PSYCH 10 Chapter 11

when n is the same or equal in each group, we state what?

N = kn where N = total number of participants in a study n = number of participants per group k = levels of the factor

for an ANOVA test, Eta-squared is often reported as _____

R²

one-way within-subjects ANOVA one-way repeated-measures ANOVA

a statistical procedure used to test hypotheses for one factor with two or more levels concerning the variance among group means. This test is used when the same participants are observed at each level of a factor and the variance in any one population is known n number of participants are observed k times

as the total degrees of freedom increases, the F distribution ?

becomes less skewed and so the tails of the distribution pull closer to the y-axis

because f distribution tests are positively skewed? what does that mean for the tails?

begins at zero and is skewed toward positive values so critical value for all tests is placed in the upper tail, and negative outcomes aren't possible in an F distribution

if the result of an ANOVA is to reject the null hypothesis, then researchers do what?

conduct post hoc tests

F distribution

positively skewed distribution derived from a sampling distribution of F ratios

pairwise comparison

statistical comparison for the difference between two group means. A post hoc test evaluates all possible pairwise comparisons for an ANOVA with any number of groups

degrees of freedom between persons (DFbp)

the degrees of freedom associated with the variance of person means averaged across groups. They are equal to the number of participants (n) - 1

sources of variation for a one-way within-subjects ANOVA

within-groups, between persons

SSt

Sum of squares total the overall sum of squares across all groups

Sphericity

assumptions of homogeneity of variance and homogeneity of covariance if violated, then the value of variance in numerator can be inflated which will increase likelihood of committing a type I error

eta squared vs. omega squared

eta squared can be biased because it tends to overestimate the proportion of variance explained by the levels of a factor

Between-subjects design

research design in which we select independent samples, meaning that different participants are observed at each level of a factor

SSbg

sum of squares between groups sum of squares attributed to variability between groups

SSbp

sum of squares between persons sum of squares attributed to variability in participant scores across groups

Steps for Turkey's HSD post hoc test

1. Compute the test statistic for each pairwise comparison 2. Compute the critical value for each pairwise comparison (different step than others) 3. Make a decision to retain or reject the null hypothesis for each pairwise comparison

MSe

Mean square within groups variance attributed to differences within each group Mean square error denominator when computing the obtained F statistic

SSe

Sum of squares within groups, or sum of squares error sum of squares attributed to variability within each group

when do we know to reject the null hypothesis in a post hoc test?

for each comparison, if the test statistic is larger than the critical value we computed for each individual group, then we REJECT

what is the test statistic used to determine?

how large or disproportionate the differences are between group means compared to the variance expected to occur by chance

Analysis of variance

measures the variance among two or more groups statistical procedure used to test hypotheses for one or more factors concerning the variance among two or more group means (k ≥ 2), where the variance in one or more populations is unknown

Smaller critical values and power?

smaller critical values = greater power

post hoc test

statistical procedure computed following a significant ANOVA to determine which pair or pairs of groups means significantly differ. These tests are necessary when k > 2 because multiple comparisons are needed. When k =2, only one comparison is made because only one pair of group means can be measured

One-way between-subjects ANOVA

statistical procedure used to test hypotheses for one factor with two or more levels concerning the variance among the group means. This test is used when different participants are observed at each level of a factor and the variance in any one population is unknown evaluates if the means in each group vary significantly

F statistic/ F obtained (Fobt)

test statistic for an ANOVA computed as the mean square between groups divided by the mean square or variance within groups

in turkey's HSD test, the real range, r, is equal to ?

the number of groups, k, in a study

the larger the differences are between group means, what happens to the variance?

the variance of group means is proportional to the variance of the differences of group means

within groups-variation

the variation attributed to mean difference within each group. This source of variation cannot be attributed to or caused by having different groups and is therefore called error variation "random chance"

between-groups variation

the variation attributed to mean differences between groups

effect size proportions for eta/omega squared

trivial: < 0.01 Small: 0.01-0.09 Medium: 0.10- 0.25 Large: >0.25

most conservative rule

use the next smallest value if they don't have the value given in a table for determining post hoc tests

all post hoc tests control for ?

