Variability is the law of life, and as no two faces are the same, so no two bodies are alike, and no two individuals react alike and behave alike under the abnormal conditions which we know as disease. A quote by Canadian physician and medical educator Sir William Osler (1859 - 1919). The quote appears in William Osler: Aphorisms from his bedside teachings and writings, (Henry Schuman; 1950, page 104).
I abhor averages. I like the individual case. A man may have six meals one day and none the next, making an average of three meals per day, but that is not a good way to live. A quote by American Supreme Court Justice Louis Dembitz Brandeis (1856 - 1951) as quoted in "Brandeis: A Free Man's Life" by Alpheus Thomas Mason Viking Press, 1946; page 145). The quote also appears in "Statistically Speaking: A dictionary of quotations" compiled by Carl Gaither and Alma Cavazos-Gaither.
RStudio Cloud makes it easy for professionals, hobbyists, trainers, teachers and students to do, share, teach and learn data science using R. Create analyses using RStudio directly from your browser - there is no software to install and nothing to configure on your computer. Share your projects - and access those of others - without worrying about data transfer or package installation. Each project defines its own environment, and RStudio Cloud automatically reproduces that environment whenever anyone accesses the project. It’s easy to share analyses with the world - but it’s also simple to collaborate with a select group in a private space. You control who can enter a space - and via roles, you have fine grained control over what each user can do. There are also many learning materials available: interactive tutorials covering the basics of data science, cheatsheets for working with popular R packages, links to Datacamp courses, and a guide to using RStudio Cloud.
This general, introductory tutorial on mathematical modeling (in pdf format) is intended to provide an introduction to the correct analysis of data. It addresses, in an elementary way, those ideas that are important to the effort of distinguishing information from error. This distinction constitutes the central theme of the material described herein. Both deterministic modeling (univariate regression) as well as the (stochastic) modeling of random variables are considered, with emphasis on the latter. No attempt is made to cover every topic of relevance. Instead, attention is focussed on elucidating and illustrating core concepts as they apply to empirical data.
Examples of real data/studies and their analyses and interpretation.
This website provides a comprehensive overview of descriptive statistics (mean/median/mode, range, standard deviation, and variance) through informative webpages with examples, links to data sets, and problems for the readers to try for themselves.
This page computes a variety of descriptive statistics and creates a stem and leaf plot. Enter data in the text area, specify a delimiter (Space, Return, Tab, New line), and click "Compute". The page returns sample size, mean, median, trimmed mean, trimean, minimum, maximum, range, first quartile, third quartile, semi-interquartile range, standard deviation, variance, standard error of the mean, skew, and kurtosis. Key Word: Calculator; Summary Statistics.
A song for use in helping students to reason about mean and median and the effect of an outlier. Lyrics & Music © 2016 Amy Adler. This song is part of an NSF-funded library of interactive songs that involved students creating responses to prompts that are then included in the lyrics (see www.causeweb.org/smiles for the interactive version of the song, a short reading covering the topic, and an assessment item).
The activity is designed to help students develop a better intuitive understanding of what is meant by variability in statistics. Emphasis is placed on the standard deviation as a measure of variability. As they learn about the standard deviation, many students focus on the variability of bar heights in a histogram when asked to compare the variability of two distributions. For these students, variability refers to the "variation" in bar heights. Other students may focus only on the range of values, or the number of bars in a histogram, and conclude that two distributions are identical in variability even when it is clearly not the case. This activity can help students discover that the standard deviation is a measure of the density of values about the mean of a distribution and to become more aware of how clusters, gaps, and extreme values affect the standard deviation. Key words: Variability, standard deviation
G*Power is a tool to compute statistical power analyses for many different t tests, F tests, χ2 tests, ztests and some exact tests. G*Power can also be used to compute effect sizes and to display graphically the results of power analyses.