Week 4-Between groups one-way analysis of variance ANOVA

between participants

each participant only provides a score for one condition

experimentwise Error rate/Family wise error rate

increased chance of ‘making a mistake’ by running more than one t-test

ANOVA controls for these errors

when to use ANOVA

with more than two groups

parametric assumptions met

assumptions for ANOVA

normal distribution

homogeneity of variance- Levene’s for between groups, Mauchly’s Test of Sphericity for within groups

independent random samples

do not need equal numbers of score in each group

Mauchly’s test of sphericity

W=, x²_(df)=, p=

ANOVA

looks for differences between the means of the groups

where the means are very different, there is a greater degree of variation between the conditions

takes account of the variance within the conditions and compares this to the variance between conditions.

between groups variance

1. treatment/condition effects

2. individual differences to the condition

3. experimental error

the variation between mean scores in each condition

within groups variance

differences or variation within a group

1. individual differences

2. experimental error

logic of ANOVA

• participants in different groups should have different scores because they have been treated differently but participants within the same group should have the same score.​

• We want to know if our different treatment groups have different scores because of the treatment condition they have been exposed to. ​

• The variability in the groups not produced by the experiment is error variance.

F ratio

if the manipulation of the IV is responsible for the differences between scores

fisher ratio is the ratio of variance

if the error variance is small compared to variance due to manipulation of the IV, the f-ratio will be greater than 1

if the effect of the IV is small or the error variance is large, the F-ratio will be less than 1 (the effect of the IV is not significant)

the greater the F-ratio, the better

the p value needs to be less than 0.05 to be significant

factors

These are the independent variables (IVs). In our study, the Factor is Condition.

levels of factors

• In our study we have three levels of factors. Our IV (condition)has been manipulated into ​

• (1) Constant low level of music, ​

• (2) No music and ​

• (3) Intermittent music.

independent measures one-way ANOVA/one way between participant

e.g. people with high blood pressure were randomly allocated to one of three groups to reduces their blood pressure

null hypothesis: there will be no difference in the reduction of blood pressure among the three treatments

alternative hypothesis: there will be a difference among the three treatments

SPSS ANOVA between participants reporting

report test used

F ratio

suggests that the observed variance among the three groups is over 9 times what we would expect if the null hypothesis is true, therefore reject/accept null hypothesis (p value)

effect size (eta squared) n2=, % of the variation can be accounted for different groups, benchmarks

planned (a priori) comparisons

Conducted when the researcher has predicted which means will differ from each other, after you have conducted the ANOVA analysis

SPSS uses linear contrasts technique and assigns weights

unplanned (post hoc) comparisons

Differences in means explored after data has been collected but have no prediction of where the means will differ from each other

• Equal Variances Assumed: Bonferroni (conservative, widely reported)​

• Equal Variances Not Assumed: Games-Howell (widely reported)

planned comparisons in SPSS

using contrast tab

read ‘assume equal variances’ row

t(df)=, p=

effect size using cohens d, does not overlap 0, talk about both even if not significant

unplanned comparisons SPSS

mean difference and p value

signposted with an asterisk

mention all outcomes even if not significant

cohen’s d