2. 1 Frequency Distributions & Graphing

3. Nomenclature  Frequency: number of cases or subjects or occurrences  represented with f  i.e. f = 12 for a score of 25  12 occurrences of 25 in the sample 1

4. Nomenclature  Percentage: number of cases or subjects or occurrences expressed per 100  represented with P or %  So, if f = 12 for a score of 25 when n = 25, then...  % = 12/25*100 = 48% 1

5. Caveat (Warning)  Should report the f when presenting percentages  i.e. 80% of the elementary students came from a family with an income < $25,000  different interpretation if n = 5 compared to n = 100  report in literature as  f = 4 (80%) OR  80% (f = 4) OR 80% (n = 4) 1

6. Frequency Distribution of Test Scores  40 items on exam  Most students >34  skewed (more scores at one end of the scale)  Cumulative Percentage: how many subjects in and below a given score 1 234

7. Eyeball check of data: intro to graphing with SPSS  Stem and Leaf Plot: quick viewing of data distribution  Boxplot: visual representation of many of the descriptive statistics discussed last week  Bar Chart: frequency of all cases  Histogram: malleable bar chart  Scatterplot: displays all cases based on two values of interest (X & Y)  Note: compare to our previous discussion of distributions (normal, positively skewed, etc…) 1 2

8. Frequency Stem & Leaf 2.00 Extremes (=<25.0) 2.0028. 00 2.0029. 00 1.0030. 0 1.0031. 0 3.0032. 000 1.0033. 0 6.0034. 000000 3.0035. 000 4.0036. 0000 8.0037. 00000000 Stem width: 1 Each leaf: 1 case Stem and Leaf (SPSS: Explore command)  Fast look at shape of distribution  shows f numerically & graphically  stem is value, leaf is f 1 2 3 4

9. 225 345 41166679 5449 60 Stem and Leaf Plots  Another way of doing a stemplot  Babe Ruth’s home runs in each of 14 seasons with the NY Yankees  54, 59, 35, 41, 46, 25, 47, 60, 54, 46, 49, 46, 41, 34, 22 12 3

10. 0 1 2 25 3 45 4 1166679 5 449 6 0 Stem and Leaf Plots  Back-to-back stem plots allow you to visualize two data sets at the same time  Babe Ruth vs. Roger Maris 8 643 863 93 1 Maris Ruth 1

11. Boxplots Maximum Q3 Median Q1 Minimum Note: we can also do side- by-side boxplots for a visual comparison of data sets 1

12. X axis (abcissa) Individual scores/categories Y axis (ordinate) f Format of Bar Chart 1

13. Test score data as Bar Chart Note only scores with non-zero frequencies are included. 1

14. Bar chart in PASW  Using the height file on the web 1 2 3

15. Bar chart in SPSS  Gives… 1 2

16. Bar chart in PASW  Note you can use the same command for pie charts and histograms (next) 1

17. Format of Histogram Can be manipulated X axis (abcissa) Groups of scores/categories Y axis (ordinate) f Now the X-axis is groups of scores, rather than individual scores – gives a better idea of the distribution underlying the data. 1

18. Test score data as Histogram 1

19. Test score data as revised Histogram With an altered number of groups, you might get a better idea of the distribution 1

20. Scatterplot  Quick way to visualize the data & see trends, patterns, etc…  This plot visually shows the relationship between undergrad GPA and GRE scores for applicants to our program 1 2 3 4

21. Scatterplot  Here’s the relationship between undergrad GPA (admitgpa) and GPA in our program 1

22. Scatterplot  Finally, here’s the relationship between GRE scores and GPA in our program 1

23. Scatterplot in PASW  Use graphs_scatter/Dot 1

24. Scatterplot in PASW  Choose “simple scatter” 1

25. Scatterplot in PASW  Choose the variables (here I’ve used a 3 rd variable too – you’ll see why in a moment) 1

26. Scatterplot in PASW As you can see, there are rather different values for males and females 1

27. Bottom line  First step should always be to plot the data and eyeball it...following is an example of what can happen when you do. 1

28. low high $$ amount Expected distribution of agent-paid claims (State Farm) One use of Frequency Distribution & Skewness 1

29. low high $$ amount f Observed distribution of an agent-paid claims (hmmm…) One use of Frequency Distribution & Skewness 1 2 3