what does ANOVA stand for?
analysis of variance
when do you use a F distribution?
when working with more than 2 samples
when do you use ANOVA?
with 2 or more nominal independent variables and an interval dependent variable
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)
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
variance between groups reflects difference among ____
sample means
variance within groups is the average of ___
sample variances
the square root of F statistic is equal to?
t statistic
estimate of the population variance based on differences among the means
between-groups variance
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
group differences in means that we have obtained from the data
between group variance
hypothesis test including one nominal variable with more than 2 levels and a scale DV
one-way ANOVA
what kind of test?: more than 2 samples, with different participants in each sample
between-group ANOVA
what kind of test?: more than 2 samples, with the same participants, also called repeated-measure
within group ANOVA
hypothesis test including 2 nominal variable with more than 2 levels and a scale DV
two way ANOVA
what are the 3 assumptions of one-way between ANOVAs?
1. random selection
2. normal distribution
3. homoscedasticity
what is homoscedasticity?
homogenity of variance; samples come from populations with the same variance
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, assum
Are all ANOVAs one-tail or two-tailed tests?
two-tailed
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
the larger the variance the (larger/ smaller) the F statistic
larger
what does the F statistic quantify?
overlap
what are the 2 ways to estimate population variance?
1. between-group variability
2. within-group variability
what is MS?
corrected variance
what is the square root of MS?
standard deviation
If calculated F is bigger than critical, we (have/ don't have) a significant difference between means.
have
If calculated F is bigger than critical, do we reject or fail to reject the null hypothesis?
reject
what is the common measure of effect size for one- way between ANOVA?
R squared= SS between/ SS total
what is Cohen's conventions for effect sizes: R squared?
small: 0.01
medium: 0.06
large: 0.14
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
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)
what is the Tukey HSD Test?
widely used post hoc test that uses means and standard error (Sm)
HSD= M1-M2/Sm
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 stu
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
how do you solve for SS within in a one way within ANOVA?
SS within= SS total- SS between -SS subjects
what's the effect size (formula) for one-way within ANOVA?
R^2= SS between / (SS total - SS subjects)
how do you calculate the standard error (Sm)?
Sm= squareroot (MS within/N)
what does the post hoc test identify?
where you have differences if your F is significant
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
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
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 are sums of squares?
measures of variability of scores from the mean
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
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 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 4 assumptions for a within-group ANOVA?
1. random selection
2. normal distribution
3. homoscedasticity
4. no order effects
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
Define the source of variability called "subjects
noise in the data caused by each participant's personal variability compared with the other participants
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 rej
what is counterbalancing?
exposing participants to different levels of the IV in different orders