511156 - STATISTICS APPLIED TO PHARMACEUTICAL SCIENCES

The course is organized into five units, each dedicated to a specific topic. Access to Unit 5 requires understanding and practice of the subjects exposed in Units 1-4. Unit 1 (8 hours, lessons 1-3): descriptive data analysis, univariate and multivariate data. Unit 2 (6 hours, lessons 4-6): probability theory. Unit 3 (10 hours, lessons 7-10): statistical inference. Unit 4 (6 hours, lessons 11-13): regression analysis; univariate and multivariate data. Unit 5 (20 hours, lessons 14-18): design of experiments. UNIT 1 LESSON 1 Univariate data analysis: descriptive statistics. Quantitative and qualitative variables. Tables and graphs. Computation of mode, mean, median, quantiles, range of variation, variance, standard deviation, relative standard deviation, pooled standard deviation. LESSON 2 Multivariate data analysis. Representation of multidimensional data. Covariance and correlation. Exploratory data analysis. Generic exploratory analysis: unsupervised pattern recognition. Guided exploratory analysis: supervised pattern recognition. LESSON 3 Principal component analysis (PCA). Multivariate data matrices. Aims of PCA. PCA: the investigation method applied. Chemical factors. Scores and Loadings. Graphic representation of scores and loadings.Data pre-processing UNIT 2 LESSON 4 Probability theory. Probability space. Events and sample space. Definitions of probability. Independent events. Random variables. LESSON 5 Probability distribution of a discrete random variable. Expectation and variance of a discrete random variable. Independent random variables. Continuous random variables. The law of large numbers. Probability distribution of continuous random variables. LESSON 6 The normal distribution. Central limit theorem. The distributions 𝜒2, Student's 𝑇, and Fischer's 𝐹. UNIT 3 LESSON 7 Inferential statistics. Estimation of the mean and variance. Modeling a measurement. Population and sample. A point estimate of a parameter. Interval estimates of a parameter. LESSON 8 Analysis of data with known population variance 𝜎2. Analysis of data with unknown population variance. Hypothesis testing. Types of errors and power of hypothesis tests. Comparison of an average with reference data. Z-test: the population variance is known a priori. T-test: population variance is unknown. Verification of the normality precondition to correctly apply the Z- and T-test. LESSON 9 Test for comparing two means. Test for data that is not independent of each other but can be made independent. Test for two independent data sets. LESSON 10 Analysis of variance (ANOVA). One-factor ANOVA. Two-factor ANOVA. Test for comparing two variances UNIT 4 LESSON 11 Simple linear regression. Estimation of the parameters 𝛽0 and 𝛽1 .Significance of the parameters 𝛽0 and 𝛽1. Proportionality check. Regression ANOVA. LESSON 12 Response prediction in one point, leverage, and confidence interval of the prediction. Verification of the construction hypotheses of the least squares method. Weighted regression. LESSON 13 Multiple linear regression. Estimation and significance of parameters. Determination index and analysis of variance. Model prediction in one point, leverage, and confidence interval of the prediction of multilinear regression models. Testing hypotheses. Introduction to the design of experiments (DoE). UNIT 5 LESSON 14 Approaches to experimental research: what is an experimental design? Matrix representation of an experimental plan. Full Factorial Designs. Full factorial designs at two levels, 2^k. Interactions in full factorial models 2^k. LESSON 15 Fractional Factor Designs. Fractional designs half of the full factorial. The fractional design for four factors: 2^(4−1) Res. IV. Fractional designs describing a quarter of the full factorial plan. Confusions in fractional factorial designs. Plackett-Burman designs. Confusion patterns in Plackett-Burman designs. LESSON 16 Response surface methodology LESSON 17 D-optimal designs LESSON 18 Mixture designs