Team Bivariate

1. Team Bivariate • Chris Bulock • Michael Mackavoy • Jennifer Masunaga • Ann Pan • Joe Pozdol

2. Independent vs. Dependent • Independent: The variable manipulated or presumed to affect a dependent variable. • Alternatively known as a predictor or experimental variable. • Dependent: The variable that changes in response to the independent variable. • Also known as outcome or subject variable.

3. Example • Hypothesis: The more library instruction a college student receives, the more he or she will use the library. • Independent Variable: Quantity of Instruction • Dependent Variable: Usage of the library

4. Hypothesis Testing • Null Hypothesis (Ho): A hypothesis set up to be nullified or refuted in order to support an alternative hypothesis. • Alternative Hypothesis (HA or H1): The hypothesis supported if the null is rejected • Alpha Level (α) and P-Values

5. Hypothesis: The more library instruction a college student receives, the more he or she will use the library. • What is the Null Hypothesis? • What is the Alternative Hypothesis? • If p is smaller than the α level, then the data is said to be “statistically significant.”

6. Kurtosis, Skewness(and other weird sounding words) • Kurtosis refers to the peakedness or flatness of a frequency distribution.

7. Skewness • Skewness describes data as symmetrical or asymmetrical about a central point.

8. Linear Regression • Analysis technique which predicts one variable from another, with the regression line being the best fit straight line drawn through paired points • Independent (X-axis) and dependent (Y-axis) variables • Slope may be negative, positive, or 0

9. Samples of Scatter Diagrams and Variable Relationships:

10. Correlation • How strongly one variable predicts another • Numerous methods for calculation of correlation coefficient • Relationship can be direct or inverse • Correlation coefficient holds a value of r = -1.00 to r = +1.00

11. Measurement of Correlation Coefficients • Parametric (used in interval/ratio data measurement) • Nonparametric (for ordinal or nominal data measurement) • Usage of parametric tests requires satisfaction of certain conditions

12. Pearson Correlation • Parametric method for calculation of coefficient of correlation (requires interval or ratio data) • r= n∑XY-∑X∑Y_________ √{[n∑X2 – (∑X)2] [n∑Y2 – (∑Y)2]} From r can calculate r2, which is the coefficient of determination, in order to determine proportion of variation in the dependent variable explained by variation in the independent variable

13. Pearson Correlation • Important to remember Pearson coefficient(r) or Pearson coefficient of determination (r2) does not indicate causation. Instead, provides statistical evidence for a relationship between the variables.

14. Nonparametric methods • Used for data expressed in ordinal or nominal scale measurements • Spearman rank order correlation coefficient, rs (uses ordinal scale data and assumes n ranked pairs) • rs tells the strength of the relationship between two variables that are measured on ordinal scales

15. Chi-squared (X^2) Test Nonparametric test (or parametric if normal distribution) Used for 2 nominal or ordinal variables (or continuous) Used for small samples, but minimum size required Tests if relationship between 2 variables Column percents show nature of relationship

16. Research question Does gender influence library type preference? Gender: male or female Library type: academic, corporate, public Independent variable? Dependent variable? Null hypothesis? Alternative hypothesis?

17. Collect data and construct table Poll class Make contingency table Calculate row and column marginals Calculate expected frequencies

18. Calculate X^2 Check that expected frequencies are >5 (Modify if necessary to illustrate) X^2 = Σ (O-E)^2 / E

19. Determine degrees of freedom For X^2, degrees of freedom = (#rows - 1) (#columns - 1)

20. 0.10 0.05 0.025 0.01 0.005 1 2.706 3.841 5.024 6.635 7.879 2 4.605 5.991 7.378 9.210 10.597 3 6.251 7.815 9.348 11.345 12.838 4 7.779 9.488 11.143 13.277 14.860 5 9.236 11.070 12.833 15.086 16.750 Are variables related? Compare calculated X^2 to critical value in table p-value d.f.

21. “Online Workplace Training in Libraries” By Connie K Haley Focused on the preference for online training versus traditional face-to-face training Purpose of the study is to reveal the relationships between variables and preference for online or traditional face-to-face training

22. “Online Workplace Training in Libraries” Aims to reveal the relationship between preference for training and variables such as: Gender, age, education level, years of experience, training locations, training providers, and professional development policies

23. Methodology The study took pace over a twenty-day period from April 10 to April 30 of 2006. Library employees were sent online survey questionnaires The surveys were anonymous and confidential Consisted of three parts: demographic variables, Likert-scale assessment of training preferences, and open-ended questions

24. Assumptions Expectations included: Younger employees would prefer online training, while older ones would prefer face-to-face training; Highly educated employees would prefer online training, while less educated employees with fewer skills would prefer face-to-face training; Employees with more library training would prefer online training while those with less experience would prefer face-to-face training

25. correlation to training providers and training locations Findings Preference for online training shows a correlation to training providers and training locations The preference for online training was not associated with ethnicity, gender, age, education, or library experience Training budgets and professional development policies were not related to the preference for online training

26. Advantages of bivariate models • Quantitative goals: • Relationships • Prediction • Causality • Simplification • Core Relationship • Parsimony

27. Disadvantages of bivariate models • Over-simplification • Many related variables • Picking the right pair • False relationships • May overlook the true relationship • Poor definitions

28. Bivariate models: when to use • Simple situations • Interested in single relationship • or • Get a handle on complex situation • Initial study