Class 8

ANOVA

• analysis or variance or R-test

• parametric stat stat test that we use to compare the means of three or more groups

which statistic is used in ANOVA

F statistic

one way ANOVA

• has ONE DV and ONE IV

• tests the differences between three or more independent groups based on the IV

two way ANOVA

• One DV and 2 IV

• testing the differences in DV between three or more independent groups based on the two IV

repeated ANOVA

used to rest if there are significant changes in the DV over time or across different conditions for the same group of people

why don’t we do multiple two sample t-tests instead of ANOVA

because when multiple t-tests are conducted type I error risk adds up

assumptions for one way ANOVA

randomly sampled, continuous DV and categorical IV, independence of observation, normality, homogeneity of variance

formula for F

F = between group variation/within group variation

what should F be to get a significant result

we hope for a large F

what does a low F-statistic mean

the between group variation is similar to or smaller than the within group variation - this suggests the group differences could be due to random chance

df between group calculation for one way ANOVA

df = number of groups minus 1

df within group calculation for one way ANOVA

number of subjects minus the number of groups

skewness of F distribution

positively skewed towards the right with a range of 0 to infinity

are F values positive or negative

only positive, no negative values

what impact the F distribution shape

df of the numerator and denominator

is there directional hypothesis in ANOVA

NOOO - so one and two tailed tests do not apply

what is the P-value

the probability of obtaining the test statistic or a more extreme value under the null

if P > a what do you do

fail to reject the null

if P < a what do you do

reject the null hypothesis

post hoc test

• test you do if you find a significant result in in ANOVA

• tells us which specific groups differ from each other

does ANOVA tell anything about strength or direction of the relationship

no, this is why we would want to do a post hoc test for more specific results

non parametric alternative to one way ANOVA

Kruskal Wallis H test

what does the Kruskal Wallis H test look at

it determines whether there is a statistically significant difference between the MEAN RANKS of three or more independent groups

ANOVA vs Kruskal Wallis

ANOVA is parametric and compares MEANS for 3 or more groups. Kruskal Wallis is the non parametric and compares MEAN RANKS for 3 or more groups

which test statistic does the kruskal wallis H test use

H statistic - it is based on the sum of ranks for each group

df formula for kruskal wallis H test

df = K - 1

• k is the number of groups being compared

what is K in the df formula for kruskal wallis H test

it is the number of groups being compared

repeated measures ANOVA

• ANOVA test for dependent samples

• deals with the same participants being measured over multiple time points

assumptions for repeated measure ANOVA

randomly sampled, continuous DV and categorical IV, normality, equal variance, groups are paired and dependent

correlation

describes the strength and direction of a relationship between two numerical variables

positive correlation

as one variable increases, the other variable also increases (variables are moving in the same direction)

negative correlation

as one variable increases the other variable decreases (the two variables move in different directions)

no correlation

changes in one variable do not influences changes in the other variable (the two variables do no move together)

Pearson correlation test

• parametric test for correlation

• measures strength and direction of a LINEAR relationship

• requires normal distribution

spearman’s rank test

• non parametric correlation test

• for skewed data

• deals with ranked values rather than raw data

when to use pearsons correlation test

relationship between two variables in linear, continuous data (interval or ratio), normality, homoscedasticity (equal variance)

pearson correlation co efficient

r

when to use spearmans rank correlation test

• when dealing with any data (ordinal, interval, ratio)

• not normal or equal variance

spearmans rank coefficient

P (greek letter rho)

which numbers are r and p always between

-1 and 1

p or r greater than 0 (>0)

means positive correlation

p or r less than 0 (<0)

negative correlation

what is direction of correlation determined by

whether r or p are positive or negative

what is the strength of correlation determined by

the actual number (absolute value) or the correlation coefficient (r or p)

correlation coefficient less than 0.3 (<0.3)

weak correlation

correlation coefficient between 0.3 - 0.5

moderate correlation

correlation coefficient greater than 0.5

strong correlation

correlation coefficient of 1

perfect correlation

correlation coefficient of 0

no correlation

does a large correlation co efficient mean that the result is statistically significant

no, we always have to check the hypothesis and check the p value

what to look at for correlation direction in scatter plots

look at the trend of the points

what to look for for correlation strength in scatter plots

how closely the points cluster around a straight line (more clustered = more strenth)

r2

co efficient of determination

• measure of how much the variability in one variable can be explained by the relationship with the other variable

r2 × 100

tells the percentage of variance

• % of variance of one variable that is explained by the other variable

most important hill’s causal criteria

TEMPORALITY

• the cause MUST precede the effect (most essential criterion)

hills causal criteria

temporality, strength of association, dose response relationship, consistency, experiment, analogy, plausibility, coherence, specificity

hills causal criteria - strength of association

a strong association makes causation more likely (ex. smoking has a very strong association with lung cancer)

hills causal criteria - dose response relationship

increasing exposure leads to a greater effect (ex. more cigarettes per day = increases risk of lung cancer)

hills causal criteria - consistency

the association is observed repeatedly in different studies, populations and settings

hills causal criteria - experiment

experimental evidence supports the association. the outcome can be altered by an intervention (ex. reducing smoking leads to decreased lung cancer incidence)

hills causal criteria - analogy

similar causal relationships exist which strengthens the argument for causation

• ex. if other environmental toxins cause cause it is more plausible that tobacco which is an environmental toxin does the same

hills causal criteria - plausibility

the proposed causal relationship is scientifically plausible based on existing knowledge

• ex. the mechanism by which smoking causes damage to lung tissue is well understood

hills causal criteria - coherence

the association is consistent with existing knowledge and theories in related fields

hills causal criteria - specificity

the effect is specific to a particular cause and not explained by other factors

when would we use Chi square

when testing the relationship between two CATEGORICAL variables (nominal or ordinal with less than 4 levels)

when can ordinal data be treated as interval for stats

if there are 4 or more levels