Independent one-way ANOVA Flashcards
ANOVA
analysis of variance
one-way ANOVA
used when we have 1 IV with MORE than 2 levels
- estimates whether the population means under the different levels of IV are different
independent one-way ANOVA
between participants
relation to t test
squared t-test statistic = F (one way anova result) for an IV with 2 levels
Family wise error rate
the probability that at least one of a ‘family’ of comparisons, run on the same data, will result in a Type I error
…instead calculated a corrected significance level, expressing the probability of making a Type I error
c=comparisons
a= 0.05
what do omnibus test, such as ANOVA, do?
control family wise error rate
F statistic from one-way ANOVA
- F value close to zero, small variance between relative to within
and vice versa
sources of variance between IV levels for independent designs
- manipulation of IV
- individual differences
- experimental error (random/constant)
sources of variance within IV levels for independent designs
- individual differences
- experimental error (random)
assumptions for independent one way ANOVA
- normality
- homogeneity of variance
- equivalent sample size
- independence of observations
normality
the DV should be normally distributed under each level of IV
homogeneity of variance
the variance in the DV under each IV level should be equivalent
what if Levene’s statistic is significant
use Welch F statistic to correct this
- under Robust test of equality means in SPSS out-put
what test do we use if we greatly violate the assumptions of the one-way independent ANOVA test
Kruskal Wallis test
large value of F
manipulation of IV has had a large effect
SPSS output one-way independent ANOVA
Model Sum of Squares (SSm)
sum of squared differences between IV level means and grand mean
- reflected between IV level variance
Residual Sum of squares (SSr)
sum of squared differences between individual values and corresponding IV level mean
- within IV level variance
SSm + SSr =
SSt
sum of squares total
how do we calculate mean square values
sum of squares / df
how do we calculate F
mean square value for between groups / mean square value for within groups
- variance between / variance within
d.f. for one way ANOVA independent between IV levels
d.f. model = k - 1
k = number of levels of IV
d.f. for one way ANOVA independent within IV levels
d.f. residual = N - k
n = total sample size
k = number of IV levels
secondary analyses for one-way independent ANOVA
post-hoc tests
.. what happens after omnibus test (ANOVA)
post-hoc tests
- used to analyse which IV level mean pairs differ
- only when F value is significant
Type I error
risk of incorrectly rejecting null hypothesis when population means are actually not different
Type II
risk of failing to reject null when population means are actually different
choice of corrections tabel
don’t need to memorize
SPSS out-put post-hoc
example
refer to bar charts for help discerning which one is more significant
significant
if less than 0.05
the two different effect sizes for ANOVA
- partial η^2
- Cohen’s d
partial η^2 (Eeta)
how much variance in the DV is explained by the manipulation of the IV overall
Cohen’s d
the magnitude of the difference between pairs of IV levels
effect sizes
small partial η^2 effect size
> 0.01
medium partial η^2
> 0.06
large partial η^2
> 0.14
partial η^2 formula
Cohen’s d formula
do it separately for each combination of IV levels
note
practice calculating partial eta squared by hand might be checked in a quiz
write up one way ANOVA: design
- IV: its levels, sunject design, steps taken to eliminate confounds (e.g. counterbalancing, random allocation)
- DV
one-way ANOVA results: step one: descriptive statistics in the table
- measure of central tendency: mean
- measure of spread: standard deviation
- interval estimate: CIs for upper and lower limit
one-way ANOVA: step 2: results write up
- refer to descriptive statistics table
- state test used
- test statistic: : F(dfM, dfR) = _.__, p = .___ (*),
- if assumption for homogeneity has been violated (Levene’s for independent, Mauchly’s for repeated measures) state what correction you use after statistic (Welch or Greenhouse-Geisser)
- state if results were significantin next sentance with directionality if so
- effect size as partial eta squared as percentage if significant *if not report after test statistic
- e.g. this represented a )large) effect size: partial eta squared revealed that x% of variance in DV COULD BE ACCOUNTED FOR for vy the different IV levels X.
one-way ANOVA: step 3: post hoc as part of results
- if significant do post-hoc write up
- Tukey HSD for between-subjects
- Bonferroni for within-subject
- p-values for each paired comparison and if significant the direction of differences: which IV level was greater
- Cohen’s d for each paired comparisons
format: Format: (p = .___ , d = _.__)
