Karl Pierson biography. Karl Pearson

Karl Pearson

Pearson, Karl (Charles) (1857-1936) - English positivist philosopher, mathematician and biologist. Studied at Cambridge, Heidelberg and Berlin. Since 1884 - professor of mathematics, and then eugenics at the University of London. According to philosophical views - a subjective idealist.

Philosophical Dictionary / ed.-comp. S. Ya. Podoprigora, A. S. Podoprigora. - Ed. 2nd, sr. - Rostov n/a: Phoenix, 2013, p. 320.

Carl Pearson (1857-1936), English mathematician and idealist philosopher machist. Known for his work in the field of mathematical theory of statistics and its applications in biology (biometrics). The main philosophical work "Grammar of Science" (1892) is devoted to the methodology of science. The task of science, according to Pearson, is not to explain, but only to classify and describe facts. Like other Machists, he considered material things only as groups of sensory perceptions, and the laws of nature, space and time as products of the human mind. Subjective idealism to Pearson stands out in all Machism by its frankness and consistency, by the absence of attempts to imitate materialism. A comprehensive critique of Pearson's views is given by Lenin in his book Materialism and Empirio-Criticism.

Philosophical Dictionary. Ed. I.T. Frolova. M., 1991, p. 341-342.

Pearson, Carl (1857-1936), English positivist philosopher and statistician. Biography. He was educated in Cambridge, Heidelberg and Berlin. Since 1884 - professor of mathematics, then eugenics at the University of London. Research. Continuing the tradition of J. Berkeley and D. Hume, he considered sensory perceptions to be the only objective reality. He was a supporter of eugenics as the science of improving the human race. Made a significant contribution to the dissemination of methods statistical analysis in biology and psychology. In order to test the theory of Charles Darwin, he conducted a voluminous mathematical analysis of various vital problems (tuberculosis, alcoholism, mental retardation).

Kondakov I.M. Psychology. Illustrated dictionary. // THEM. Kondakov. - 2nd ed. add. And a reworker. - St. Petersburg, 2007, p. 423.

Compositions: The Ethics of Free Thought. L" 1888; The Grammar of Science, 1892; in Russian trans.: Grammar of science. SPb., 1911; The Chances of Death and Other Studies in Evolution. V. 1-2, L., 1897; Biomerika, 1900; Natural Life from the Standpoint of Science. L., 1901; The Life, Letters and Labors of E Galton. v. 1-4. Camb., 1914-1930.

Literature: K. Pearson // Psychology: Biographical Bibliographic Dictionary / Ed. N. Sheehy, E. J. Chapman, W. A. Conroy. St. Petersburg: Eurasia, 1999.

Carl Pearson (March 27, 1857 – April 17, 1936) was an English scientist and philosopher. received biological and mathematical education. Professor of Applied Mathematics at University College, University of London (he took this post after his teacher W. Clifford), in 1911-13 he was a professor of eugenics at the same university. In philosophy, Pearson is a typical representative of the "second positivism", the successor of the phenomenal tradition of D. Berkeley, D. Hume and D.S. Mill. He considered the world of external things as a projection outside the internal processes of consciousness. Close to E. Mach (who dedicated his "Mechanics" to him) in understanding the essence of modern science.

Pearson saw the task of science not in explanation, but in the description and classification of facts. At the same time, the scientist should strive to formulate impersonal (intersubjective) judgments about the facts. At the heart of any facts are sensations, a cause, or a source that is unknown. Pearson interpreted causality itself as a relation of regular succession between sensations. The scientific law only describes the sequence of sensations, it is a purely mental construction that saves our thinking. The science of mechanics is a convenient language that generalizes the sensory experience of a scientist. But this language should be cleared of such confusing metaphysical concepts as "matter", "force", "causality", "mass", and a number of others. Many concepts of science (such as the concept of "atom") do not denote any reality, but are constructions of the mind.

Pearson compared metaphysics with poetry, and metaphysics with a poet, who, however, is dangerous, because he claims the rationality of his statements. Science for Pearson is one and all-encompassing, for it there are no inaccessible topics (including philosophical or religious ones). Scientific progress is the main criterion for the progress of mankind, including moral progress. Pearson's positivist philosophy of science was the immediate forerunner of logical positivism and logical empiricism.

A.F. Gryaznov

New Philosophical Encyclopedia. In four volumes. / Institute of Philosophy RAS. Scientific ed. advice: V.S. Stepin, A.A. Huseynov, G.Yu. Semigin. M., Thought, 2010, vol. III, N - S, p. 235.

Read further:

Philosophers, lovers of wisdom (biographical index).

