Inferential Statistics

Role of statistics in data science. Different types of data. Random variable, numerical variable, categorical variable. Data collection and types of sampling. Descriptive statistics: measures of central tendency (mean, median, mode); measures of dispersion (range, quartiles, standard deviation, variance). Distribution of data: skewness and kurtosis. Covariance and correlation, the difference between them and its significance. Python tutorials: statistics packages, descriptive statistics, and correlation analysis.

Permutation and combination. Types of probability. Rules for computing probability. Marginal probability, conditional probability. Bayes theorem and its applications, problem-solving with Bayes theorem. Probability distributions: binomial and Poisson. Normal distribution. Python tutorials: probability computation, Bayes theorem applications, plotting and analysing distributions.

Sampling distribution and the central limit theorem. Point estimate, confidence interval. Hypothesis testing basics: null and alternative hypothesis formulation, types of hypotheses, the hypothesis testing process. Errors in hypothesis testing (Type I and Type II). Power of a test. Number of tails. Choice of test statistic with examples. Python tutorials: simulating the central limit theorem, and a case study using estimation and hypothesis testing.

Test of mean: one-sample z-test, one-sample t-test, two-sample tests (independent and dependent). Test of proportion: one-sample z proportion test and two-sample z proportion test. Case study: categorical vs continuous. More than two samples. Python tutorials: implementing z-tests and t-tests, one-sample and two-sample tests, and a case study in Python.

Analysis of variance: one-way ANOVA and two-way ANOVA. Categorical vs categorical: chi-square test, test of goodness of fit, test of independence. Test of variance. Python tutorials: implementing the chi-square test and non-parametric tests, and a case study in Python.