1. Chapter 9 Describing Variations in Data

2. A variable is…  A single characteristic that can vary and can be measured  Medical Variables:  Biological Differences  Presence, Absence & Stage of Disease  Conditions of Measurement  Techniques of Measurement  Measurement Error

3. How to Interpret Data The Decision Factor  Decide if data is “quantitative” or “qualitative”  Identify any variable which may affect data usage

4. Types of Variables  Nominal:  “the name game”, classifying in a non- numerical way. Ex: Male/Female; Yes/No; A,B,AB,O (BLOOD TYPES)  Each classification can be given a numerical data code or point for ease of statistical inference. Example: Male = 1; Female = 2.

5. 1.00 = Male 2.00 = Female 3.00 = Unknown

6. Types continued…  Dichotomous or Binary Variable:  Variables that reflect two extreme opposites  Example: Living/Dead  Dichotomous and nominal variables are also called “discrete variables” because the categories are different from one another

7. Variables, continued  Ordinal Variables:  Ranked variables that follow an order.  Example: Surveys that ask participants to rank answers/opinions as “very satisfied”; “satisfied” and “not satisfied”  Continuous (Dimensional) Variables:  Measurements which may reflect a continuous line of data.  Example: Height, Weight, Blood Pressure, other readings that can change regularly

8. Ratio Variables: - A continuous scale in which “0” has a meaning  Fahrenheit/Celsius Scale  Centrigrade Scale Both pictures are taken from google images.com

9. Methods of Documenting Observations  Frequency Table  Consists of a x and y axis and is used to show two characteristics that relate to one another  X Axis = Scores  Y Axis = Frequency of each score ScoreFrequency Below 754 76 - 8014 81 - 852 86 - 908 91 - 955 96 - 1001

10. Taken from google images

11. Combining Data  The grouping of similar values together in order to simplify examination of the data  Of the two sets of birth weights of babies at Cabbage Patch Hospital which is easier to decipher?  1-3 pounds = 10  4-6 pounds = 45  7-9 pounds = 25  10-12 pounds = 12  13+ pounds = 8 2,11,13,14,16,12,10,7,6,8,2, 6,1,12,11,10,9,4,7,2,9,1,8 7,2,6,1,8,7,6,5,6,3,5,2,4,1 2,13

12. Frequency Distribution  Recording observations of one variable by using X Axis for variable and Y Axis for the frequency of occurrence  Look at Table 9-2 and 9-3 (pp. 142, 143)  Which has more interpretive meaning to you?  Why?

13. Gaussian Distribution  Also Known as “normal distribution”  Real data seldom follows this slope  The larger the data, the more Gaussian or “bell shaped” it would look Images taken from google images.com

14. Types of Visual Representation  Histogram: A bar graph of vertical bars. The area of the bars represent proportions of all observations that fall within range of the bar  Frequency Polygon: This is a histogram minus the bars which are replaced by dots which are then connected Histogram of Smokers Images taken from google images.com

15. Measurements  Mode: Most commonly seen value in a group of measurements  Example:  6 9 6 8 10 6 4 4 8 11 6 10  The mode is 6  Median: Middle observation of a data group is derived by putting numbers in order and finding the center number. If there are an even amount of data points, take the middle two and take an average.

16. Median continued…  Example:  1 4 9 20 23 27 31 48 56 58  23 + 27/2 = 25  Mean: The average of a group of data points (add all numbers then divide by the number of numbers) Example: Using the numbers above the mean is 27.7

17. Your Turn (time limit: 5 minutes)  Compute the Mode, Median and Mean of the following monthly glucose readings for Fred:  Jan = 120July = 98  Feb = 100Aug = 127  Mar = 110Sept = 134  April = 128Oct = 141  May = 138Nov = 128  June = 121Dec = 146

18. Answer  Mode = 128  Median = 127.5  Mean = 124.5

19. Questions…

20. Homework Time  This chapter covered a great deal, so…  Please re-read the remainder of the chapter beginning with page 149 – “Problems in analyzing a Frequency Distribution.  This information is a review/continuance of what we have covered tonight  Please drop me an e-mail after you have re-read this area and indicate if you have any further questions or if you are in complete understanding of the information.

21. Any Further Questions