Historical Persons of England (Biographical Index).

Compositions:

Grammar of Science. L., 1892;

The Chances of Death and Other Studies in Evolution, v. 1–2. L., 1897;

Natural Life from the Standpoint of Science. L., 1901;

Grammar of science. SPb., 1911.

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Abstract work

Topic: “Karl Pearson. Biography and scientific activity».

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Introduction. 3

1. Biography. 4

2. Scientific activity 7

2.1 8

Conclusion. 20

Literature. 21

Introduction.

Statistical methods of data analysis are used in almost all areas of human activity. They are used whenever it is necessary to obtain and substantiate any judgments about a group (objects or subjects) with some internal heterogeneity.

Modern stage development statistical methods can be counted from 1900, when the Englishman K. Pearson founded the journal "Biometrika". First third of the 20th century passed under the sign of parametric statistics. Methods based on the analysis of data from parametric families of distributions described by Pearson family curves were studied. The most popular was the normal distribution. The Pearson, Student, and Fisher criteria were used to test the hypotheses. The maximum likelihood method, analysis of variance were proposed, and the main ideas for planning the experiment were formulated.

Karl Pearson (eng. Karl (Carl) Pearson, March 27, 1857, London - April 27, 1936, ibid) - English mathematician, statistician, biologist and philosopher; founder of mathematical statistics, one of the founders of biometrics. Author of over 650 published scientific works. In Russian-language sources, he is sometimes called Charles Pearson.

1. Biography.

The famous mathematician-statistician, biologist and philosopher, a prominent representative of idealistic philosophy, was born on March 27, 1857 in the family of an outstanding lawyer and royal adviser William Pearson.

Average and higher education received Pearson at University College London and at one of the colleges of the University of Cambridge, where he entered in 1875, graduating in 1879 with a master's degree. At first, Pearson intended to follow in his father's footsteps, that is, to become a lawyer, but he soon abandoned this idea and completely indulged in the pleasures of student life.

Nevertheless, after some time, Pearson left for Germany, where he attended lectures on physics at Heidelberg University, and lectures on Roman law and Darwin's theory at Berlin University. It is interesting that Pearson got acquainted with the customs and culture of the Germans with great zeal. He willingly communicated with ordinary people with whom he debated as easily as with eminent scientists.

Pearson's views and his scientific interests were largely influenced by the professor at the University of Cambridge, John Roots. Apparently, he was the greatest mathematician who ever worked at Cambridge. Of his 700 students, about 500 later became scientists. For almost his entire life, Pearson was associated with the University of London. After returning from Germany, at only twenty-seven years of age, Pearson was appointed professor of applied mathematics and mechanics at that university. From that time until his death, which followed suddenly on April 27, 1936, Pearson worked uninterruptedly within the walls of the University of London.

The short summer holidays that Pearson spent in the village house, he also devoted to his beloved science, and worked there as intensively as in his city office. During summer holidays he wrote his monumental work, The Life, Letters, and Works of Francis Galton. In the field of mathematical statistics, Pearson's greatest achievements lie in the development of the following problems:

1) the development of the theory of correlation and its application to the problems of heredity and the evolution of species;

2) the introduction of the "chi-square" criterion into science, used, in particular, to compare the results of an experiment with the results provided theoretically. This criterion has found wide application in mathematical statistics;

3) the introduction of a system of frequency curves (called the Pearson curve system) as a tool for the mathematical description of natural phenomena;

4) application for the first time in mathematical statistics of the method of moments;

5) publication of tables for biometrics and statisticians with detailed explanations regarding their application.

Pearson is considered a major authority on so-called eugenics. He was a professor at the University of London in this discipline and director of the F. Galton International Eugenics Laboratory. For numerous works on the mathematical theory of evolution and heredity, Pearson was awarded the medal. Darwin of the Royal Society of Eugenics, of which Pearson became a member in 1896. The great merit of this scientist is the foundation of the journal "Biometrics", the publication of which Pearson directed for 36 years until his death. In 1925-1926, Pearson published the "Yearbook of Eugenics". Pearson was an outstanding teacher: he had the rare gift of clearly communicating his knowledge to others.

In 1896 he was elected a Fellow of the Royal Society, and in 1898 he was awarded the Darwin Medal. In 1900 he founded the journal Biometrika, dedicated to the application of statistical methods in biology.

2. Scientific activityKarl Pearson in the field of mathematical statistics.

Pearson's name is associated with such widely used terms and methods as:

Pearson curves

Pearson distribution

Pearson's goodness-of-fit test (chi-square test)

Pearson correlation coefficient and correlation analysis

Rank correlation

Multiple Regression

· The coefficient of variation

· Normal distribution

and many others.

