Statistics for the Sciences
Statistical methods for laboratory and field data: designing studies with randomization, replication and blocking, describing data and measurement uncertainty, probability and Bayes’ theorem, probability models for counts and measurements, sampling distributions and the central limit theorem, confidence intervals and the bootstrap, hypothesis tests, power and effect sizes, comparing two groups with t tests and rank-based alternatives, categorical data analysis, correlation, calibration and simple linear regression, multiple regression and model checking, and analysis of variance for factorial and blocked experiments, ending in an end-to-end study with multiple-comparison control and reproducible, ethically reviewed research.
STAT-151 Year 1 3 credits 12 lessons · 5 h 38 min
Offered by HSM University · Mathematics & Statistics
This is the American version of this course. See the Canadian version.
What you'll learn
- Distinguish experiments from observational studies, identify experimental units, replication and pseudoreplication, and design randomized, blocked and controlled studies for laboratory and field research.
- Summarize scientific data with appropriate graphs and robust or classical statistics, distinguish accuracy from precision and propagate measurement uncertainty through calculations.
- Apply the rules of probability, conditional probability and Bayes’ theorem, including the positive predictive value of diagnostic and screening tests.
- Use the binomial, Poisson, normal and lognormal distributions to model counts and measurements, and recognize overdispersion and skewness in real data.
- Explain sampling distributions, the standard error and the central limit theorem, and use simulation to study the behavior of estimators.
- Construct and interpret t intervals, Wilson and exact intervals for proportions, and bootstrap confidence intervals, and plan sample sizes for a required precision.
- Carry out and interpret hypothesis tests correctly, calculate power and effect sizes, and apply the ASA principles on p-values when reporting results.
- Compare two groups with paired, Welch and pooled t tests or with rank-based and permutation alternatives, choosing the method that matches the design and the data.
- Analyze categorical data with tests for proportions, chi-square goodness-of-fit and independence tests and Fisher’s exact test, and report relative risks and odds ratios with intervals.
- Fit and interpret correlation and simple linear regression, build calibration curves with inverse prediction, and distinguish confidence intervals from prediction intervals.
- Fit multiple regression models with categorical predictors and interactions, diagnose multicollinearity and influential points, and choose models with AIC or cross-validation.
- Analyze one-way, factorial and randomized block experiments with ANOVA, control multiple comparisons, and plan reproducible studies that meet Common Rule and US animal welfare requirements.
Course content
12 lessons · 5 h 38 min total · final exam
- 1 Statistics and the scientific method: designing studies 32 min · quiz
- 2 Describing data and measurement uncertainty 28 min · quiz
- 3 Probability and Bayes’ theorem 32 min · quiz
- 4 Probability models for scientific data 28 min · quiz
- 5 Sampling distributions and the central limit theorem 26 min · quiz
- 6 Confidence intervals and the bootstrap 28 min · quiz
- 7 Hypothesis tests, power and effect sizes 27 min · quiz
- 8 Comparing two groups: t tests and nonparametric alternatives 27 min · quiz
- 9 Categorical data analysis 25 min · quiz
- 10 Correlation and simple linear regression 24 min · quiz
- 11 Multiple regression and model checking 26 min · quiz
- 12 Analysis of variance and experimental design 33 min · quiz
- E Final exam 20 questions
Requirements
Recommended background. You can start any course at any time.
Description
Statistical methods for laboratory and field data: designing studies with randomization, replication and blocking, describing data and measurement uncertainty, probability and Bayes’ theorem, probability models for counts and measurements, sampling distributions and the central limit theorem, confidence intervals and the bootstrap, hypothesis tests, power and effect sizes, comparing two groups with t tests and rank-based alternatives, categorical data analysis, correlation, calibration and simple linear regression, multiple regression and model checking, and analysis of variance for factorial and blocked experiments, ending in an end-to-end study with multiple-comparison control and reproducible, ethically reviewed research.
Part of the Science stream, typically taken in year 1.