the average of several group variances. It is used to calculate the standard error of mean differences. 

S²p = 

how much impact does the IV have on the DV. what is the proportion of change in DV that can be attributed to the IV.

η² =

An assumption of the independent t-test and of ANOVA that states the population variances of the independent groups are equal. Homogeneity of variance is tested with Fmax test. 

Fmax = s²max
           _______ 

           s²min

if significant the homogeneity of variance is VIOLATED!

Assumptions underlying the ANOVA

1. homogeneity of variance

2. normal distribution for the DV

3. subjects are randomly samples (so that we can generalize)

4. independent observations 

FIXED: all the levels of the IV have been chosen on purpose and only those levels are of interest to the researcher 

RANDOM: levels of IV are only chosen as examplars of the many other levels that could be of interest to the researcher.

a measure of how spread out the samples scores are from the mean

S² =

MS= ss
        __ 
      df 

1 bound or power transformaitons 

-square root = all the scores (when dv is a count)

-logarithm (RT)

-reciprocal 

2 bound transformations

arcsine = spread out the scores 

Non orthogonality 

the fact that the cources of variation account for the overlapping portions of the variation in the DV. 

we can no longer say exactly what part of the variation in the DV is accounted for by each source.

When the overlap is too large, the ANOVA will not yield useful informaiton. 

Expected Mean Squares

(1 way ANOVA)

E(MSg) = σ² +nσg²

a seriesof means comparisons used to explain a significant ANOVA result. 

Post-hoc tests in an LSD t-test

Bongerroni corrections can also be used to reduce the # of significant results and better control fro type 1 error. 

FIXED: an experimental design in which all the factors are fixed (except the replication factor)

MIXED: an experiemental design in which some factors are fixed and some are random

An IV in which all the subjects are nested

an experimental design in which all factors (except for the replication factor) are independent groups factors.

Type 1 error is a false significance/ accept H1 when should have retained H0. controlled for through a=.05

Type 2 error is that you missed the significance when there was one. incorrectly retaining H0 = β. controlled through sample size. 

1 way ANOVA

SSg = R-1

SSs(g) = N-K

2 way ANOVA

SSa = a-1

SSs(ab) = N-#of cells

SSab = (a-1) (b-1)

1. if the source is crossed with NO random factor, error term is MSs(x)

2. if the source is crossed with 1 random factor, B, the error term is MSab

3. if the source is crossed with more than 1 random factors, no simple error term exists = QUASI-F (construct an error term)