Pearson made great efforts to popularize his results in mathematical statistics for their application in other applied sciences, primarily in biology, eugenics, and medicine. A number of his works relate to philosophy and the history of science.

Ronald Aylmer Fisher became a well-known successor and continuer of his work on applied mathematical statistics.

Karl Pearson is best known for:

Pearson's goodness-of-fit test (chi-square test) and Pearson's distribution.

2.1 Pearson's goodness-of-fit test (chi-square test).

Purpose of the criterion χ 2 - Pearson's criterion

The χ 2 criterion is used for two purposes:

1) to compare the empirical distribution of the trait with the theoretical one - uniform, normal or some other;

2) to compare two, three or more empirical distributions of the same feature.

Description of the criterion

The χ 2 criterion answers the question of whether different values of a feature occur with the same frequency in the empirical and theoretical distributions or in two or more empirical distributions.

The advantage of the method is that it allows comparing the distributions of features presented in any scale, starting from the scale of names. In the simplest case of the alternative distribution "yes - no", "allowed marriage - did not allow marriage", "solved the problem - did not solve the problem", etc., we can already apply the criterion χ 2 .

The greater the discrepancy between two comparable distributions, the greater the empirical value of χ 2.

Automatic calculation of χ 2 - Pearson's criterion

To produce automatic calculation of χ 2 - Pearson's criterion, you need to follow the steps in two steps:

Step 1. Specify the number of empirical distributions (from 1 to 10);

Step 2. Enter the empirical frequencies in the table;

Step 3. Get an answer.

The advantage of the Pearson criterion is its universality: it can be used to test hypotheses about various distribution laws.

1. Testing the hypothesis of a normal distribution.

Let a sample of a sufficiently large size be obtained P with a lot of different variant values. For the convenience of its processing, we divide the interval from the smallest to the largest of the values of the variant by s equal parts and we will assume that the values of the options that fall into each interval are approximately equal to the number that specifies the middle of the interval. Having counted the number of options that fell into each interval, we will make the so-called grouped sample:

options……….. X 1 X 2 … x s

frequencies…………. P 1 P 2 … n s ,

where x i are the values of the midpoints of the intervals, and n i is the number of options included in i th interval (empirical frequencies).

Based on the data obtained, it is possible to calculate the sample mean and sample standard deviation σ B. Let us check the assumption that the general population is distributed according to the normal law with parameters M(X) = , D(X) = . Then you can find the number of numbers from the volume sample P, which should be in each interval under this assumption (that is, theoretical frequencies). To do this, using the table of values of the Laplace function, we find the probability of hitting i-th interval:

where a i and b i- borders i-th interval. Multiplying the resulting probabilities by the sample size n, we find the theoretical frequencies: p i =n p i.Our goal is to compare the empirical and theoretical frequencies, which, of course, differ from each other, and to find out whether these differences are insignificant, not disproving the hypothesis of a normal distribution of the studied random variable, or they are so large that they contradict this hypothesis. For this, a criterion is used in the form of a random variable

. (20.1)

Its meaning is obvious: the parts are summed up, which are the squares of the deviations of the empirical frequencies from the theoretical ones from the corresponding theoretical frequencies. It can be proved that regardless of the actual distribution law population the distribution law of a random variable (20.1) as tends to the distribution law (see lecture 12) with the number of degrees of freedom k = s - 1 – r, where r is the number of parameters of the estimated distribution estimated from the sample data. The normal distribution is characterized by two parameters, so k = s - 3. For the selected criterion, a right-handed critical region is constructed, determined by the condition

(20.2)

where α - significance level. Therefore, the critical region is given by the inequality and the acceptance area of the hypothesis is .

So, to test the null hypothesis H 0: the population is normally distributed - you need to calculate the observed value of the criterion from the sample:

, (20.1`)

and according to the table of critical points of the distribution χ 2 find the critical point using the known values of α and k = s - 3. If - the null hypothesis is accepted, if it is rejected.

2. Testing the hypothesis of uniform distribution.

When using the Pearson test to test the hypothesis of a uniform distribution of the general population with an assumed probability density

it is necessary, having calculated the value from the available sample, to estimate the parameters a and b according to the formulas:

where a* and b*- estimates a and b. Indeed, for uniform distribution M(X) = , , from where you can get a system for determining a* and b*: , whose solution is expressions (20.3).

Then, assuming that , you can find the theoretical frequencies using the formulas

Here s is the number of intervals into which the sample is divided.

