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Bivariate Description

Bivariate Description. Heibatollah Baghi, and Mastee Badii. OBJECTI VES. Define bivariate and univariate statistical tests. Explain when to use correlational techniques to answer research questions. Understand measure of Pearson Product Moment Correlation Coefficient (Pearson’s r).

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Bivariate Description

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  1. Bivariate Description Heibatollah Baghi, and Mastee Badii

  2. OBJECTI VES • Define bivariate and univariate statistical tests. • Explain when to use correlational techniques to answer research questions. • Understand measure of Pearson Product Moment Correlation Coefficient (Pearson’s r).

  3. Definitions • Univariate: examination of variable’s frequency distribution, central tendency, and variability. • Bivariate: examination of two variables simultaneously. • Is SES related to intelligence? • Do SAT scores have anything to do with how well one does in college? • The question is: do these variables correlate or covary?

  4. Typical Situations • Two nominal variables • Gender and readmission status • A nominal and interval/ratio variables • Delivery type and weight of child • Bed rest and weight gain during pregnancy • Two interval ratio variables • Respiratory function and extent of anxiety

  5. Cross Tabulation • Describes relationship between two nominal variables • Two dimensional frequency distribution Also appropriate if either or both variables are ordinal-level with a small number of categories

  6. Elements of Cross Tabulation Column Row

  7. Elements of Cross Tabulation Cell count Row % Column % Total %

  8. Elements of Cross Tabulation Marginal Joint distribution Marginal

  9. Group Mean Comparison • Describes a nominal variable and an interval/ratio variable

  10. Linear Association • The correlation coefficient is a bivariate statistic that measures the degree of linear association between two interval/ratio level variables. (Pearson Product Moment Correlation Coefficient)

  11. Scatter plot • Reveals the presence of association between two variables. The stronger the relationship, the more the data points cluster along an imaginary line. • Indicates the direction of the relationship. • Reveals the presence of outliers.

  12. Scatter Plot of Positively Correlated Data

  13. Scatter Plot of Negatively Correlated Data

  14. Scatter Plot of Non Linear Data

  15. Scatter Plot of Uncorrelated Data

  16. Covariance Formula

  17. Covariance of X & Y Standard Deviation of X Standard Deviation of Y Correlation Formula

  18. Example Data

  19. Calculation of Covariance & Correlation

  20. Correlations in SPSS

  21. Limitation of the Covariance It is metric-dependent

  22. Properties of Pearson r • r is metric-independent • r reflects the direction of the relationship • r reflects the magnitude of the relationship

  23. What does positive correlation mean? • Scores above the mean on X tend to be associated with scores above the mean on Y • Scores below the mean on X tend to be accompanied by scores below the mean of Y • Note for this reason deviation score is an important part of Covariance

  24. What does negative correlation mean? • Scores above the mean on X tend to be associated with scores below the mean on Y • Scores below the mean on X tend to be accompanied by scores above the mean of Y.

  25. Strength of association r2 = Coefficient of determination 1 – r2 = Coefficient of non-determination

  26. Analysis of Relationships

  27. Take Home Lessons • Always make a scatter plot • See the data first • Examining the scatter plot is not enough • A single number can represent the degree and direction of the linear relation between two variables

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