① Descriptive statistics, whose task is to study and describe the reduced data. For example, a large number of collected data are classified and expressed in the form of tables or charts. By calculating the characteristic values such as concentration, difference and correlation coefficient of the obtained data, the typicality, fluctuation range and relationship of related things are described, and the internal laws of things are revealed.
(2) Inference statistics, that is, statistical testing, statistical analysis and nonparametric statistical methods are used to make decisions. That is to say, with a certain degree of certainty, we can infer a more general situation from some data, so that the conclusion can be applied to a wider range, or make predictions based on known data combined with educational characteristics. At the beginning of the 20th century, American psychologist E.L. Thorndike used psychology and statistics as tools to study pedagogy in order to make education scientific. 1904 wrote the handbook of social statistics application-introduction to psychological and social measurement, which is the first monograph on educational statistics in the world. Since then, American universities have offered psychology and statistics courses and published textbooks. For example, the Outline of Statistics by psychologist L·L· thurston (1925) and Statistics in Psychology and Education by experimental psychologist H·E· Garrett (1926). Most of these textbooks are descriptive statistics.
Since the 1940s, mathematical statistics has been widely used in European and American countries to study psychological and educational problems, and the main contents such as small sample theory, statistical estimation and statistical test have been added to the textbooks used. Since thurston and others studied human intelligence with factor analysis under the influence of British psychologist C·E· Spearman, educational statistics has entered the stage with inferential statistic as the main content. The representative work at that time was Statistical Analysis in Educational Research by E.F. Ringkvist (1940). Subsequently, statisticians discovered the hypotheses involved in the statistical hypothesis test. For example, if the basic distribution form of the population is that the normal distribution density can't be satisfied or the basic distribution form is simply unknown, they introduce a statistical method that has nothing to do with the density form-nonparametric method, which makes the content of educational statistics more substantial and rich, and the practical scope more extensive.
The representative works in this field are "Educational Statistics-Application and Interpretation" co-authored by W·J· Pophan and K·A· Serotti Nick (1973) and "Basic Statistics in Psychology and Education" co-authored by J·P· guildford and B Frescher (1978). In the 1970s, due to the wide application of electronic computers, many educational statistics textbooks also introduced the use of electronic computers to process data. For example, "Educational Statistics with Data Processing" written by D. White in 1973 is one of them. I. Descriptive statistics
It is to process and sort out the collected data according to statistical methods, and analyze and describe the data in the form of charts and typical quantities.
The main ways of collecting statistical data by investigation and laboratory; Statistical tables and charts are the main forms of presenting statistical data; The typical quantity of statistical data mainly includes centralized quantity, difference quantity and related quantity, reflecting the trend of concentration. Such as the average score and excellent rate in academic examinations; The enrollment rate mastered by the education administrative department, etc.
Second, infer statistical data.
This paper mainly studies the theory and method of explaining the whole by local area, that is, according to local information, using statistical principles and methods, analyzing and demonstrating the quantitative characteristics or distribution characteristics of the whole under a certain credibility. It is based on descriptive statistics. ① The original data of educational statistics processing comes from the data provided by educational measurement, and the authenticity and reliability of the data depends on the effectiveness and reliability of educational measurement itself. The determination of validity and reliability in educational measurement and item analysis must also use statistical correlation coefficient and factor analysis. ② Statistical knowledge, such as percentile, mean, standard deviation, standard score, normal distribution, etc. It must be used when compiling various scales of educational metrology and determining various quotas.
The rise of experimental statistics has greatly enriched the content of statistics. Its influence has also expanded the scope of educational statistics. This is manifested in the following aspects: ① The data used in educational research are diverse. As for the "level" of variables, there are not only intervals and ratios, but also many variables are nominal and ordinal, and each variable with different "level" has its own corresponding statistical method. For example, for the latter two variables, the average value should not be used. (2) In educational problems, there is often a large sample size, so the law of large numbers can be used as an approximate method for an alternative statistical analysis.
China's educational statistics was introduced with the achievements of western science and technology after the Revolution of 1911. At that time, the department of university education and secondary normal schools all took educational statistics as a compulsory course. Many scholars have taught this course and written monographs. For example, Xue Hongzhi's Education Statistics (1925), Junyi Zhu's Education Statistics (1930), Shen Yougan's Education Statistics Lecture (1946) and Experimental Design and Statistical Methods (1947). After 1950s, due to the simplification of the curriculum, the school stopped educational statistics. Since 1979, with the development of educational scientific research, educational statistics have been restored. The Ministry of Education organized Ye Peihua (editor-in-chief), Wan, Hao and Chen to compile Education Statistics (1983), a national textbook. In recent years, due to the use of electronic computers, many innovative measures have appeared in the field of statistics. These measures have had an impact on education statistics.
① In order to save time and simplify procedures, the current textbooks of educational statistics all list the definition formulas and calculation formulas of various statistics. In order to improve efficiency, when using electronic computers, the calculation formulas accepted by electronic computers are paid more and more attention and applied. For example, the definition formula for calculating pearson product correlation is:
② In the past, most educational statistics textbooks devoted considerable space to the simple statistical processing method of the so-called grouping frequency distribution. Although this has a certain descriptive function, compared with electronic computers, the calculation program is not simple and the results are not accurate. The electronic computer directly processes the data, which is not only faster and more accurate, but also can directly compile the frequency distribution table without manually recording all the data one by one. So there are many teaching materials now, which only introduce the compilation of frequency distribution table, correlation table or related scatter diagram. However, it is not explained how to use the frequency distribution table and correlation table as the basis for further statistical processing.
(3) The content of regression analysis was discussed in previous educational statistics textbooks. Because of the complexity of calculation, only one-dimensional regression and two-dimensional regression are introduced, and the regression problem above three-dimensional regression is only theoretical introduction at most, and the practical application is rarely discussed in detail. This is obviously not enough to predict the educational problem of "effects caused by various related variables". With the popularization and use of computers in educational statistics, multivariate statistical analysis will be paid more and more attention and applied.
In a word, due to the application of electronic computers and the development of experimental statistics, the practical educational statistics will delete those impractical contents and introduce many necessary statistical methods, which will be the development trend of educational statistics in the future.