The observed value of the Pearson criterion is calculated by the formula (20.1`), and the critical value is calculated from the table, taking into account the fact that the number of degrees of freedom k = s - 3. After that, the boundaries of the critical region are determined in the same way as for testing the hypothesis of a normal distribution.

3. Testing the hypothesis about the exponential distribution.

In this case, dividing the existing sample into intervals of equal length, we consider a sequence of options equidistant from each other (we assume that all options that fall into i-th interval, take a value coinciding with its middle), and their corresponding frequencies n i(number of sample options included in i– th interval). We calculate from these data and take as an estimate of the parameter λ value . Then the theoretical frequencies are calculated by the formula

Then, the observed and critical values of the Pearson criterion are compared, taking into account that the number of degrees of freedom k = s - 2.

2.2 Pearson distribution (chi-squared distribution).

The chi-square distribution is one of the most widely used in statistics for testing statistical hypotheses. On the basis of the "chi-square" distribution, one of the most powerful goodness-of-fit tests, Pearson's "chi-square" test, was constructed.

The goodness-of-fit test is a criterion for testing the hypothesis about the proposed law of the unknown distribution.

The χ2 ("chi-square") test is used to test the hypothesis of different distributions. This is his merit.

The calculation formula of the criterion is equal to

where m and m' are the empirical and theoretical frequencies, respectively

distribution under consideration;

n is the number of degrees of freedom.

For verification, we need to compare empirical (observed) and theoretical (calculated under the assumption of a normal distribution) frequencies.

If the empirical frequencies completely coincide with the frequencies calculated or expected, S (E - T) = 0 and the criterion χ2 will also be equal to zero. If S (E - T) is not equal to zero, this will indicate a discrepancy between the calculated frequencies and the empirical frequencies of the series. In such cases, it is necessary to evaluate the significance of the χ2 criterion, which theoretically can vary from zero to infinity. This is done by comparing the actually obtained value of χ2ph with its critical value (χ2st). The null hypothesis, i.e., the assumption that the discrepancy between the empirical and theoretical or expected frequencies is random, is refuted if χ2ph is greater than or equal to χ2st for the accepted significance level (a) and number of degrees of freedom (n).

The distribution of probable values of the random variable χ2 is continuous and asymmetric. It depends on the number of degrees of freedom (n) and approaches a normal distribution as the number of observations increases. Therefore, the application of the χ2 criterion to the estimate discrete distributions is associated with some errors that affect its value, especially for small samples. To obtain more accurate estimates, the sample distributed in the variation series should have at least 50 options. The correct application of the χ2 criterion also requires that the frequencies of variants in the extreme classes should not be less than 5; if there are less than 5 of them, then they are combined with the frequencies of neighboring classes so that their total amount is greater than or equal to 5. According to the combination of frequencies, the number of classes (N) also decreases. The number of degrees of freedom is set according to the secondary number of classes, taking into account the number of restrictions on the freedom of variation.

Since the accuracy of determining the criterion χ2 largely depends on the accuracy of calculating the theoretical frequencies (T), unrounded theoretical frequencies should be used to obtain the difference between the empirical and calculated frequencies.

As an example, take a study published on a website dedicated to the application of statistical methods in the humanities.

The Chi-square test allows comparison of frequency distributions, whether they are normally distributed or not.

Frequency refers to the number of occurrences of an event. Usually, the frequency of occurrence of an event is dealt with when the variables are measured in the scale of names and their other characteristics, except for the frequency, are impossible or problematic to select. In other words, when the variable has qualitative characteristics. Also, many researchers tend to translate test scores into levels (high, medium, low) and build tables of score distributions to find out the number of people at these levels. To prove that in one of the levels (in one of the categories) the number of people is really more (less), the Chi-square coefficient is also used.

Let's take a look at the simplest example.

A self-esteem test was conducted among younger adolescents. Test scores were translated into three levels: high, medium, low. The frequencies were distributed as follows:

High (H) 27 pers.

Medium (C) 12 people

Low (H) 11 pers.

Obviously, children with high self-esteem majority, but this needs to be statistically proven. To do this, we use the Chi-square test.

Our task is to check whether the obtained empirical data differ from the theoretically equally probable ones. To do this, it is necessary to find the theoretical frequencies. In our case, theoretical frequencies are equiprobable frequencies that are found by adding all frequencies and dividing by the number of categories.

In our case:

(B + C + H) / 3 \u003d (27 + 12 + 11) / 3 \u003d 16.6

The formula for calculating the chi-square test is:

χ2 = ∑(E - T)І / T

We build a table:

Empirical (Uh)	Theoretical (T)	(E - T)І / T

12 people.

