15. descriptive statistics
- 1. Descriptive Statistics Dr. A.P. Kulkarni
- 2. Necessity Required for inference Meaningful reduction Raw data reduced Depends on variable Availability of software
- 3. What descriptive stats? Rate • Numerator, denominator & multiplier • Has reference period (Usually year) • Example: Crude birth rate, Crude death rate CBR • Numerator: Live births • Denominator: MYP • Multiplier: 1000 • Reference period: Year
- 4. What descriptive stats? Ratio • Mathematical relation of numerator with denominator • Denominator does not include numerator • Example: A / B • B does not include A • May have multiplier Example • Sex ratio • F * 1000/M
- 5. What descriptive stats? Proportion • Relation of numerator with denomianator • Denominator includes numerator • Example: A/(A+B) • May have multiplier Cure rate • Cured *100 / (Cured +Not cured) Case Fatality Rate Died *100/ (Died + Survived)
- 6. What descriptive stats? Nominal & Ordinal • Count • Proportion (%) Interval & Ratio • Minimum • Maximum • Centering Const • SD • Percentiles • Box-plot
- 7. What descriptive stats? Nominal & Ordinal Count • Absolute number of individuals with/ without characteristic of interest Example Number of individuals cured / not cured Number of males/ females Display Table, Graph
- 8. What descriptive stats? Interval / ratio scale Minimum & Maximum • Minimum / Maximum value Example • Minimum & maximum height in the group • Used to ascertain that inclusion / exclusion criteria are followed
- 9. What descriptive stats? Interval / ratio scale Centering constants: Mean, Median, Mode • Mean: Arithmetic mean. • Median: Middle value when arranged in ascending / descending order • Mode: Most common value • Used to compare groups • Mean is most commonly used statistics • Limitations of Mean
- 10. What descriptive stats? Interval / ratio scale Standard deviation: • Measure of variation. • Has the same unit of measurement as mean • Higher the SD higher is the variation in the data • Can compare two groups • Required for further statistics • Variance is square of SD
- 11. What descriptive stats? Interval / ratio scale Quartiles • Measure of variation. • Observations arranged in ascending order • If there are 500 observations, 125th observation indicates 1st quartile (Q-1) 250th observation indicates 2nd quartile (Q-2) 375th observation indicates 3rd quartile (Q-3)
- 12. What descriptive stats? Interval / ratio scale Percentile: • Measure of variation. • Observations arranged in ascending order • If there are 500 observations, 5th observation indicates 1st percentile, • 475th observation is 95th percentile • Used in studies related to nutrition, education, psychiatry • 50th percentile is median
- 13. What descriptive stats? Interval / ratio scale Coefficient of Variation: • SD divided by mean. • May be expressed as % • Useful to compare variables with different units of measurement • Example: Is height more variable or weight? Is Hb% more variable or ESR?
- 14. BOX PLOT • Graphical presentation of Quantitative variable • Can be drawn with help of software • Lot of information in one graph
- 15. What descriptive stats? Interval / ratio scale Skeweness & NORMAL distribution: • To decide if distribution is Normal or not • Types • Skewed to right (+ve) • Skewed to Left (-ve) • It can be quantified • Tests presuming normal distribution not apllicable
- 16. Tables & Descriptive Statistics What do tables present Counts Vs Characteristic Number of persons with characteristic Groups: Di-chotomous Poly-chotomous • How many groups? K = 1+ (3.332 x Log 10 (n)) K Number of categories N = number of observations •
- 17. Tables & Descriptive Statistics 2 by 2 table Count of a variable in 2 groups Gender Group Total Study Control M 60 64 124 F 40 36 076 Total 100 100 200
- 18. Tables & Descriptive Statistics 2 by 2 table • Count of a 2 variables in 2 groups • Showing association Tuberculin Lepromin Total + (ve) (-) ve (+) ve 189 011 200 (-) ve 023 377 400 Total 212 388 600
- 19. Tables & Descriptive Statistics Frequency distribution table • Frequency of categories in or more groups • More than 2 categories/ 1 or more groups Blood Group Cancer stomach Control group A B AB O
- 20. Graphs in Describing Data Qualitative data Bar chart Pie chart Pictogram Quantitative data Box plot Scatter chart Histogram Depending on objective Trend: Line chart Correlation: Scatter diagram
- 21. Bar Chart Distribution of blood groups in donors 300 318 222 160 0 50 100 150 200 250 300 350 A B AB O
- 22. Pie Chart Distribution of blood groups in donors 300 318 222 160 A B AB O
- 23. Histogram
- 24. Scatter diagram
- 25. Line Diagram
- 26. Soft ware in descriptive statistics MS-EXCEL Master chart Rows: Records Columns: Variable Coding the Qualitative variables Use of functions Export to other software like SPPSS