PY2501.2 ~ {one way repeated measures ANOVA recap}
what's a one way ANOVA
ANOVA = Analysis of Variance
parametric tests that allow us to look at differences between 3 or more conditions
parametric equivalents/alternatives to ANOVA
we use these when the assumptions of parametric test [normality / homogeneity of variances] are not met
Kruskall - Wallis
Friedman's
kruskal-wallis test
non-parametric alternative to one-way ANOVA
used to compare the medians of 3 or more independent groups to determine if there is a statistically significant difference between them
when to use kruskall-wallis test
more than 2 independent groups + ordinal / continuous data not normally distributed + data violates assumptions of normality + homogeneity of variances
friedman test
non-parametric equivalent to repeated measures ANOVA
used to compare medians of 3 or more related groups [repeated / within-subject designs] to see if they are any significant differences between them
when to use friedman test
more than 2 related groups [repeated measures / matched groups] + ordinal / continuous data not normally distributed + data violates assumptions of normality + spherity [for repeated measures ANOVA]
kruskall-walis post hoc test
KW is an omnibus test so only tells you about significant difference but not where difference lies so we use post-hoc
Mann-Whitney U test
friedman post hoc test
omnibus test so only tells us about sig diff but not where diff is
if friedman test is sig use Wilcoxon signed-rank test for each pair of conditions
non-parametric test
statistical test that doesn't assume a specific distribution for the data, used when these assumptions [normality of data / homogeneity of variances] are not met / when data are on an ordinal scale
2 diff types of one-way ANOVA
within subjects [repeated measures]
between subjects [independent groups]
both compare scores if you have 3 or more conditions
f statistic
tells you about the ratio between condition (signal) to within condition (error/noise) variance
f statistic formula
between condition variance / diff between conditions
f = _________________________________________________
within condition (error / unexplained) variance
what does f-statistic determine
bigger f = bigger differences between the conditions than within
smaller f = bigger diiferences within the conditions than between
f<1 is sometimes reported as 'it'll never be significant'
how far each participant throws a dog + cat + guniea pig measuring distance [ between vs within]
between group differences [signal] - between guinea pigs + dogs + cats
within group differences [noise] - dogs and dogs + cats and cats + gp and gp
what does ANOVA do
calculate how much variance there is BETWEEN conditions [eg dogs vs cats: signal] then calculate how much variance there is WITHIN conditions [eg dogs vs dogs: noise]
shapiro wilk test
used to assess whether a dataset comes from a normal distribution, [developed in 1965]
helps determine is a given sample data is likely to come from a normal distribution [closer the W is to 1 the data is likely to follow normal distribution]
mauchly's test of sphericity
ensures that the variances of the differences between all pairs of groups are equal
assesses the assumption of spherity
what is sphericity
in repeated measures designs, where the same objects are measured multiple times under different conditions / over time
the ides of s is that the variances between all possible pairs of condition are equal
greenhouse-geisser + huynh-feldt corrections
used in repeated measures ANOVA when the assumption of sphericity is violated. the corrections adjust the degrees of freedom for thr within-group variance estimate [makes test more conservative and reduces risk of type I errors]
when to use post-hoc test
used after performing an ANOVA when NH is rejected indicating that there are significant differences between groups [but you dont know which groups differ from one another ph allows ua to explore diff in more details]
eta^2
estimate of the amount of variance in the DV explained by differences in the conditions
how big is eta^2 effect size
according to Cohen (1988)
.01 = small
.06 = medium
.14 = large
what does cohen's d tell us
how many standard deviations difference there is between one condition and another [used for t-tests]
bonferroni test
used to correct for multiple comparisons when performing multiple hypothesis test. it helps reduce the risk of type I errors [ when you do it simultaneously, the likelihood of you mkaing an error increases with each comparison you make from the same data set]
Levene's homogeneity of variance
the assumption that the variance within each group or sample being compared is roughly equal, so when it holds it means that each group has a soimilar level of variability, making comparisons between groups more meaningful
difference between homogeneity of variance and spericity test
HOV - assumes that diff groups have similar levels of variability / spread in their data points
assessed in: ANOVA + t-tests +regression analysis
ST - assumes correlation between any 2 conditions should be the same across all pairs of conditions [ specific to repeated measures data]
assessed in: repeated measures ANOVA + mixed design ANOVA
what do ANOVAs do?
they analyse variance [shock]
you end up with an f statistic that tells you about the ratio between condition [signal] to within condition variance [noise]
what the IV and DV: an employer wants to know if recent graduates who attended a brief practical course / completed distance learning did better on a jamvi test....they gave each group a test and compared the scores
IV = education group with 3 levels [graduates + prac course + distance learning]
DV = jamovi test scores
what to do if Shapiro-Wilk test is significant
check data for outliers + correct / use KW non-parametric test
what to do if Levene's test for homogeneity is significant
report this + ask for Welch's test
if it isnt sig use Fisher's