Statistics and Hypothesis Testing for Data science

Explore the two main data types, numerical and categorical, and their subtypes, while showing how descriptive and inferential statistics, hypothesis testing, and data quality shape analysis and decision making.

Learn about mean, median, and mode as measures of central tendency, their sensitivity to extremes, and their interpretation in skewed data, with a Python example.

Learn how to use measures of spread (dispersion)—range, variance, and standard deviation—to assess salary variability in a monthly income data set using Python and Pandas.

Explore how measures of dependence quantify the relationship between variables, support prediction and decision making, and illustrate a strong positive correlation of about 0.77 between income and total working years.

Explore measures of shape and position, including skewness, kurtosis, percentiles, and quartiles, and see how they describe data distribution, central tendency, and outliers in finance risk analysis.

Explore measures of standard scores, or z scores, and how data relate to the mean and standard deviation. Use standardized comparisons, detect outliers, and interpret percentiles with SciPy z-score.

Explore the basics of probability, its 0-to-1 scale, and its use in weather, sports, politics, and insurance, with hands-on Python calculations using numpy and pandas on IPL data.

Explore set theory foundations in probability and statistics, visualize with Venn diagrams, and apply union, intersection, and difference to data analysis and decision making, with Python and IPL matches data.

Explore conditional probability, its notation P(A|B), and how to compute conditional and joint probabilities using Python examples with the Mumbai Indians dataset to estimate outcomes like 57% and 13.8%.

Learn Bayes theorem, updating posterior probabilities from prior, likelihood, and marginal probability with new evidence. Apply Bayes inference across medicine, machine learning, and data science using conditional probabilities.

Explore permutations and combinations, distinguishing when order matters versus when it doesn't, and apply formulas for P(n,k) and C(n,r) with repetition cases.

Learn how random variables assign numerical values to outcomes, distinguish discrete and continuous types with examples like dice and measurements, and use this framework to analyze distributions and uncertainty.

Explore probability distribution functions, including pmf and pdf, for discrete and continuous variables, with examples like binomial, Poisson, normal, exponential, and uniform distributions.

Learn the normal distribution and the empirical rule, and see how the bell curve supports inference via the central limit theorem, hypothesis testing, and confidence intervals.

Explore skewness and kurtosis to understand distribution shape, asymmetry, and departure from the normal distribution. Identify outliers and heavy tails to guide preprocessing and model choice.

Explore statistical transformations to reduce skewness and normalize data distributions by applying square root, cube root, log, and Box-Cox transformations, with visualization via histograms in Python.

Explore the concepts of sample, sample mean, and population mean, and see how the sample mean estimates the population mean using x-bar and mu with a practical employee data example.

Explore the central limit theorem, which shows that sample means become normal as the sample size grows, enabling confidence intervals, hypothesis testing, and estimation in data science and machine learning.

Explore the bias and variance concepts that affect accuracy and generalization, and learn to balance model complexity to avoid underfitting and overfitting through examples like linear and polynomial regression.

Learn maximum likelihood estimation to infer model parameters by maximizing the likelihood function, using a data generating process, and applying it to regression, GLMs, and survival analysis.

Learn how to estimate population parameters with confidence intervals, understand the confidence level and margin of error, and apply the standard normal distribution formula.

Explore how correlations quantify the strength and direction of relationships between variables, distinguish correlation from causation, and compare Pearson, Kendall, and Spearman methods with practical examples.

Explore popular sampling methods in statistics and data science, including random, systematic, and stratified sampling, and learn to draw representative samples from a population with minimal bias.

Learn to formulate null and alternate hypotheses, test them with experiments or surveys, and interpret type I and II errors, p-values, and decision rules for rejecting or failing to reject.

Explore the student's t distribution and perform one-sample, two-sample, and paired t tests to assess means, degrees of freedom, p-values, and hypothesis testing in data science.

Learn how z tests compare population means with known sigma, cover one-sample and two-sample cases, compute z scores, interpret p values, and test hypotheses.

Explore chi-squared tests, including goodness-of-fit and test of independence, by comparing observed and expected frequencies in contingency tables, forming hypotheses, and interpreting p-values in practical applications.

Explore anova to compare means across three or more groups using the F test, and learn about independence, homogeneity of variances, normality, and between- and within-group degrees of freedom.