Descriptive statistics using spreadsheets
Introduction: problems of descriptive and inferential statistics and their applications in the experimental sciences. Introduction to the use of spreadsheets.
Elements of descriptive statistics: dot plot; bar graph, pie chart and computations of main statistics: indexes of positions, of variability, of symmetry and of kurtosis.
Dependence analysis: two-variables data table; conditional distribution and independence; scatterplots; Chi-Square for contingency table; Cramer's V index; linear regression and least squares technique; association; regression coefficient and its interpretation; variance of regression and its decomposition; coefficient of determination; polynomial regression; linearization methods. Use of spreadsheets for dependence analysis.
Analysis of interdependence: the concept of interdependence; measure of concordance; discordance; the correlation coefficient of Bravais -Pearson and its interpretation. Use of spreadsheets for dependence analysis.
Elements of partial correlation and multiple regression: plane and hyperplane of regression; partial regression coefficient; coefficient of determination; partial correlation coefficient.
Examples and applications in bio-pharmaceutical sciences
Elements of probability
The algebra of Events: standard event, implication between events, equal events; complement of an event; the union event; the intersection event; mutually exclusive events; sample space; conditional events. The axiomatic definition of probability, some simple propositions on the probability of events. Sample spaces having equally likely outcomes. Introduction to conditional probability: the multiplication rule; independent events; Bayes' Formula (proof and application).
The random variables: random variable (r.v.); distribution function; probability mass function; density function; the Bernoulli r.v.; the Binomial r.v.; the Normal r.v.; the Standard Normal r.v.; the Student's t r.v.; moments of a r.v. Use of spreadsheets for simulations and computations involving random variables.
Limit theorems: the Central Limit Theorem; the weak law of large
numbers; the strong law of large numbers.
Examples and applications in bio-pharmaceutical sciences
Elements of hypothesis testing
Hypothesis Testing: basic concept of random samples: research hypothesis; statistical hypothesis, null hypothesis; alternative hypothesis (uni and bi-directional); statistical significance; statistical distribution of the test statistic, critical values, rejection regions and acceptance region, error probabilities and the power function; the Z test for a sample mean; the T test for a sample mean; degrees of freedom; confidence intervals for the mean; sample size determination; p-values. Implementation of tests of hypothesis using spreadsheets.
Examples and applications in bio-pharmaceutical sciences.
