4 (anova)

what does ANOVA test for / what is its purpose?

ANOVA tests if there is a statistical difference between 2 or more groups

purpose: determine if atleast one group has a different mean from the others, and assesses the effect of a single categorical independent variable on a single continuous dependent variable

describe key concepts of ANOVA including: null hypothesis, F-stat, p-value

null hypothesis: all group means are equal/the same

alternative hypothesis: at least one group has a different mean

between group variance: the variability attributed to between group differences

within group variances: variability within each group

F-stat: ratio of between group variance to within group variance.

• this is the distribution that allows us to determine p-value

p-value: probability of observing F statistic

why are statistical tests important?

datasets have measurement error, variability due to experiemental conditions etc

test help quantify variability

what is considered a ‘WEIRD’ sample/data

Western, educated, industrialised and democratic

what is chance variation the same as?

within group variation

t-tests: what distribution is looked at

t-tests look at the distribution of differences between scores

F-statistic: what does it compare? what does a large F-value suggest?

f-statistic compares the variation between groups and within groups

large f-value suggests samples come from different populations, and it is likely that there was an effect/null hypothesis is less likely to be true

what is the sum of squares & what is it sensitive to?

a measure of variation, sensitive to the sample size

what do the dfs account for?

number of groups and sample size

what does the F-ratio mean? what determines the shape of the distribution?

95% of f-ratios in the main part of distribution, whereas 5% of f-ratios are in tail. the p-value tells us where are f-ratio is in the f distribution

• the dfs determine the shape of the distribution

p values: define type I error (false positives), type II error (false negatives) - how are they controlled?

type I error: concluding that there is an effect when there isn’t (a false positive). can be controlled via alpha or significance level

type II error: failing to detect an effect when there is one. can be controlled by statistical power, increased sample size

describe 3 assumptions for ANOVA/statistical testing

1. indepdence of observations

   • value of one observation does not influence others →> this can increase type I and type II error

     2. normally distributed

        • data within each group should be normally distributed - for all sample sizes

     3. homogeneity of variance

   • each group must have approx the same amount of variance, as unequal variances can affect the validity of F stat

post-hoc tests: why are they used & what does the bonferroni correction do?

post hoc tests are used to compare all groups against every other group to spot where the significant difference lies