11. INTRODUCTION TO ANALYSIS OF VARIANCE (ANOVA)

ANALYSIS OF VARIANCE (ANOVA)

- a hypothesis-testing procedure that is used to

evaluate mean differences between two or more

treatments/groups/populations

F RATIO

- Ratio of the between-groups population variance

estimate to the within-groups population variance

estimate

F TABLE

Table at cutoff scores on the F distribution

BASIC LOGIC OF ANOVA

- The null hypothesis is an anova is that the

population being compared all have the same

mean

ASSUMPTIONS OF ANOVA

1. Your dependent variable should be measured at

the interval or ratio level (i.e., they are continuous).

2. Your independent variable should consist of two or

more categorical, independent groups.

3. You should have independence of observations,

which means that there is no relationship between

the observations in each group or between the

groups themselves.

4. There should be no significant outliers.

5. Your dependent variable should be approximately

normally distributed for each category of the

independent variable. Alternatively, the residuals of

the dependent variable is approximately normally

distributed

6. There needs to be homogeneity of variances.

POST HOC COMPARISONS

- also known as Post Hoc Tests or Posttests, are

additional hypothesis tests that are done after an

ANOVA to determine exactly which mean

differences are significant and which are not

TUKEY’S HONESTLY SIGNIFICANT DIFFERENCE (HSD) TEST

- or Tukey Test, is a single-step multiple comparison

procedure and statistical test. It can be used on raw

data or in conjunction with an ANOVA to find means

that are significantly different from each other

- most commonly used for equal sample sizes

GAMES-HOWELL

- a nonparametric approach in comparing

combinations of groups or treatments

- it is like the Tukey’s test, but it does not assume

equal variances and sample sizes

SCHEFFE’S TEST

- method of figuring the significance of post hoc

comparisons that takes into account all possible

comparisons that could be made1

- It is customarily used for unequal sample sizes2

BONFERRONI PROCEDURE

- is a multiple-comparison procedure in which the

total alpha percentage is divided among the set of

comparisons so that each is tested at a more

stringent significance level

KRUSKAL-WALLIS H TEST

- (sometimes also called the "one-way ANOVA on

ranks") is a rank based nonparametric test that can

be used to determine if there are statistically

significant differences between two or more groups

of an independent variable on a continuous or

ordinal dependent variable

ASSUMPTIONS OF THE KRUSKAL-WALLIS H TEST

1. The dependent variable should be measured at the

ordinal or continuous level.

2. The independent variable should consist of two or

more categorical, independent groups.

3. You should have independence of observations

4. The two or more dependent variables are not

normally distributed.

REPEATED MEASURES ANOVA

an ANOVA for a repeated-measures design--a

design with one group of individuals participating in

three (3) or more treatment conditions

TWO-WAY ANOVA

- an ANOVA used for a factorial design--a design

with more than one independent variable and one

dependent variable

MAIN EFFECT

- The action of a single independent variable in an

experiment; the change in the dependent variable

produced by the various levels of a single factor

INTERACTION

- the effect of one independent variable changes

across the levels of another independent variable;

can only be detected in a factorial design

ANALYSIS OF COVARIANCE (ANCOVA)

- analysis of variance that controls for the effect of

one or more additional variables

- Covariate - variable controlled for in an analysis of

variance

MULTIVARIATE ANALYSIS OF VARIANCE (MANOVA)

- analysis of variance with more than one dependent

variable

MULTIVARIATE ANALYSIS OF COVARIANCE (MANCOVA)

- analysis of covariance with more than one

dependent variable