Analyses of Variance. Block 2b

Transcription

1 Analyses of Variance Block 2b

2 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

3 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.

4 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.

5 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

6 Main effects and interactions 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 on long words and short words) high frequency low frequency short words long words

7 1-way ANOVA Analogue to independent groups t-test for 3 or more levels of one factor. A 1-way anova with 2 levels is equivalent to a t- test. P-values the same: F=t 2 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

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

9

10 options

11 Options Descriptives: means, standard deviations, etc. Estimates of Effect Size: eta-squared larger = better Observed power: 1-β Homogeneity tests: Levene s test

12 One way Anova F (2, 141) = 8.97, p <.001

13 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.

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

15 Dependent measure Independent variables covariates Options and plots

16 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.

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

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

19 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.

20 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.

21 Each column is a different condition; no grouping variable

22

23

24 between factors here Covariates here You move the columns in the correct order to the right. Numbers represent levels of conditions, like + and -. Make sure you map correctly!!!

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

26

27

28 1 factor with 4 levels

29 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.

30

31

32 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)).

33

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

35 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