Learning Outcomes Use statistical vocabulary. Construct various frequency distributions of grouped and ungrouped data.
MATHS 2103 - Probability & Statistics II
Calculate and interpret descriptive statistics of samples and populations. Measures of central tendency, measures of dispersion. Calculate simple probabilities.
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- Probability and statistics;
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Find the mean and variance of a probability distribution including the binomial distribution. Understand and calculate expected values.
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Calculate the probabilities or scores of normal distributions and the normal approximation of the binomial distribution. The Probability and Statistics course contains four main units that have several sections within each unit. The general approach is to provide participants with a framework that will help them choose the appropriate descriptive methods in various data analysis situations.
Probability: In this course the unit is a classical treatment of probability and includes basic probability principles, finding probability of events, conditional probability, discrete random variables including the Binomial distribution and continuous random variables with emphasis on the normal distribution. The probability unit culminates in a discussion of sampling distributions that is grounded in simulation.
For a streamlined version of probability that forgoes the classical treatment of probability in favor of an empirical approach using relative frequency, participants may see the OLI Statistical Reasoning course. Inference: This unit introduces participants to the logic as well as the technical side of the main forms of inference: point estimation, interval estimation and hypothesis testing.
The unit covers inferential methods for the population mean and population proportion, inferential methods for comparing the means of two groups and of more than two groups ANOVA , the Chi-Square test for independence and linear regression. Descriptive statistics.
Mean arithmetic geometric harmonic Median Mode. Central limit theorem Moments Skewness Kurtosis L-moments. Index of dispersion. Grouped data Frequency distribution Contingency table. Pearson product-moment correlation Rank correlation Spearman's rho Kendall's tau Partial correlation Scatter plot. Data collection.
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Sampling stratified cluster Standard error Opinion poll Questionnaire. Scientific control Randomized experiment Randomized controlled trial Random assignment Blocking Interaction Factorial experiment. Adaptive clinical trial Up-and-Down Designs Stochastic approximation. Cross-sectional study Cohort study Natural experiment Quasi-experiment.
Probability and Statistics
Statistical inference. Z -test normal Student's t -test F -test. Bayesian probability prior posterior Credible interval Bayes factor Bayesian estimator Maximum posterior estimator.
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