1. DATA VISUALIZATION UNIVARIATE (no review- self study) STEM & LEAF BOXPLOT BIVARIATE SCATTERPLOT (review correlation) Overlays; jittering Regression line overlay (see ASA website: http://nlvm.usu.edu/en/nav/frames_asid_144_g_4_t_5.html?open=activities

2. DATA VISUALIZATION TOPICS GRAPHICAL DISPLAYS UNIVARIATE BIVARIATE ASSUMPTIONS OF MULTIPLE REGRESSION LINEARITY HOMOSCEDASTICITY ERROR INDEPENDENCE NORMALITY FIXING VIOLATIONS

3. GRAPHICAL DISPLAYS Frequency Histogram: –SPSS ANALYZE: Descriptive Statistics: Explore: Plot: Stem and Leaf –SPSS GRAPH: Boxplot (normal curve overlay available or INTERACTIVE: Boxplot or Analyze: Frequencies – SPSS GRAPH: Histogram or Interactive: Histogram # “bins” = 1 + log 2 (N) Example: N= 500; #bins = 1+ 9 = 10 Log 2 (512) = 9 (eg., 2x2x2x2x2x2x2x2x2=512)

4. ANXIETY Stem-and-Leaf Plot Frequency Stem & Leaf.00 3. 22.00 3. 4444444444455555555555 35.00 3. 66666666777777777777777777777777777 7.00 3. 9999999 39.00 4. 000000000000000000000000011111111111111 22.00 4. 2222222222222222222222 26.00 4. 44455555555555555555555555 22.00 4. 6666666667777777777777 26.00 4. 88888888888999999999999999 12.00 5. 111111111111 26.00 5. 22222222222222222223333333 14.00 5. 44444444444444 24.00 5. 666666777777777777777777 31.00 5. 8888888888888999999999999999999 28.00 6. 1111111111111111111111111111 6.00 6. 333333 15.00 6. 444444444444444 24.00 6. 666666666666666666666666 14.00 6. 88888899999999 Stem width: 10 Each leaf: 1 case(s)

8. GRAPHICAL DISPLAYS Kernel Smoothing –SPSS Graph: INTERACTIVE: Line: Dots and Lines: Spline or Lagrange 3 rd and 5 th order fits – does not give you the smoother options (available for bivariate scatterplots- see later slides)

11. Bivariate Displays Scatterplots –Interval data –Category by interval- jittering –Regression fits- lowess lines Scatterplot Matrices

12. Interval Scatterplot: SPSS Graphics: Interactive: Scatterplot: Fit: Method:Smoother No Smootherwith Normal Smoother

13. Interval Scatterplot: SPSS Graphics: Interactive: Scatterplot: Fit: Method:Smoother with Uniform Smoother

14. Category X-axis: without and with jittering (adding normal random deviate with SD=.15 for sex)

15. Jittering Basic idea- when looking at displays for two or more groups, it is hard to tell where data lie due to overlaying of points in most plot programs, so Add a small random score to each “group” score –For example, for males (score 1) and females (score 2), add a random number with std dev. of say.1 to each male and female score

16. Jittering The result is a spreading out of all scores around the Male or Female column in a scatterplot: Male=1Female=2 Y.

17. DATA VISUALIZATION BIVARIATE Loess lines: in SPSS an option under GRAPH/ Interactive / Scatterplot labeled “FIT” with METHOD = SMOOTHER The Bandwidth multiplier has a 1.0 default; a smaller value will create more bumps or curves in the overall curve

18. GRAPH/INTERACTIVE/SCATTERPLOT/FIT/BANDWIDTH=1.0