never could do anything with figures, never had any talent for mathematics, never accomplished anything in my efforts at that rugged study, and to-day the only mathematics I know is multiplication, and the minute I get away up in that, as soon as I reach nine times seven— [He lapsed into deep thought, trying to figure nine times seven. Mr. McKelway whispered the answer to him.] I've got it now. It's eighty-four. Well, I can get that far all right with a little hesitation. After that I am uncertain, and I can't manage a statistic.

I've come loaded with statistics, for I've noticed that a man can't prove anything without statistics. No man can.

If one in twenty does not seem high enough odds, we may, if we prefer it, draw the line at one in fifty (the 2 per cent. point), or one in a hundred (the 1 per cent. point). Personally, the writer prefers to set a low standard of significance at the 5 per cent. point, and ignore entirely all results which fail to reach this level. A scientific fact should be regarded as experimentally established only if a properly designed experiment rarely fails to give this level of significance.

If we betake ourselves to the statistical method, we do so confessing that we are unable to follow the details of each individual case, and expecting that the effects of widespread causes, though very different in each individual, will produce an average result on the whole nation, from a study of which we may estimate the character and propensities of an imaginary being called the Mean Man.

It will be noticed that the fundamental theorem proved above bears some remarkable resemblances to the second law of thermodynamics. Both are properties of populations, or aggregates, true irrespective of the nature of the units which compose them; both are statistical laws; each requires the constant increase of a measurable quantity, in the one case the entropy of a physical system and in the other the fitness, measured by m, of a biological population. As in the physical world we can conceive the theoretical systems in which dissipative forces are wholly absent, and in which the entropy consequently remains constant, so we can conceive, though we need not expect to find, biological populations in which the genetic variance is absolutely zero, and in which fitness does not increase. Professor Eddington has recently remarked that 'The law that entropy always increases—the second law of thermodynamics—holds, I think, the supreme position among the laws of nature'. It is not a little instructive that so similar a law should hold the supreme position among the biological sciences. While it is possible that both may ultimately be absorbed by some more general principle, for the present we should note that the laws as they stand present profound differences—-(1) The systems considered in thermodynamics are permanent; species on the contrary are liable to extinction, although biological improvement must be expected to occur up to the end of their existence. (2) Fitness, although measured by a uniform method, is qualitatively different for every different organism, whereas entropy, like temperature, is taken to have the same meaning for all physical systems. (3) Fitness may be increased or decreased by changes in the environment, without reacting quantitatively upon that environment. (4) Entropy changes are exceptional in the physical world in being irreversible, while irreversible evolutionary changes form no exception among biological phenomena. Finally, (5) entropy changes lead to a progressive disorganization of the physical world, at least from the human standpoint of the utilization of energy, while evolutionary changes are generally recognized as producing progressively higher organization in the organic world.

Killing one man is murder. Killing millions is a statistic

Like the statistician who was drowned in a lake of average depth six inches.

Medical statistics are like a bikini. What they reveal is interesting but what they conceal is vital.

More discoveries have arisen from intense observation of very limited material than from statistics applied to large groups. The value of the latter lies mainly in testing hypotheses arising from the former. While observing one should cultivate a speculative, contemplative attitude of mind and search for clues to be followed up. Training in observation follows the same principles as training in any activity. At first one must do things consciously and laboriously, but with practice the activities gradually become automatic and unconscious and a habit is established. Effective scientific observation also requires a good background, for only by being familiar with the usual can we notice something as being unusual or unexplained.

Most variables can show either an upward or downward trend, depending on the base year chosen.

Statistical science is indispensable to modern statesmanship. In legislation as in physical science it is beginning to be understood that we can control terrestrial forces only by obeying their laws. The legislator must formulate in his statutes not only the national will, but also those great laws of social life revealed by statistics.

Statistics are far from being the barren array of figures ingeniously and laboriously combined into columns and tables, which many persons are apt to suppose them. They constitute rather the ledger of a nation, in which, like the merchant in his books, the citizen can read, at one view, all of the results of a year or of a period of years, as compared with other periods, and deduce the profit or the loss which has been made, in morals, education, wealth or power.

Statistics are somewhat like old medical journals, or like revolvers in newly opened mining districts. Most men rarely use them, and find it troublesome to preserve them so as to have them easy of access; but when they do want them, they want them badly.

Statistics are the triumph of the quantitative method, and the quantitative method is the victory of sterility and death.

Statistics can be made to prove anything—even the truth.

Statistics has been the handmaid of science, and has poured a flood of light upon the dark questions of famine and pestilence, ignorance and crime, disease and death.

Statistics is a science which ought to be honourable, the basis of many most important sciences; but it is not to be carried on by steam, this science, any more than others are; a wise head is requisite for carrying it on.

Statistics, one may hope, will improve gradually, and become good for something. Meanwhile, it is to be feared the crabbed satirist was partly right, as things go: 'A judicious man,' says he, 'looks at Statistics, not to get knowledge, but to save himself from having ignorance foisted on him.'

