psyc 60 steiner chps 16-19

ANOVA

a statistical technique for testing differences in the means of several groups

one-way ANOVA

an analysis of variance wherein the groups are defined on only one independent variable

assumptions in order to do ANOVAs

1. populations are normally distributed

2. populations have homogenous variances

3. the individual observations are independent from one another, ie, one person's score doesn't influence another person's score

omnibus null hypothesis

the hypothesis that all population mean are equal

sum of squares (SS)

the sum of squared deviations around some point (usually around a mean or predicted value)

MS_between groups (MS_groups, MS_treatment):

variability among group means

MS_within (MS_error)

variability among subjects in the same treatment group

MS

mean square; SS/df

F statistic

the ratio of MS_group to MS_error, or MS_between to MS_within

η²

eta squared; SS_group/SS_total

ω²

omega squared

multiple comparison techniques

techniques for making comparisons between 2 or more group means subsequent to an analysis of variance

familywise error rate

the probability that a family of comparisons contains at least one type 1 error

• we want to keep this down

3 of many post hoc procedures that control type 1 error

1. Protected t (fisher's least significant difference (LSD))

2. Bonferroni correction

3. Tukey procedure

protected t (fisher's least significant difference (LSD))

a technique in which we run t tests between pairs of means only if the analysis of variance was significant

bonferroni correction

a multiple comparison procedure in which the family-wise error rate is divided by the number of comparisons

• divide α by the number of comparisons you want to make

tukey procedure

a multiple comparison procedure for making pairwise comparisons among means while holding the familywise error rate at α

factors

another word for IVs in the ANOVA

factorial design

an experimental design in which every level of one variable is paired with each level of one variable

two-way factorial design

an experimental design involving two IVs in which every level of one variable is paired with each level of one variable

two advantages of factorial designs over using multiple one-way ANOVAs

1. they allow us to look the interaction of variables

2. they allow us to use fewer participants without sacrificing power

interaction

a situation in a factorial design or contingency table in which the effects of one independent variable depend on the level of another independent variable

grand mean

the mean of all observations

main effect

the effect of one IV

simple effect

the effect of one IV at one level of another IV

between-subjects designs

designs in which different subjects serve under the different treatment levels

repeated-measures designs

experimental designs in which each subject receives all levels of at least one IV

within-subjects designs

experimental designs in which each participant produces multiple scores

assumptions of repeated-measures designs (are the same for any other F test)

1. normality in the distributions

2. homogeneity of variance

3. assumption of homogeneity of covariance: correlations among DV scores must be the same

advantages of repeated-measures designs

1. avoids the problem of person-to-person variability

2. controls for extraneous variables

3. requires fewer participants then between-subjects designs to have same amount of power

disadvantages of related samples

1. order effect

2. carry-over effect

order effect

the effect on performance attributable to the order in which treatments were administered

carry-over effect

the effect of previous trials (conditions) on a subject's performance on subsequent trials

counterbalancing

an arrangement of treatment conditions designed to balance out practice effects

chi-square test

a statistical test often used for categorical data

-dv is number of observations

-is non-parametric

one-classification variable

the chi-square goodness of fit test

goodness-of-fit test

a test for comparing observed frequencies with theoretically predicted frequencies

E

expected frequency

O

observed frequency

two classification variables

analysis of contingency tables using chi-square

contingency table

a two-dimensional table in which each observation is classified on the basis of two variables simultaneously

ex: Walsh tested the effectiveness of using antidepressants after treatment for anorexia nervosa

degrees of freedom for expected frequencies

(R-1)*(C-1)

chi square tests assume

independence of observations

you have independence if

one person's scores do not affect another person's scores

N

must equal the total of the rows, or the total of the columns

risk

number of occurrences on one event divided by total number of occurrences of events

risk ratio (relative risk)

ratio of two risks

odds

frequency of occurrence of one event divided by the frequency of occurrence of the other event

prospective study

a study in which you select participants on the basis of some current condition and follow them into the future

ex: if you're interested in the relationship between smoking and cancer, and you find people who smoke and then track over time who develops cancer

retrospective study

a study in which you select participants on some criterion and then look back at their behavior in the past

ex: if you study the relationship between smoking and cancer and you examine data that already exist in terms of who smoked and developed cancer

in a prospective study

you have to collect the data and analyze it

in a retrospective study

the data already exists and you just have to analyze it