DOI: 10.16904/envidat.177
title: 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 Environmental Data" at Berkeley in the 1990's and 2000's. They are not intended to be comprehensive, and thus are not a substitute for a good textbook or a good education!
License: These notes are released by James Kirchner under a Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA 4.0) license.
description: Resource Title: Toolkit 1: graphically displaying data distributions
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 URL: https://www.envidat.ch/dataset/4652e79e-1ad4-4045-a6c8-1b621ba18b28/resource/40c94808-e96f-4826-812d-844de07dfe42/download/toolkit-01-graphing-distributions.pdf
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description: Resource Title: Toolkit 2: quantifying data distributions using descriptive statistics
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 URL: https://www.envidat.ch/dataset/4652e79e-1ad4-4045-a6c8-1b621ba18b28/resource/90b055a6-f835-4029-b926-52d5b96c9022/download/toolkit-02-quantifying-distributions.pdf
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description: Resource Title: Toolkit 3: tools for transforming data
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 URL: https://www.envidat.ch/dataset/4652e79e-1ad4-4045-a6c8-1b621ba18b28/resource/bb3d4263-4c88-4886-bc74-ba48f0398144/download/toolkit-03-transforming-distributions.pdf
 Description: The ladder of powers and a few other cool transformations
description: Resource Title: Toolkit 4: confidence intervals
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 URL: https://www.envidat.ch/dataset/4652e79e-1ad4-4045-a6c8-1b621ba18b28/resource/a06f6e74-1065-4dd3-af6b-9af0acf44f61/download/toolkit-04-confidence-intervals.pdf
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description: Resource Title: Toolkit 5: uncertainty analysis and error propagation
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 URL: https://www.envidat.ch/dataset/4652e79e-1ad4-4045-a6c8-1b621ba18b28/resource/5074901f-3168-4b40-b8f0-20dc5acc6248/download/toolkit-05-error-propagation.pdf
 Description: Gaussian error propagation, monte carlo methods, and first-order, second-moment error propagation
description: Resource Title: toolkit 6: averaging in nonlinear functions
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 URL: https://www.envidat.ch/dataset/4652e79e-1ad4-4045-a6c8-1b621ba18b28/resource/35650811-6329-4025-9240-bad37169e31f/download/toolkit-06-nonlinear-averaging.pdf
 Description: 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.
description: Resource Title: Toolkit 7: hypothesis testing, significance, and power
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 URL: https://www.envidat.ch/dataset/4652e79e-1ad4-4045-a6c8-1b621ba18b28/resource/8c6c7021-0811-480f-ab52-00fbe3886591/download/toolkit-07-hypothesis-testing.pdf
 Description: An overview of basic concepts -- and common pitfalls -- in statistical hypothesis testing, statistical significance, and power analysis
description: Resource Title: Toolkit 8: Hodges-Lehmann estimators
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 URL: https://www.envidat.ch/dataset/4652e79e-1ad4-4045-a6c8-1b621ba18b28/resource/b796d0b3-535a-481c-8110-4947b8408186/download/toolkit-08-hodges-lehmann-estimators.pdf
 Description: A quick introduction to Hodges-Lehmann estimators (nonparametric measures of effect size)
description: Resource Title: Toolkit 9: Experimentwise error rates and statistical fishing expeditions
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 URL: https://www.envidat.ch/dataset/4652e79e-1ad4-4045-a6c8-1b621ba18b28/resource/557b276f-7c37-4687-bb6b-665bb6e040eb/download/toolkit_09.pdf
 Description: Statistical fishing expeditions, and how to avoid being misled by them
description: Resource Title: Toolkit 10: linear regression
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 URL: https://www.envidat.ch/dataset/4652e79e-1ad4-4045-a6c8-1b621ba18b28/resource/12fa9470-b900-4858-9ba9-ddf0978c2470/download/toolkit-10-linear-regression.pdf
 Description: An overview of the math, logic, and pitfalls of ordinary least-squares linear regression
description: Resource Title: Toolkit 11: serial correlation
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 URL: https://www.envidat.ch/dataset/4652e79e-1ad4-4045-a6c8-1b621ba18b28/resource/8ed5ef3a-173f-4089-b6f0-f5095c9d1b2d/download/toolkit-11-serial-correlation.pdf
 Description: Tools for detecting and correcting for serial correlation in analyses of time series
description: Resource Title: Toolkit 12: weighted averages and their uncertainties
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 URL: https://www.envidat.ch/dataset/4652e79e-1ad4-4045-a6c8-1b621ba18b28/resource/78995d64-cf7c-4564-96f2-72763bc2288b/download/toolkit-12-weighted-averages-and-uncertainties.pdf
 Description: 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.