Ch. 11 One-Way ANOVA

what does post hoc mean? when are these tests needed with ANOVA?

"after this," when an ANOVA is significant and we want to discover where the significant differences exist between the groups

what are the 2 ways to estimate population variance?

1. between-group variability 2. within-group variability

why do you use ANOVA instead of a multiple T test?

1. fishing for a finding 2. increases probability of type 1 error (using ANOVA will tell you if null can be rejected or not. And if you can reject it, you can go on with your test but if you fail to reject it, there's no need to do any more tests)

what are the 3 assumptions of one-way between ANOVAs?

1. random selection 2. normal distribution 3. homoscedasticity

what are the 4 assumptions for a within-group ANOVA?

1. random selection 2. normal distribution 3. homoscedasticity 4. no order effects

what are the benefits of an one-way within-groups ANOVA?

1. reduce error due to differences between groups 2. know that the groups are identical for all of the relevant variables b/c each group includes exactly the same participants 3. reduce within-group variability due to differences for the people in the study across groups

what do the F distributions allow us to do that the t distributions do not?

F distributions allow us to compare numerous variables within a single study

The F distribution is a way to analyze variability to compare means. What is the formula for F?

F= variance between groups/ variance within groups

what is the common measure of effect size for one- way between ANOVA?

R squared= SS between/ SS total

what's the effect size (formula) for one-way within ANOVA?

R^2= SS between / (SS total - SS subjects)

how do you solve for SS within in a one way within ANOVA?

SS within= SS total- SS between -SS subjects

how do you calculate the standard error (Sm)?

Sm= squareroot (MS within/N)

what does ANOVA stand for?

analysis of variance

why is there only one cutoff for a F distribution (2-tailed test)?

because F is a squared version of the z or t statistic

why do you have to square the deviations from the mean to get sum of squares?

because the deviations from the mean always sum to zero

group differences in means that we have obtained from the data

between group variance

what kind of test?: more than 2 samples, with different participants in each sample

between-group ANOVA

estimate of the population variance based on differences among the means

between-groups variance

we typically measure the effect size with ___ for a z test or a t test and with ___ for an ANOVA

cohen's d; R^2

what is MS?

corrected variance

one way ANOVA: what is the formula for df within and between?

df= (df between)(df subjects) df= sum of all df of the groups

what are order effects?

differences between responses that are a function of the order of presentation rather than real differences between the levels of the variable of interest

what is the research hypothesis for ANOVA?

differences exist between groups--any groups; any combination of differences between means is possible when we reject the null

what is counterbalancing?

exposing participants to different levels of the IV in different orders

If calculated F is bigger than critical, we (have/ don't have) a significant difference between means.

have

what is homoscedasticity?

homogenity of variance; samples come from populations with the same variance

the larger the variance the (larger/ smaller) the F statistic

larger

what are sums of squares?

measures of variability of scores from the mean

Define the source of variability called "subjects"

noise in the data caused by each participant's personal variability compared with the other participants

hypothesis test including one nominal variable with more than 2 levels and a scale DV

one-way ANOVA

what does the F statistic quantify?

overlap

statistical procedure carried out after we have rejected the null hypothesis in ANOVA; allows us to make multiple comparisons across several means

post hoc test

If calculated F is bigger than critical, do we reject or fail to reject the null hypothesis?

reject

variance between groups reflects difference among ____

sample means

variance within groups is the average of ___

sample variances

what is Cohen's conventions for effect sizes: R squared?

small: 0.01 medium: 0.06 large: 0.14

what is the square root of MS?

standard deviation

the square root of F statistic is equal to?

t statistic

hypothesis test including 2 nominal variable with more than 2 levels and a scale DV

two way ANOVA

Are all ANOVAs one-tail or two-tailed tests?

two-tailed

what is the advantage of the design of the within groups ANOVA over that of the between groups?

variability due to individual differences among the participants is subtracted our from the variability that we expect by chance. this makes the denominator of the F ratio smaller which makes the F statistic larger and INCREASES the likelihood that we reject the null

what is the harmonic mean? (N')

weighted sample size; used when we have unequal N's in our different groups N'= N groups/ Sum (1/N)

when do you use a F distribution?

when working with more than 2 samples

what does the post hoc test identify?

where you have differences if your F is significant

what is the Tukey HSD Test?

widely used post hoc test that uses means and standard error (Sm) HSD= M1-M2/Sm

when do you use ANOVA?

with 2 or more nominal independent variables and an interval dependent variable

what kind of test?: more than 2 samples, with the same participants, also called repeated-measure

within group ANOVA

estimate of population variance based on differences within (3 or more) sample distributions

within-group variance

the variance that is reflecting the differences between means that we would expect to occur just by chance

within-group variance

what's the difference between a within-group ANOVA & a between-group ANOVA?

within: test in which there are more than 2 samples and each sample is composed of the same participants between: test in which there are more than 2 samples and each sample is composed of different participants

why do we need to check for homoscedasticity in ANOVA?

Homogeneity of variance is necessary because we are pooling the estimates of the variance in these different distributions to construct our sampling distribution. We are taking individuals within their group and comparing them with their group mean, assuming that they all have about the same amount of variability.