2. Public Health Methodologies Biostatistics2/4/2012 Dr. Riaz A. Bhutto 2
3. Ratio• is a relationship between two numbers of the same kind (e.g., objects, persons, students, spoonful s, units of whatever identical dimension)• usually expressed as "a to b" or a:b• For example, suppose I have 10 pairs of socks for every pair of shoes then the ratio of shoes:socks would be 1:10 and the ratio of socks:shoes would be 10:12/4/2012 Dr. Riaz A. Bhutto 3
4. Coefficient of variation• Is the ratio of the standard deviation to the mean• Used to compare the relative variation or spread of the distribution of different series, samples, or population; or the different characteristics of a single series• Expressed in percentage SD CV (%) = -------- X 100 __ X2/4/2012 Dr. Riaz A. Bhutto 4
5. Example• In a medical college, the mean weight of 100 medical students is 140 lbs, with S.D of 28 lbs. The mean height of these students is 66”, with S.D of 6”• CV for weight = 28/140 x 100 = 20% CV for height = 6/66 x 100 = 9%• Based on the CV, therefore, the relative spread of weight among the students is greater than that of height2/4/2012 Dr. Riaz A. Bhutto 5
6. Percentile• Are the points which divide all measurements/value into 100 equal parts• In statistics, a percentile (or centile) is the value of a variable below which a certain percent of observations fall.• For example, the 20th percentile is the value (or score) below which 20 percent of the observations may be found.2/4/2012 Dr. Riaz A. Bhutto 6
7. • The 25th percentile is also known as the first quartile (Q1), the 50th percentile as the median or second quartile (Q2), and the 75th percentile as the third quartile (Q3).2/4/2012 Dr. Riaz A. Bhutto 7
8. Normal Distribution• Data can be "distributed" (spread out) in different ways.• It can be spread out more on the left ... or more on the right• Or it can be all jumbled up2/4/2012 Dr. Riaz A. Bhutto 8
9. A Normal DistributionBut there are many cases where the data tends to be around a central value withno bias left or right, and it gets close to a "Normal Distribution" like this: The "Bell Curve" is a Normal Distribution. It is often called a "Bell Curve" because it looks like a bell. 2/4/2012 Dr. Riaz A. Bhutto 9
10. Many things closely follow a Normal Distribution: Heights of people Size of things produced by machines Errors in measurements Blood pressure Marks on a test We say the data is "normally distributed".2/4/2012 Dr. Riaz A. Bhutto 10
11. The Normal Distribution has: mean = median = mode symmetry about the center 50% of values less than the mean and 50% greater than the mean2/4/2012 Dr. Riaz A. Bhutto 11
12. 68% of values are within 1 standard deviation of the mean 95% are within 2 standard deviations 99.7% are within 3 standard deviations2/4/2012 Dr. Riaz A. Bhutto 12
13. Example: 95% of students at school are between 1.1m and 1.7m tall.Assuming this data is normally distributed can you calculate the mean and standarddeviation?The mean is halfway between 1.1m and 1.7m: Mean = (1.1m + 1.7m) / 2 = 1.4m 95% is 2 standard deviations either side of the mean (a total of 4 standard deviations) so: 1 standard deviation = (1.7m-1.1m) / 4 = 0.6m / 4 = 0.15m And this is the result: It is good to know the standard deviation, because we can say that any value is: likely to be within 1 standard deviation (68 out of 100 will be) very likely to be within 2 standard deviations (95 out of 100 will be) almost certainly within 3 standard Riaz A. Bhutto (997 out of 1000 will be) 2/4/2012 Dr. deviations 13
14. Standard Scores The number of standard deviations from the mean is also called the "Standard Score", "sigma" or "z-score". Get used to those words!Example: In that same school one of your friends is 1.85m tallYou can see on the bell curve that 1.85m is 3standard deviations from the mean of 1.4, so:Your friends height has a "z-score" of 3.0It is also possible to calculate how manystandard deviations 1.85 is from the meanHow far is 1.85 from the mean?It is 1.85 - 1.4 = 0.45m from the meanHow many standard deviations is that? Thestandard deviation is 0.15m, so:0.45m / 0.15m = 3 standard deviations 2/4/2012 Dr. Riaz A. Bhutto 14
15. So to convert a value to a Standard Score ("z-score"): •first subtract the mean, •then divide by the Standard Deviation And doing that is called "Standardizing": You can take any Normal Distribution and convert it to The Standard Normal Distribution.2/4/2012 Dr. Riaz A. Bhutto 15
16. Presentation of DataMethods• Tables• Charts and Graphs• Diagrams2/4/2012 Dr. Riaz A. Bhutto 16
17. Tables• Simple tables• Frequency Distribution table• Cumulative Frequency table• Relative Frequency table2/4/2012 Dr. Riaz A. Bhutto 17
18. Frequency Distribution Rating Frequency Poor 2 Below Average 3 Average 5 Above Average 9 Excellent 1 Total 20
19. Relative Frequency andPercent Frequency Distributions Relative Percent Rating Frequency Frequency Poor .10 10 Below Average .15 15 Average .25 25 .10(100) = 10 Above Average .45 45 Excellent .05 5 Total 1.00 100 1/20 = .05
20. Tabulating Numerical Data: Cumulative Frequency Data in ordered array:12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58 Cumulative Cumulative Class Frequency % Frequency 10 but under 20 3 15 20 but under 30 9 45 30 but under 40 14 70 40 but under 50 18 90 50 but under 60 20 100
21. Tabulating Numerical Data: Frequency Distributions (continued) Data in ordered array: 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58 Relative Class Frequency Frequency Percentage10 but under 20 3 .15 1520 but under 30 6 .30 3030 but under 40 5 .25 2540 but under 50 4 .20 2050 but under 60 2 .10 10Total 20 1 100
22. Charts and Graphs Bar Charts (for presentation of categorical data)• Simple• Multiple• Component Pie Charts / graph (for presentation of categorical data) Dot frequency graphs2/4/2012 Dr. Riaz A. Bhutto 22
23. Good? Bar GraphBad? Quality Ratings 10 9 8 7 Frequency 6 5 4 3 2 1 Rating Poor Below Average Above Excellent Average Average
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26. Pie Chart Most common way of presenting the categorical data. The value of each category is divided by the 360° and then each category is allocated the respective angles to present the proportion it has.2/4/2012 Dr. Riaz A. Bhutto 26
27. Dot Frequency Plot Tune-up Parts Cost . . .. . . . . . .. ..... .......... .. . .. . . ... . ... . .. .. .. .. .50 60 70 80 90 100 110 Cost (Rs.) Not used much anymore. Common when graphical drawing tools were primitive.
28. Diagrams• Histogram (for presentation of continuous data)• Frequency polygon• Line diagram• Pictogram (are a form of bar charts)• Scatter diagram (shows the relationship between two variables)2/4/2012 Dr. Riaz A. Bhutto 28
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