1. Ogive, Stem and Leaf plot & Crosstabulation

2. Ogive n An ogive is a graph of a cumulative distribution.. n The data values are shown on the horizontal axis. n Shown on the vertical axis are the: cumulative frequencies, or cumulative relative frequencies, or cumulative percent frequencies

3. Ogive The frequency (one of the above) of each class is plotted as a point. The plotted points are connected by straight lines.

4. Parts Parts Cost ($) Parts Parts Cost ($) 20 40 60 80 100 Cumulative Percent Frequency 50 60 70 80 90 100 110 (89.5, 76) Ogive with Cumulative Percent Frequencies Cumulative Percent Frequencies Example of an Ogive

5. Stem and Leaf Plots 1. Sort data *** 2. Round data (if necessary) 3. Create TWO new columns (stem and leaf) 4. Put “stem” in one column and “leaves” in another. 5. Format the leaves column to be left-aligned.

6. What we have done Summary of variables  Qualitative: Numeric: Frequency, relative frequency, percentage frequency, cumulative frequency, cumulative relative frequency, cumulative Percentage Graphical: Bar (column) chart, pie chart

7. What we have done II  Quantitative: Numeric: Frequency, relative frequency, percentage frequency, cumulative frequency, cumulative relative frequency, cumulative Percentage Graphical: histogram, stem and leaf, Ogive, boxplot

8. Another thing of interest to statisticians Relationship between variables  Variables: Quantitative Qualitative

9. Relationship between variables Qualitative vs. qualitative: Crosstabulation Qualitative vs. quantitative: ANOVA etc. Quantitative vs. quantitative: Regression etc.

10. Example of Crosstab Sum of countfactor b factor a12345Grand Total 11020363251149 26987523212252 31462325383244 46991922025297 Grand Total162260212137171942

11. What crosstab tells us? Cross Tabs: a tabular summary of data for two variables Marginal Distributions/Probabilities: totals/probabilities in the margins of the cross tabulation.

12. An example that makes more sense Sum of CountWin Ginobli Played N YTotal N162238 Y123244 Total285482

13. Marginal Distributions Ginobli’s game play distribution  Played: 44; Missed: 38 Spurs’ season breakdown  Win: 54; Lose: 28

14. Marginal Probabilities Ginobli’s chance of playing: 44/82 Spurs’ winning percentage: 54/82 Row (column ) total / grand total

15. Some other Probabilities Conditional Probability Spurs’ winning percentage when Ginobli played. 32/44 Cell count / row (column ) total Joint Probability: cell count /grand total E.g. The percentage of games that Spurs won and Ginobli played.

16. Crosstab

17. Example cont.

18. Components of the table Column1Column2Column3Total Row 1Cell count Row 1 total Row 2Cell count Row 2 total Row 3Cell count Row 3 total Total Column 1 total Grand Total

19. Probabilities From Crosstab Marginal, joint and conditional Marginal probability  row(column) total/grand total Joint probability  cell count / grand total Conditional probability  Cell count / row (column) total

20. What is the percentage of all patients who received a CHEAP positive test result? Is this a joint, marginal, or conditional percentage? Marginal: 37.0%

21. Out of all the patients given the CHEAP test, what is the percentage of false negatives? Is this a joint, marginal, or conditional percentage? Joint, 2% (this is where CHEAP is negative, but Actual SFI is positive)

22. What is the percentage of subjects diagnosed as positive by BOTH tests? Is this a joint, marginal, or conditional percentage? Joint: 30%.

23. What is the percentage of correct diagnosis? =(30+61)/100 = 91% That is correct diagnosis of positive AND negative.

24. If someone gets the test result and it is “positive”, what is the chance that this person really has the disease. 30/37=81% (conditional) That means there is still 19% chance that this person does not have the disease.

25. Check this one out! Homicide convictions in the state of Florida between 1976 and 1980. Did convicted person get death sentence? Is there a racial bias? YESNOTotal (% YES) White 3930834711.2% Black 323453778.5% Total 716537249.8%

26. The other side of the story ii. Table for those cases involving white victims YESNOTotal (% YES) White 3927931812.3% Black 2912115019.3% Total 6840046814.5%

27. The other side of the story i. Table for those cases involving black victims YESNOTotal (% YES) White029 0% Black32242271.3% Total32532561.2%

28. This is what we call Simpson’s Paradox in statistics Simpson’s paradox refers to the reversal in the direction of an X versus Y relationship when controlling for a third variable Z.

29. Another Example Numbers of flights on time and delayed for two airlines at five airports in June 1991. Alaska AirlineAmerican West Airline On TimeDelayedDelay %On TimeDelayedDelay % 372450113.3%643878710.9%

30. Another Example (contd) Alaska Airline American West Airline On Time Delay ed Delay % On Time Delay ed Delay % L.A.4976211.1%69411714.4% Phoenix221125.4%48404157.9% San Diego212208.6%3836514.5% San Francisco50310216.9%32012928.7% Seattle 184130514.2 % 2016123.3%