Data Driven Decision Making, Kash Barker: EXAM 1

Mean Squared Treatments (MST - variance Between each of the treatments)

Mean Squared Error (MSE - variance Within the treatments)

Expected Value of the Mean Squared Error, E[MSE]

Expected Value of the Mean Squared Treatments, E[MST]

The ratio for the F statistic, which follows an F distribution of (a-1) and (N-a) degrees of freedom.

Degrees of freedom between treatments.

a - 1

Degrees of freedom error (within treatments)

N - a

Degrees of freedom total

N - 1

N

i * j

Tukey HSD value, when balanced.

Tukey HSD value, when unbalanced.

How does one conduct the Tukey test, and was is it used for?

Start by comparing the largest mean to the smallest mean, and then the largest mean with the next smallest, etc., until the largest mean has been compared to all other means (or until no difference is found) - After this, compare the second largest mean w

Sample size, and Operating Characteristic Curve for the Fixed Effects Model Analysis of Variance equation.

Fixed Effects Model

Fixed Effects Model with Blocking

Sum of Squares Equations with Blocking

An interaction effect exists when...

The effect of one factor on the response varies across the levels of another factor. That is, the effect of Factor A isn't the same for all levels of Factor B

Fixed Effects Model for a Two Factor Design.

General Factorial Design of Fixed Effects Model.

Fixed Effects Model for Single Factor Design/Experiment.

Residuals equation

eij = Yij - YBARij
= observed value - estimated mean

Null and alternate hypothesis for F test.

H0: Sigma1^2 = Sigma2^2
H1: Sigma1^2 =/= Sigma2^2

T-statistic when variances are equal.

T-statistic when variances are unequal.

Sum of Squares equations for Single Factor