BUSSTAT 208 Final Harless

one-way analysis of variance (one-way ANOVA)

a statistical test that determines whether responses from the different conditions are essentially the same or whether the responses from at least one of the conditions differ from the others

one-way ANOVA

Null Hypothesis

All the means equal

one-way ANOVA

ALT Hypothesis

at least two of the populations means are different

Balanced Design

Equal Sample Size for each level

One-Way Analysis of Variance - Layout

Single Factor

4 Levels (populations)

Equal Sample Size for each level - Balanced Design

factor

A quantity under examination in an experiment as a possible cause of variation in the response variable

Levels

The categories, measurements, or strata of a factor of interest in the current experiment (aka Populations)

Balanced Design

An experiment has a balanced design if the factor levels have equal sample sizes.

One-Way ANOVA Assumptions

All populations are normally distributed.

The population variances are equal.

The observations are independent - that is, the occurrence of any one individual value does not affect the probability that any other observation will occur.

The data are interval or ratio level.

Total Variation (SST)

The aggregate dispersion of the individual data values across the various factor levels is called the total variation in the data.

Between-Sample Variation (SSB)

Dispersion among the factor sample means is called the between-sample variation.

Within-Sample Variation (SSW)

The dispersion that exists among the data values within a particular factor level is called the within-sample variation.

SSW =

SST-SSB

SST =

SSB + SSW

Mean Square Between Samples

MSB

MSB=

SSB/k-1

Mean Square Within Samples

MSW

MSW =

SSW/nt-k

Compare MSB to MSW. If MSB is large relative to MSW,

the null hypothesis should be rejected.

F statistic > F-Critical

Reject null hypothesis that populations have equal means

F =

MSB/MSW

k=

number of populations

nt

sum of sample sizes from all populations

df

degrees of freedom

Between Samples DF

k-1

Within Samples DF

nt-k

Total DF

nt-1

Tukey-Kramer test used?

One-Way ANOVA test rejects null hypotheis. To find at least one pair of populations that have different means

Tukey-Kramer Decision Rule

Absolute Difference > Critical Range, means there is a difference

Randomized Complete Block Analysis of Variance

When an additional factor with two or more levels is involved, a design technique called blocking can be used to eliminate the additional factor's effect on the statistical analysis of the main factor of interest

Randomized Complete BlockANOVA Assumptions

The populations are normally distributed.

The populations have equal variances.

The observations within samples are independent.

The data measurement must be interval or ratio level.

Sum of Squares Partitioning for Randomized Complete Block Design:

SST = SSB + SSBL = SSW

MSBL =

SSBL/b-1

MSB =

SSB/k-1

MSW =

SSW/(k-1)(n-1)