Used in statistical analysis to represent the uncertainty in an estimate of a curve or function based on limited or noisy data.

Confidence Bands

An element of a particular basis for a function space.
Every continuous function in the function space can be represented as a linear combination of basis functions, just as every vector in a vector space can be represented as a linear combination of basis vectors.

Basis function

1. Analysis of variance (a special case of regression analysis)
2. constructing simultaneous confidence bands for regressions involving basis functions.

University of Michigan - Ann Arbor

Method for adjusting significance levels in a linear regression analysis to account for multiple comparisons.
Scheffé's method is a single-step multiple comparison procedure which applies to the set of estimates of all possible contrasts among the factor level means, not just the pairwise differences considered by the Tukey–Kramer method.
It works on similar principles as the Working–Hotelling procedure for estimating mean responses in regression, which applies to the set of all possible factor levels.

Scheffe's Method

James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An introduction to statistical learning (Vol. 112, pp. 3-7). New York: springer.

An Introduction to Statistical Learning with Applications in R

What is Scheffe's method useful for?

Single-step multiple comparison procedure and statistical test. It can be used to find means that are significantly different from each other.
Compares all possible pairs of means, and is based on a studentized range distribution

Tukey-Kramer Method

A method of simultaneous estimation in linear regression models.
One of the first developments in simultaneous inference, it was devised by Working and Hotelling for the simple linear regression model in 1929.
Provides a confidence region for multiple mean responses

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