experimentwise alpha make sure the overall likelihood of committing a type I error is always at 0.05, no matter how many tests are conducted

As degrees of freedom increase, the critical values?

get smaller

when the same participants are observed across the levels of a factor, we use what kind of ANOVA test?

within-subjects design

advantages for omega squared

1. it corrects for the size of error by including MSe in the formula 2. it corrects for the number of groups by including the degrees of freedom between groups (DFbg) in the formula

Source of variation

any variation that can be measured in a study. In the one-way between-subjects ANOVA, there are two sources of variation: variation attributed to differences between group means and variation attributed to error

degrees of freedom increase? what happens to power?

as df increase, power also increases

for ANOVA, n = ? N = ?

n = number of participants per group N = total number of participants in a study

four assumptions made about one-way between subjects anova

1. normality 2. random sampling 3. Independence 4. Homogeneity of variance (we assume that the variance in each population is equal to that of the others. Violating this assumption can inflate the value of the variance in the numerator of the test statistic which will cause a type 1 error)

best post hoc test to use for a significant one-way repeated-measures ANOVA

Bonferroni Procedure

MSbg

Mean square between groups variance attributed to difference between group means numerator of the test statistic

observed power

a type of post hoc or retrospective power analysis that is used to estimate the likelihood of detecting a population effect, assuming that the observed results in a study reflect a true effect in the population

ranking of post hoc tests conservative to liberal

conservative (least power) to liberal (most power) 1. Scheffé Test 2. Bonfoerroni Procedure 3. Turkey's HSD test 4. SNK test 5. FIsher's LSD test (one and two are perceived as being too conservative for a between-subjects test though Bonfoerroni is only too conservative when the number of pair-wise comparisons is greater than three)

in behavior testing, there is always a ________ group in addition to the hypotheses being tested

control

DFbg

degrees of freedom between groups are the degrees of freedom associated with the variance of the group means in the numerator of the test statistic number of groups (k-1) minus one k-1

Turkeys HSD critical value equation:

q(α) √(MSe ÷ n) where q is the studentized range statistic

testwise alpha

the alpha level or probability of committing a type I error, for each test or pairwise comparison made on the same data

the null hypothesis for an anova test says what about the group means in the population?

they do not vary

the alternative hypothesis for an ANOVA test says what about the group means in the population?

they do vary

when is one way within-subjects ANOVA used?

to analyze data when the same participants are observed across two or more levels of one factor

rejection region is located where for an f distribution?

upper tail; so the critical value is always positive

between-persons variation

variance attributed to the differences between person means averaged across groups. Using a within-subjects design, the same participants are observed across groups, so this source of variation is removed from the error term in the denominator of the test statistic for the one-way ANOVA

Experimentwise alpha

alpha level, or overall probability of committing a Type I error, when multiple tests are conducted on the same data

within subjects design is generally associated with ________ ________ to detect an effect than the between-subjects design when changes in the dependent variable are consistent across groups

more power (typically because within-group testing is associated with more consistency!) but not always!

What does "one way" mean for ANOVA testing?

one way indicates that we only test one factor if we tested two factors, we would call the test a two way ANOVA

when different participants are observed across the levels of a factor, we use what kind of ANOVA test?

one-way between subjects ANOVA

studentized range statistic

q a statistic used to determine critical values for comparing pairs of means at a given range. This statistic is used in the formula to find the critical value for Turkey's HSD post hoc test

DFe

degrees of freedom error degrees of freedom within groups degrees of freedom denominator degrees of freedom associated with the error variance in the denominator. They are equal to the total sample size (N) minus the number of groups (k) N-k

levels of the factor

symbolized as k number of groups or different ways in which an independent or quasi-independent variable is observed

Four assumptions for computing a one-way within-subjects ANOVA

1. Normality 2. Independence within groups 3. Homogeneity of Variance-- we assume that the variance in each population is equal to that in the others 4. Homogeneity of covariance-- we assume that the participant scores in each group are related because the same participants are observed across or between groups