Find the sum of the last column:

Now you need to find the critical value of the criterion according to the table of critical values (Table 1 in the Appendix). To do this, we need the number of degrees of freedom (n).

n = (R - 1) * (C - 1)

where R is the number of rows in the table, C is the number of columns.

In our case, there is only one column (meaning the original empirical frequencies) and three rows (categories), so the formula changes - we exclude the columns.

n = (R - 1) = 3-1 = 2

For the error probability p≤0.05 and n = 2, the critical value χ2 = 5.99.

The empirical value obtained is greater than the critical value - the frequency differences are significant (χ2= 9.64; p≤0.05).

As you can see, the calculation of the criterion is very simple and does not take much time. The practical value of the chi-square test is enormous. This method is most valuable in the analysis of responses to questionnaires.

Let's take a more complex example.

For example, a psychologist wants to know if it is true that teachers are more biased towards boys than towards girls. Those. more likely to praise girls. To do this, the psychologist analyzed the characteristics of the students written by the teachers for the frequency of occurrence of three words: "active", "diligent", "disciplined", the synonyms of the words were also counted. Data on the frequency of occurrence of words were entered in the table:

	"Active"	"Diligent"	"Disciplined"
boys

To process the obtained data, we use the chi-square test.

To do this, we construct a table of distribution of empirical frequencies, i.e. the frequencies that we observe:

	"Active"	"Diligent"	"Disciplined"
boys

Theoretically, we expect the frequencies to be distributed equally, i.e. the frequency will be distributed proportionally between boys and girls. Let's build a table of theoretical frequencies. To do this, multiply the row sum by the column sum and divide the resulting number by the total sum (s).

	"Active"	"Diligent"	"Disciplined"
boys	(21 * 16)/48 = 7	(21 * 17)/48 = 7.44	(21 * 15)/48 = 6.56
	(27 * 16)/48 = 9	(27 * 17)/48 = 9.56	(27 * 15)/48 = 8.44

The resulting table for calculations will look like this:

		Empirical (Uh)	Theoretical (T)	(E - T)І / T
boys	"Active"
	"Diligent"
	"Disciplined"
	"Active"
	"Diligent"
	"Disciplined"
				Amount: 4.21

χ2 = ∑(E - T)І / T

n = (R - 1), where R is the number of rows in the table.

In our case, chi-square = 4.21; n = 2.

According to the table of critical values of the criterion, we find: at n = 2 and an error level of 0.05, the critical value χ2 = 5.99.

The resulting value is less than the critical value, which means that the null hypothesis is accepted.

Conclusion: teachers do not attach importance to the gender of the child when writing his characteristics.

Conclusion.

K. Pearson made a significant contribution to the development of mathematical statistics (a large number of fundamental concepts). Pearson's main philosophical position is formulated as follows: the concepts of science are artificial constructions, means of describing and ordering sensory experience; rules for linking them to scientific proposals are singled out by the grammar of science, which is the philosophy of science. To connect heterogeneous concepts and phenomena allows a universal discipline - applied statistics, although according to Pearson it is also subjective.

Many constructions of K. Pearson are directly related or developed using anthropological materials. He developed numerous methods of numerical classification and statistical criteria used in all fields of science.

Literature.

1. A. N. Bogolyubov, Mathematics. Mechanics. Biographical guide. - Kyiv: Naukova Dumka, 1983.

2. Kolmogorov A. N., Yushkevich A. P. (ed.). Mathematics of the 19th century. - M.: Science. - T.I.

3. 3. Borovkov A.A. Mathematical statistics. Moscow: Nauka, 1994.

4. 8. Feller V. Introduction to the theory of probability and its applications. - M.: Mir, T.2, 1984.

5. 9. Harman G., Modern factorial analysis. - M.: Statistics, 1972.

(1857-1936). Pearson contributed to the development of the biological, behavioral and social sciences. His applications of mathematical and statistical methods occupy an honorable place among the great scientific achievements.

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"Pearson, Karl" in books

Karl May Karl May

From the book The Author's Encyclopedia of Films. Volume I author Lurcelle Jacques

Karl May Karl May 1971 - Germany (187 min)? Prod. TMS Film (Bernd Eichinger)? Dir. HANS-JURGEN SIEBERBERG Scene. Hans-Jurgen Sieberberg Oper. Dietrich Lohmann (color) Music. Mahler, Chopin, Liszt Cast Helmut Kautner (Karl May), Christina Soderbauem (Emma), Kate Gold (Clara), Attila Horbiger (Dittrich),

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