1. Introduction to statistics - explanation of its applicability to metallurgists. Graphical representation of a data set, assessment of data type. General principles of testing.
2. Verification of homogeneity of the data set using graphs. Outliers - their display, detection (box plot) and resolution.
3. Verification of data independence using graphs. Effect of data dependency on the quality of file processing.
4. Verification of data normality: normal distribution, Gaussian curve and its parameters, empirical histogram. Reasons for the required normality and procedure if it is not met.
5. Numerical characteristics of position, variability, skewness and peakedness. Concept of robustness of numerical characteristics.
6. Theoretical distributions of Student's, Fisher's and Pearson's: graphs of distributions. Examples of these distributions, working with tables of quantiles and critical values.
7. Point and interval estimation. Concepts of 'confidence level' and 'significance level'.
8. Analysis of two sets of statistics: testing the significance of the difference between sample means and sample variances; two-sample t-test, F test.
9. Evaluation of the degree of dependence (correlation) of two variables: Pearson correlation coefficient, Spearman's rank correlation coefficient.
10. Regression analysis - simple (pairwise) linear regression. Estimation of regression coefficients using the least squares method. Evaluation of significance and quality of the regression function. Simple non-linear regression models (power, exponential, logarithmic, quadratic and polynomial).
11. Regression analysis - multiple linear regression. Evaluation of model significance and regression coefficients. Application of multiple regression.
2. Verification of homogeneity of the data set using graphs. Outliers - their display, detection (box plot) and resolution.
3. Verification of data independence using graphs. Effect of data dependency on the quality of file processing.
4. Verification of data normality: normal distribution, Gaussian curve and its parameters, empirical histogram. Reasons for the required normality and procedure if it is not met.
5. Numerical characteristics of position, variability, skewness and peakedness. Concept of robustness of numerical characteristics.
6. Theoretical distributions of Student's, Fisher's and Pearson's: graphs of distributions. Examples of these distributions, working with tables of quantiles and critical values.
7. Point and interval estimation. Concepts of 'confidence level' and 'significance level'.
8. Analysis of two sets of statistics: testing the significance of the difference between sample means and sample variances; two-sample t-test, F test.
9. Evaluation of the degree of dependence (correlation) of two variables: Pearson correlation coefficient, Spearman's rank correlation coefficient.
10. Regression analysis - simple (pairwise) linear regression. Estimation of regression coefficients using the least squares method. Evaluation of significance and quality of the regression function. Simple non-linear regression models (power, exponential, logarithmic, quadratic and polynomial).
11. Regression analysis - multiple linear regression. Evaluation of model significance and regression coefficients. Application of multiple regression.