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Statistics for Linguistics Students

Statistics for Linguistics Students. Michaelmas 2004 Week 7 Bettina Braun www.phon.ox.ac.uk/~bettina/teaching.html. Overview. Problems from last assignment Correlation analyses Repeated measures ANOVA One-way (one IV) Two-way (two IVs) Transformations. Chi-square using SPSS.

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Statistics for Linguistics Students

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  1. Statistics for Linguistics Students Michaelmas 2004 Week 7 Bettina Braun www.phon.ox.ac.uk/~bettina/teaching.html

  2. Overview • Problems from last assignment • Correlation analyses • Repeated measures ANOVA • One-way (one IV) • Two-way (two IVs) • Transformations

  3. Chi-square using SPSS • Organisation of data:

  4. Chi-square using SPSS • Where to find it…

  5. Chi-square using SPSS • How to interpret the output Table similar to ours Result: sign. interaction (x2=5.7, df=1, p=0.017

  6. More on interactions MaleFemale No effect of region, nor gender, no interaction Effect of region and gender and interaction North South No effect of gender, effect of region, no interaction North South Effect of region and gender and interaction North South Effect of region and gender no interaction North South North South

  7. Correlation analyses • Often found in exploratory research • You do not test the effect of an independent variable on the dependent one • But see what relationships hold between two or more variables

  8. Correlation coefficients • Scatterplots helpful to see whether it is a linear relationship… r = -1Neg. corr. r = 0no corr. r = 1pos. corr.

  9. Bivariate correlation • Do you expect a correlation between the two variables? • Try “line-fitting” by eye ?

  10. Pearson correlation • T-test is used to test if corr. coefficient is different from 0 ( => data must be interval!) • If not, use Spearmans correlation (non-parametric)

  11. Pearson correlation • Correlation coefficient • For interval data • For linear relationships • r2 is the proportion of variation of one variable that is “explained” by the other • Note: even a highly significant correlation does not imply a causal relationship (e.g. There might be another variable influencing both!)

  12. Repeated measures ANOVA • Recall: • In between-subjects designs large individual differences • repeated measures (aka within-subjects) has all participants in all levels of all conditions • Problems: • Practice effect (carry-over) effect

  13. Missing data • You need to have data for every subject in every condition • If this is not the case, you cannot include this subject • If your design becomes inbalanced by the exclusion of a subject, you should randomly exclude a subject from the other group as well (or run another subject for the group with the exclusion)

  14. Requirements for repeated measures ANOVA • Same as for between-subjects ANOVA • You can have within- and between-subject factors (e.g. boys vs. girls, producing /a/ and /i/ and /u/) • Covariates • factors that might have an effect on the within-subjects factor • Note: covariates can also be specified for between-subjects designs!

  15. Covariates: example • You want to study French skills when using 2 different text-books. Students are randomly assigned to 2 groups. If you have the IQ of these students, you can decrease the variability within the groups by using IQ as covariate • Problem: if the covariate is correlated with between-groups factor as well, F-value might get smaller (less significant)! • You can also assess interaction between covariates and between-groups factors (e.g. one textbook might be better suited for smart students)

  16. One-way repeated measures ANOVA in SPSS 1. Define new name and levels for within-subject factor 3 2

  17. One-way repeated measures ANOVA in SPSS • Factor-name • Four levels of the within-subjects variable • Enter between-subjects and covariates (if applicable)

  18. Post-hoc tests for within-subjects variables • SPSS does not allow you to do post-hoc tests for within-subjects variables • Instead do “Contrasts” and define them as “Repeated” 2 1

  19. Post-hoc tests for within-subjects variables • You can also askfor a comparsonof means

  20. SPSS output: test of Sphericity • Test for homgeneity of covariances among scores of within-subjecs factors • Only calculated if variable has more than 2 levels If test is significant, you have to reject the null-hypothesis that the variances are homogenious

  21. SPSS output: within-subjects contrasts • Post-hoc test for within-subjects variables

  22. 3 x 3 designs • 3 x 3 between subjects

  23. 3 x 3 designs • 3 x 3 within subjects Group1 Group1 Group1 Group1 Group1 Group1 Group1 Group1

  24. 3 x 3 designs • 3 x 3 mixed design Group1 Group1 Group2 Group2 Group2 Group3 Group3 Group3

  25. Data transformation • If you want to caculate an ANOVA but your interval data is not normally distributed (i.e. skewed) you can use mathematical transformations • The type of transformation depends on the shape of the sample distribution • NOTE: • After transforming data, check the resulting distribution again for normality! • Note that your data becomes ordinal by transforming it!! (but you can do an ANOVA with it)

  26. Transformation e.g.f(x) = log(x)f(x) = atan(x) e.g.f(x) = x1.5 What kind of tranformation?

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