Statistics: The only science that enables different experts using the same figures to draw different conclusions.

The American Cancer Society's position on the question of a possible cause-effect relationship between cigarette smoking and lung cancer is:
1. The evidence to date justifies suspicion that cigarette smoking does, to a degree as yet undetermined, increase the likelihood of developing cancer of the lung.
2. That available evidence does not constitute irrefutable proof that cigarette smoking is wholly or chiefly or partly responsible for lung cancer.
3. That the evidence at hand calls for the extension of statistical and laboratory studies designed to confirm or deny a causual relationship between cigarette smoking and lung cancer.
4. That the society is committed to furthering such intensified investigation as its resources will permit.

The chief instrument of American statistics is the census, which should accomplish a two-fold object. It should serve the country by making a full and accurate exhibit of the elements of national life and strength, and it should serve the science of statistics by so exhibiting general results that they may be compared with similar data obtained by other nations.

The development of statistics are causing history to be rewritten. Till recently the historian studied nations in the aggregate, and gave us only the story of princes, dynasties, sieges, and battles. Of the people themselves—the great social body with life, growth, sources, elements, and laws of its own—he told us nothing. Now statistical inquiry leads him into the hovels, homes, workshops, mines, fields, prisons, hospitals, and all places where human nature displays its weakness and strength. In these explorations he discovers the seeds of national growth and decay, and thus becomes the prophet of his generation.

The equations of dynamics completely express the laws of the historical method as applied to matter, but the application of these equations implies a perfect knowledge of all the data. But the smallest portion of matter which we can subject to experiment consists of millions of molecules, not one of which ever becomes individually sensible to us. We cannot, therefore, ascertain the actual motion of anyone of these molecules; so that we are obliged to abandon the strict historical method, and to adopt the statistical method of dealing with large groups of molecules ... Thus molecular science teaches us that our experiments can never give us anything more than statistical information, and that no law derived from them can pretend to absolute precision. But when we pass from the contemplation of our experiments to that of the molecules themselves, we leave a world of chance and change, and enter a region where everything is certain and immutable.

The first nonabsolute number is the number of people for whom the table is reserved. This will vary during the course of the first three telephone calls to the restaurant, and then bear no apparent relation to the number of people who actually turn up, or to the number of people who subsequently join them after the show/match/party/gig, or to the number of people who leave when they see who else has turned up.
The second nonabsolute number is the given time of arrival, which is now known to be one of the most bizarre of mathematical concepts, a recipriversexcluson, a number whose existence can only be defined as being anything other than itself. In other words, the given time of arrival is the one moment of time at which it is impossible that any member of the party will arrive. Recipriversexclusons now play a vital part in many branches of math, including statistics and accountancy and also form the basic equations used to engineer the Somebody Else's Problem field.
The third and most mysterious piece of nonabsoluteness of all lies in the relationship between the number of items on the check [bill], the cost of each item, the number of people at the table and what they are each prepared to pay for. (The number of people who have actually brought any money is only a subphenomenon of this field.)

The law of diminishing returns means that even the most beneficial prinicple will become harmful if carried far enough.

The same set of statistics can produce opposite conclusions at different levels of aggregation.

The statistical method is required in the interpretation of figures which are at the mercy of numerous influences, and its object is to determine whether individual influences can be isolated and their effects measured. The essence of the method lies in the determination that we are really comparing like with like, and that we have not overlooked a relevant factor which is present in Group A and absent from Group B. The variability of human beings in their illnesses and in their reactions to them is a fundamental reason for the planned clinical trial and not against it.

The statistician cannot excuse himself from the duty of getting his head clear on the principles of scientific inference, but equally no other thinking man can avoid a like obligation.

There are three kinds of lies: lies, damned lies, and statistics.

To call in the statistician after the experiment is done may be no more than asking him to perform a postmortem examination: he may be able to say what the experiment died of.

To understand God's thoughts one must study statistics ... the measure of his purpose.

Torture numbers, and they will confess to anything.

What the use of P [the significance level] implies, therefore, is that a hypothesis that may be true may be rejected because it has not predicted observable results that have not occurred.

When there are two independent causes of variability capable of producing in an otherwise uniform population distributions with standard deviations s₁ and s₂, it is found that the distribution, when both causes act together, has a standard deviation vs₁² + s₂². It is therefore desirable in analysing the causes of variability to deal with the square of the standard deviation as the measure of variability. We shall term this quantity the Variance of the normal population to which it refers, and we may now ascribe to the constituent causes fractions or percentages of the total variance which they together produce.

Whenever you can, count.

You can always create a fraction by putting one variable upstairs and another variable downstairs, but that soes not establish any causal relationship between them, nor does the resulting quotient have any necessary relationship to anything in the real world.

[Like people] if you torture statistics long enough, they'll tell you anything you want to hear.

…all models are approximations. Essentially, all models are wrong, but some are useful. However, the approximate nature of the model must always be borne in mind…