Psych 10 Ch 11

F obt for ANOVA formula

(MSbg) / (MSe) --> variance between groups / variance within groups

rules for power of the one way within subjects ANOVA:

1) as SSbp increases, power increases 2) as SSe decreases, power increases 3) as MSe decreases, power increases

test statistic is the same for the within subjects and between subjects designs using ANOVA

F obt = (MSbg) / (MSe)

Most liberal (greatest power) tests

Turkey's HSD test SNK test Fisher's LSD test

partial omega squared

[(SSbg - DFbg)(MSe)] / [(SSt - SSbg) + (MSe)]

experimentwise alpha

alpha level, or overall probability of committing a Type 1 error, when multiple tests are conducted on the same data

degrees of freedom within groups (degrees of freedom error or degrees of freedom denominator)

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

degrees of freedom between groups (degrees of freedom numerator)

degrees of freedom associated with the variance of the group means in the numerator of the test statistic equal to the number of groups (k) - 1

f distribution

positively skewed distribution derived from a sampling distribution of F ratios

as degrees of freedom increase, the critical values get smaller --> greater power

true

as the total degrees of freedom increase, the f distribution becomes less skewed (tails pull closer to the y axis)

true

calculations of SS between persons are unique to the one way within subjects ANOVA all remaining calculations of SS are the same as those computed using the one way between subjects ANOVA

true

the mean squares for each source of variation are computed by dividing SS by df for each source of variation

true

observed power

type of post hoc 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

3 sources of error in the one way within subjects ANOVA

1) between groups 2) within groups 3) between persons

post hoc tests

procedure computed following a significant ANOVA to determine which pair or pairs of groups means significantly differ necessary when k>2 because multiple comparisons needed k=2 only one comparison is made because only one pair of group means can be compared

assumption of homogeneity of variance and covariance are called ______

sphericity

studentized range statistic (q)

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

eta squared formula for ANOVA (sometimes reported as R^2)

sum of squares between groups / sum of squares total (SSbg) / (SSt)

levels of the factor (k)

the number of groups or different ways in which an independent or quasi independent variable is observed

between groups variation

the variation attributed to mean differences between groups

sum of squares within groups (sum of squares error SSe)

the sum of squares attributed to variability within each group

F statistic (F obtained)

the test statistic for ANOVA the mean square (variance) between groups divided by the mean square (variance) within groups

using a partial proportion of variance, we remove or partial out the between persons variation before calculating the proportion of variance

true

the null hypothesis for ANOVA states that the group means in the population do not vary the alternative hypothesis states that group means in the population do vary

true

advantages to using omega squared over eta squared:

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

pairwise comparision

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

one way within subjects ANOVA (one way repeated measures ANOVA)

procedure used to test hypotheses for one factor with two or more levels concerning the variance among group means used when the same participants are observed at each level of a factor and the variance in any one population is unknown

testwise alpha

the alpha level, or probability, of committing a Type 1 error, for each test or pairwise comparison made on the same data

sum of squares total (SSt)

the overall sum of squares across all groups

mean square error (MSe)

the variance attributed to differences within each group denominator of the test statistic

between persons variation

the 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 within subjects ANOVA

within groups variation

the variation attributed to mean differences within each group cannot be attributed to or caused by having different groups and is therefore called error variation

eta squared is biased in that it tends to overestimate the proportion of variance explained by the levels of a factor

true

for ANOVA, k is the number of groups, n is the number of participants, and N is the total number of participants in a study T/F

true

partial measures of proportion of variance are used to estimate the effect size for the one way within subjects ANOVA

true

post hoc tests are computed following a significant one way ANOVA to determine which pair or pairs of group means significantly differ

true

the formulas for partial eta squared and partial omega squared have between persons variation removed or partialled out of the denominator

true

the rejection region is always located in the upper tail of the F distribution, so the critical value is always positive

true

using partial eta squared can be biased in that it tends to overestimate the effect size

true

within subjects design is more powerful than the between subjects design when changes in the dependent variable are consistent across groups

true

one way between subjects ANOVA

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

four assumptions to compute one way within subjects ANOVA

1) normality - data normally distributed 2) independence within groups - same participants observed within groups. independently observed within groups but not between groups 3) homogeneity of variance - assume the variance in each population is equal to that in the others 4) homogeneity of covariance - assume participant scores in each group are related because the same participants are observed across or between groups

what are the two sources of variation in a one way between subjects ANOVA?

1) variation attributed to differences between group means 2) variation attributed to error

Most conservative (least power) tests:

Scheffe test Bonferroni procedure

omega squared formula for ANOVA

[(SSbg) - (DFbg)(MEe)] / [(SST) + (MSe)]

source of variation

any variation that can be measured in a study

between subjects design

select independent samples, meaning that different participants are observed at each level of a factor

analysis of variance (ANOVA)

statistical test 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

steps to compute Tukey's HSD

1) compute the test statistic for each pairwise comparison 2) compute the critical value for each pairwise comparison 3) make a decision to retain or reject the null hypothesis for each pairwise comparison

4 assumptions to compute the one way between subjects ANOVA:

1) normality: we assume that data in the population being sampled are normally distributed 2) random sampling: data measured were obtained from a sample that was selected using random sampling procedure 3) independence: assume the probabilities of each measured outcome in a study are independent 4) homogeneity of variance: assume 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, thereby increasing the likelihood of committing a type 1 error

mean square between persons (MSbp)

the measure of the variance attributed to differences in scores between persons

sum of squares between groups (SSbg)

the sum of squares attributed to variability between groups

sum of squares between persons (SSbp)

the sum of squares attributed to variability in participant scores across groups

mean square between groups (MSbg)

the variance attributed to differences between group means numerator in the test statistic

partial omega squared advantages:

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