1. Distributions & Graphs

2. Variable Types Discrete (nominal) Discrete (nominal) Sex, race, football numbers Sex, race, football numbers Continuous (interval, ratio) Continuous (interval, ratio) Temperature, Test score, Reaction time Temperature, Test score, Reaction time

3. Frequency Distributions Graphic representation of data Graphic representation of data Easier to understand than raw numbers Easier to understand than raw numbers Helps communicate to others Helps communicate to others Basic kinds of frequency distributions Basic kinds of frequency distributions Ungrouped – simple tally Ungrouped – simple tally Grouped – used to simplify Grouped – used to simplify Uses Uses Relative and cumulative frequency Relative and cumulative frequency Shape Shape

4. Common of Graphs Bar Chart (discrete) Bar Chart (discrete) Histogram (continuous) Histogram (continuous) Scatterplot (2 variables) Scatterplot (2 variables)

5. Distribution Shapes Normal Normal Center Center Spread Spread Shoulders Shoulders Skew Skew There will be numerical ways to describe all these, but for now, just consider the shape visually.

6. Normal

7. Central Tendency

8. Variability (spread) Central tendency and Variability

9. Skew The tail!

10. Kurtosis - shoulders

11. Odd Shapes

12. Modern Stat Graphs Box plot Box plot Stem-leaf Stem-leaf

13. Boxplot Boxplot for a normal distribution Same distribution as a (sort of) histogram

14. Boxplot with outliers

15. Boxplot with Skewed Distribution

16. Exam and Course Distributions Psych Stats Fall 2007

17. Course Grades Sp 2008

18. Stem-leaf diagram Frequency Stem & Leaf 1.00 2. 0 2.00 3. 00 3.00 4. 000 4.00 5. 0000 3.00 6. 000 2.00 7. 00 1.00 8. 0 Stem width: 1.00 Each leaf: 1 case(s) (Approximately) Normal distribution

19. Stem-leaf of volcano heights Frequency Stem & Leaf 8.00 0. 25666789 8.00 1. 01367799 23.00 2. 00011222444556667788999 21.00 3. 011224445555566677899 21.00 4. 011123333344678899999 24.00 5. 001122234455666666677799 18.00 6. 001144556666777889 26.00 7. 00000011112233455556678889 12.00 8. 122223335679 14.00 9. 00012334455679 13.00 10. 0112233445689 10.00 11. 0112334669 9.00 12. 111234456 5.00 13. 03478 2.00 14. 00 3.00 15. 667 2.00 16. 25 2.00 17. 29 6.00 Extremes (>=18500) Stem width: 1000.00 Each leaf: 1 case(s)

20. Final Grade Pct Sp 08 TotPct08 Stem-and-Leaf Plot Frequency Stem & Leaf 12.00 Extremes (=<.48) 3.00 5. 669 12.00 6. 011333344444 18.00 6. 555566677777889999 28.00 7. 0000111122222223333333444444 34.00 7. 5555555566666667777777888888889999 29.00 8. 00000111111112222223333344444 13.00 8. 5555566667788 16.00 9. 0000011111123344 3.00 9. 566 Stem width:.10 Each leaf: 1 case(s) Note that SPSS has the boxplot with larger numbers at the top, but the stem-leaf shows larger numbers at the BOTTOM, so one is backwards from the other.

21. Definition Political party is an example of what kind of variable? Political party is an example of what kind of variable? 1 continuous 1 continuous 2 discrete 2 discrete 3 intensity 3 intensity 4 objective 4 objective

22. Definition A distribution with a long tail to the right (high) end is called ________ A distribution with a long tail to the right (high) end is called ________ 1 leptokurtic 1 leptokurtic 2 negatively skewed 2 negatively skewed 3 platykurtic 3 platykurtic 4 positively skewed 4 positively skewed

23. Graphs Which boxplot shows a skewed distribution? Which boxplot shows a skewed distribution? 1 2 3 4

24. Discussion Question When might you prefer a graph to a table of numbers for presenting a result? When might you prefer a graph to a table of numbers for presenting a result? Name a variable you think would be interesting for college students to see as a graph. What kind of data would you put in the graph? Why would it be of interest? Name a variable you think would be interesting for college students to see as a graph. What kind of data would you put in the graph? Why would it be of interest?