Suppose you've designed a study and found a "null" result, and you'd like to argue that you've found evidence against the phenomenon in question producing a large effect. Should you emphasize how statistically powerful your study was?
You can, but there are much better ways to describe the evidence. Provide an upper bound on the plausible magnitude of the effect given the theory tests your data permit. For example, report a confidence interval. [1/3]
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Many researchers treat missing values in a categorical variable as a separate category, but balk at doing the same for a numeric variable.
The implications of using one variable to indicate the missingness of another are often misunderstood. Although this approach must be used cautiously, learning about it helps illustrate general principles about regression.
https://saraemilyburke.com/stats/MissingnessIndicatorsLinearRegression.pdf
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If you Z-score two variables, the regression slope between them will be equal to the Pearson correlation between them. But why doesn't it matter which variable is presented as the predictor and which is presented as the response? The images on the page linked below attempt to make this concept more intuitive.
https://saraemilyburke.com/stats/correlationZscores.html
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The notation for regression coefficients is often inconsistent. Sometimes, students with prior experience in statistics classes find the notation conventions common in psychology confusing, and vice versa. This table lists some different symbols that are used to refer to regression coefficients. Reply to let me know about more symbols (or more fields) that I should (or could) add.
https://saraemilyburke.com/stats/regressioncoefficientnotation.pdf
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If we have two groups of n observations each, and we know the mean and sample variance of each group separately, can we calculate the mean and sample variance of the combination of the two groups? This question came up in a class many years ago. It may be unlikely to come up again, but just in case, a formula can be found in the document linked below.
https://saraemilyburke.com/stats/CombinedVarianceEqualNs.pdf
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Students sometimes need quick, memorable reminders of miscellaneous stats concepts. Here are some:
- what positive and negative skew look like
https://saraemilyburke.com/stats/skewdirection.html
- why the expected value of F is not the square of the expected value of t
https://saraemilyburke.com/stats/ExpectedTvsF.html
- side-by-side simple two-way interaction plots can "look different" without there being a three-way interaction
https://saraemilyburke.com/stats/ThreeWayInteractionPlotsHeuristic.pdf
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We might run a chi-squared test of independence to see if a categorical variable is related to a yes/no decision. But why not a chi-squared test of goodness of fit? After all, the null hypothesis assumes that the yesses will be evenly distributed across the categorical variable. This document explains why the test of independence is more appropriate and what happens if you run a goodness-of-fit test instead.
https://saraemilyburke.com/stats/ChiSqIndepvsGoodFit.pdf
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With a factorial ANOVA model, a main effect is just a main effect -- or is it? Why do tests of main effects sometimes differ between software packages? What do "Type II" and "Type III" mean? For that matter, what does "main effect" mean?
It can be annoying to deal with these questions when you were just trying to do a simple ANOVA, but a deeper understanding can make things easier in the long run. See this document for clarification:
https://saraemilyburke.com/stats/types_of_main_effects.html
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What actually happens when you add a covariate to a regression model? What does it mean to "control for" or "adjust for" a variable? What is the difference between a model with two main effects and a model with a two-way interaction?
A deeper understanding of these questions can make advanced regression concepts much more accessible. Check out my tutorial using a silly dog-related example:
https://saraemilyburke.com/stats/main_effects_vs_interaction.html
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