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Correlational analysis

Correlational analysis. Scatterplot. Correlational tests. Correlation coefficient + effect size. Beispiel: MLU & Age. Beispiel: MLU & Age.

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Correlational analysis

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  1. Correlational analysis

  2. Scatterplot

  3. Correlational tests

  4. Correlation coefficient + effect size

  5. Beispiel: MLU & Age

  6. Beispiel: MLU & Age Long: There is an association between age and MLU. The r of .887 showed that 78.6% (r2) of the variation in MLU was accounted for by the variation in age. The associated probability level of 0.001 showed that such a result is unlikely to have arisen from sampling error. Short: As can be seen in the table above, there is a strong correlation between age and MLU (r = .887, p = .001).

  7. Beispiel: Typicality & Frequency

  8. Beispiel: Typicality & Frequency Kendall’s tau ( = .733, p = .003)Spearman’s rho (rs = .879, p = .001)

  9. Partial correlation Phoneme & Silben r = .898, p = .001Phoneme & Häufigkeit r = .795, p = .006Silben & Häufigkeit r = .677, p = .031 Phoneme & Häufigkeit r = .578, p = .103(Silben Konstant)

  10. Nominal Daten Es gibt eine signifikante Korrelation zwischen Geschlecht (Boys vs. Girls) und der Präferenz für ein bestimmtes Spielzeug (mechanisch vs. nicht-mechanisch) (χ2 = 49,09, df = 2, p = .001). Phi-Koeffizient  = .70, p < .001Cramer’s V = .70, p < .001

  11. Regression

  12. Correlation - Regression Correlational analysis gives us a measure that represents how closely the data points are associated. Regression analysis measures the effect of the predictor variable x on the criterion y. – How much does y change if you change x. A correlational analysis is purely descriptive, whereas a regression analysis allows us to make predictions.

  13. Types of regression analysis

  14. Types of regression analysis

  15. Types of regression analysis

  16. Line-of-best-fit

  17. Linear Regression y = bx + a y = variable to be predictedx = given value on the variable xb = value of the slope of the line a = the intercept (or constant), which is the place where the line-of-best-fit intercepts the y-axis.

  18. Linear Regression Given a score of 20 on the x-axis, a slope of b = 2, and an interception point of a = 5, what is the predicted score? y = (2  20) + 5 = 45

  19. Beispiel: MLU & Age How much does MLU increase with growing age?

  20. Linear Regression There is s strong association between age and MLU (R = 0.887). Specifically, it was found that the children’s MLU increases by an average of .088 words each months (t = 6,069, p < 0.001), which amounts to about a word a year. Since the F-value (36,838, df = 1) is highly significant (p < 001), these results are unlikely to have arisen from sample error.

  21. Multiple Regression Several predictor variables influence the criterion. Plane-pf-best-fit 1. Simultaneous multiple regression2. Stepwise multiple regression

  22. Simultaneous Multiple Regression Eine Universität möchte wissen, welche Faktoren am besten dazu geeignet sind, den Lernerfolg ihrer Studenten vorherzusagen. Als Indikator für den Wissensstand der Studenten gilt die Punktzahl in einer zentralen Abschlussklausur. Als mögliche Faktoren werden in Betracht gezogen: (1) Punktzahl beim Eingangstest, (2) Alter, (3) IQ Test, (4) Punktzahl bei einem wissenschaftlichen Projekt.

  23. Simultaneous Multiple Regression Predictor entrance exam age IQ Scientific project Criterion final exam

  24. There is s strong association between the predictor variables and the result of the final exam (Multiple R = 0.875; F = 22,783, df = 4, p = .001 ). Together they account for 73% of the variation in the exam succes. If we look at the four predictor variables individually we find that the result of the entrance exam (B = .576, t = 5.431, p = .001) and the IQ score (B = .447, t = 4.606, p = .001) make the strongest contributions (i.e. they are the best predictors). The predictive value of age (B = .099, t = 5.431, p = .327 and the score on the scientific project is not significant (B = 0.141, t = 1,417, p = 0.168.).

  25. Stepwise Multiple Regression In stepwise regression you begin with one independent variable and add one by one. The order of addition is automatically determined by the effect of the independent variable on the dependent variable.

  26. Assumptions Multiple Regression 1. At least 15 cases 2. Interval data 3. Linear relationship between predictor variables and criterion. 4. No outliers (or delete them) 5. Predictor variables should be independent of each other

  27. Logistic Regression In Linguistics, you often use logistic regression: Multiple factors determine the choice of linguistic alternates:1. look up the number - look the number up2. that-complement clauses - zero-complement clause3. intial adverbial clause - final adverbial clause4. aspirate /t/ - unaspirated /t/ - glottal stop - flap

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