Analyses of Variance Block 2b Types of analyses 1 way ANOVA For - - PowerPoint PPT Presentation

Analyses of Variance

Block 2b

Types of analyses

• 1 way ANOVA

– For more than 2 levels of a factor between subjects

• ANCOVA

– For continuous co-varying factor, between subjects

• ANOVA for factorial design

– Multiple factors and between subjects.

• Repeated measures ANOVA

– Multiple factors and within subjects

• Contrasts and Post-hocs

ANOVA

• Analysis of Variance

– Similar to t-test in that it also calculates a Signal-to-noise ratio, F.

• Signal = variance between conditions
• Noise = variance within conditions

– Can analyze more than 2 levels of a factor. – Can analyze more than 1 factor. – Can reveal interactions between factors.

Types of effects

• Each factor in your analysis can reveal a main effect.

This is the effect of a variable averaged over all values of another variable.

• Within factor comparisons can also reveal simple

effects, the effect of an IV in only one level of an another IV.

• Between factor comparison can reveal interactions,

when the effect of one IV depends on the level of another IV.

Main effects and interactions

• Let‘s assume we have 2 factors with 2 levels

each that we manipulated in an experiment:

– Factor one: lexical frequency of words (high frequency and low frequency) – Factor two: word length (long words and short words)

• We measured reaction times for a naming task.
• In an ANOVA we can potentially find 2 main

effects and an interaction

• Main effect of word length (long words 350 ms, short words 250 ms)
• No main effect of frequency (high frequency 300 ms, low frequency 300 ms)
• Interaction between word length and frequency (i.e., frequency has a different influence
• n long words and short words)

Main effects and interactions

200 400 300 300 50 100 150 200 250 300 350 400 450 short words long words high frequency low frequency

1-way ANOVA

• Analogue to independent groups t-test for 3
• r more levels of one factor.

– A 1-way anova with 2 levels is equivalent to a t-

• test. P-values the same: F=t2
• Data must be in two columns

– One for DV and one to code levels of IV.

• This analysis is found under ‘compare means’
• Non-parametric = k-independent samples

Task & prime Are IV’s and Grouping variables RT is DV Var00001 is covariate

• ptions

Options

• Descriptives: means, standard deviations,

etc.

• Estimates of Effect Size: eta-squared

– larger = better

• Observed power: 1-β
• Homogeneity tests: Levene’s test

One way Anova

F (2, 141) = 8.97, p < .001

ANCOVA

• Analysis of Covariance

– If you have a continuous variable that was not manipulated but that might add variance,

• like word frequency, subject age, years of

programming experience, sentence length, ect…

– you can factor out the variance attributed to this covariate. – This removes the error variance and makes a large ratio more likely.

Univariate can be used if you only have 1 dependent measure. Multivariate is used if you have multiple dependent measures

Dependent measure Independent variables covariates Options and plots

Factorial ANOVA

• When you have more than one IV but

the analysis remains between subjects, you can use the univariate interface for the analysis.

• This analysis allows you to test the

‘main effect’ of each independent variable but also the interaction between the variables.

Main effect of Prime Main effect of Task Interaction of two factors F (2, 137) = 9,76 p < .001 Df for factor Df for Error Effect of covariate

Same analysis without covariate Old prime F = 9.76 Old task F = 2.09 Old interaction = .028

Interactions

• Interactions indicate that independent

variable X influences the dependent variable differently depending on the level of independent variable Y.

– Interpret your main effects with the consideration of the interaction. – You can have an interaction with no main effects.

Repeated measures design

• Within subjects
• Data must be entered into separate

columns for each condition in the experiment.

– No coding variable needed.

• This analysis is appropriate for data

from just 1 IV or multiple IVs and for mixed designs.

Each column is a different condition; no grouping variable

You move the columns in the correct

• rder to the

right. Numbers represent levels of conditions, like + and -. Make sure you map correctly!!! between factors here Covariates here

Using the plot option button, you can ask for graphs of the data.

1 factor with 4 levels

This analysis shows that we have a significant effect of our IV, but which levels are significantly different from other levels? Look at the graph. The analysis doesn’t tell us if 1 > 2 or 1 < 4. For that, we have to do either contrasts or paired comparisons.

Pairwise comparisons

• Similar in principle to running multiple t-

tests on all combinations of conditions.

– Under the options window if you want all comparisions. – chose the comparisons that are interesting to you and run t-tests. – Then correct alpha based on number of t- tests performed. (e.g., .05/x, x=# of tests)).

I conducted 6 tests, so .05/6 = .008. 4 of my tests are still significant.

Summary

• If you have 1 factor with K levels all between

subjects: 1-way ANOVA

• If you have a covarying factor and a between

subjects manipulated factor, use univariate ANOVA

• If you have more than one between subjects

factor and they are factorially related, use univariate ANOVA

• If you have repeated measures design, with 1 or

more manipulated factors, with or without a covariate or an additional between subjects factor, use Repeated Measures