Environmental Data: Data analysis toolkits
Description
These are condensed notes covering selected key points in data analysis and statistics. They were developed by James Kirchner for the course "Analysis of ...
Citation
Kirchner, J. (2020). Data analysis toolkits. EnviDat. https://www.doi.org/10.16904/envidat.177.
Resources
Toolkit 1: graphically displaying data distributions
Toolkit 1: graphically displaying data distributionsToolkit 2: quantifying data distributions using descriptive statistics
Toolkit 2: quantifying data distributions using descriptive statisticsToolkit 3: tools for transforming data
The ladder of powers and a few other cool transformations
Toolkit 3: tools for transforming dataToolkit 4: confidence intervals
Toolkit 4: confidence intervalsToolkit 5: uncertainty analysis and error propagation
Gaussian error propagation, monte carlo methods, and first-order, second-moment error propagation
Toolkit 5: uncertainty analysis and error propagationtoolkit 6: averaging in nonlinear functions
The average of a nonlinear function will not equal the function evaluated at its average inputs (the mean of the function will differ from from the function of the mean). This toolkit shows how to estimate that averaging bias.
toolkit 6: averaging in nonlinear functionsToolkit 7: hypothesis testing, significance, and power
An overview of basic concepts -- and common pitfalls -- in statistical hypothesis testing, statistical significance, and power analysis
Toolkit 7: hypothesis testing, significance, and powerToolkit 8: Hodges-Lehmann estimators
A quick introduction to Hodges-Lehmann estimators (nonparametric measures of effect size)
Toolkit 8: Hodges-Lehmann estimatorsToolkit 9: Experimentwise error rates and statistical fishing expeditions
Statistical fishing expeditions, and how to avoid being misled by them
Toolkit 9: Experimentwise error rates and statistical fishing expeditionsToolkit 10: linear regression
An overview of the math, logic, and pitfalls of ordinary least-squares linear regression
Toolkit 10: linear regressionToolkit 11: serial correlation
Tools for detecting and correcting for serial correlation in analyses of time series
Toolkit 11: serial correlationToolkit 12: weighted averages and their uncertainties
There are two different ways to calculate the uncertainty of a weighted average. Software packages often don't tell you which one they are reporting, and the resulting errors can be huge.
Toolkit 12: weighted averages and their uncertainties