Informatics and Statistics for Biotechnologies

Introduction to statistics. Elements of mathematics and logic required for statistics.

Descriptive and inferential statistics. Presentation of the data: frequency tables, line graphs, bar graphs, frequency polygons, relative frequency graphs, pie charts. Grouped data and histograms, the problem of the bin size; steam-and-leaf plots.
Summarizing data sets: arithmetic mean, weighted arithmetic mean (weighted average), geometric mean, quadratic mean, median, mode (unimodal, bimodal, multimodal distributions). Outliers. Percentiles and box plots.
Measures of variability: deviations, absolute deviations, variance, alternative expression for the variance, standard deviation, alternative expression for the standard deviation, interpretation of the standard deviation (empirical rule).

Sets of paired data. Symbolic notation, graphical representation (scatter diagram). Positive and negative correlation. Linear and nonlinear regression.
Least squares regression line: vertical offsets, slope (linear regression coefficient) and intercept of the regression line of Y on X. Alternative expressions. Graphical interpretation (vertical offsets). Variability in a set of paired data. Horizontal offsets. Least squares regression line of X on Y. Graphical interpretation (horizontal offsets). Comparison between the regression line of Y on X and the regression line of X on Y, centre of the distribution. Pearson correlation coefficient ('r'), sign convention, interpretation of 'r'. Expression of 'r' in terms of covariance of X and Y, standard deviation of X and standard deviation of Y (alternative expressions). Necessity and sufficiency in logic. Correlation and causation, spurious relationships. The coefficient of determination 'R^2'.

Probability. Experiment, outcome, sample space, event. Union of events, intersection of events, disjoint events, null event, complement of an event. Venn diagrams. Properties of the probability. Probability of complex events: addition rule, conditional probability, multiplication rule (for dependent and independent events). Test results: true positives, false positives, true negatives, false negatives. Sensitivity and specificity. Derivation of the Bayes theorem, interpretation of diagnostic test results.

Discrete random variables. Probability distribution. Expected value, properties of the expected value. Variance, standard deviation. Continuous random variables. Probability density function, expected value, standard deviation. Normal continuous random variables, normal probability density function (Gaussian distribution). Approximation rule. Standard normal continuous random variables, standard normal probability density function.

Elements of theory of measurement and error. Absolute error, relative error. Types of errors in experimental data: gross errors, determinate (systematic) errors, indeterminate (random) errors. Sources of errors, removing sources of errors. Accuracy and precision. Hints of error propagation. Normal distribution of random errors.

Population and sample. Sample mean and sample standard deviation, population mean and population standard deviation. Confidence intervals.