Basic biostatistics dr.eezn
- 1. Basic Biostatistics Dr. Ei Ei Zar Nyi Assistant Director Central Epidemiology Unit
- 2. Statistics • Statistics is a field of study concerned with (1) collection, organization, summarization and analysis of data and (2) the drawing of inferences about a body of data when only a part of the data is observed. Biostatistics (Biomedical statistics) • When the data analyzed are derived from the biological sciences and medicine, we use the term biostatistics. Synonym = Medical statistics
- 3. Uses Biostatistics is necessary for • To measure the status of health and disease in a community. • Provide the basic not only to monitor the health status of the community but also for the scientific advancement of medicine. • For the collection, analysis, and interpretation of scientific data gathered from clinical, laboratory or field investigation. • Clear thinking and sound understanding of statistical methods is fundamental for the research project.
- 5. Descriptive Statistics • Descriptive Statistics are Used by Researchers to Report on Populations and Samples. • Descriptive Statistics are a means of organizing and summarizing observations, which provide us with an overview of the general features of the set of data.
- 6. • Raw data: Measurements which have not been organized, summarized, or otherwise manipulated • Descriptive measures: Single numbers calculated from organized and summarized data to describe these data. eg. Percentage, average
- 7. Sample vs. Population Population Sample Data Parameter statistic Sample size N n Mean μ x Variance 𝜎2 𝑠2 SD 𝜎 s
- 8. Descriptive Statistics Class A--IQs of 13 Students 102 115 128 109 131 89 98 106 140 119 93 97 110 Class B--IQs of 13 Students 127 162 131 103 96 111 80 109 93 87 120 105 109 An Illustration: Which Group is Smarter? Each individual may be different. If you try to understand a group by remembering the qualities of each member, you become overwhelmed and fail to understand the group.
- 9. Descriptive Statistics Which group is smarter now? Class A--Average IQ Class B--Average IQ 110.54 110.23 They’re roughly the same! With a summary descriptive statistic, it is much easier to answer our question.
- 10. Descriptive Statistics Types of descriptive statistics: • Organize Data – Tables – Graphs • Summarize Data – Central Tendency – Variation
- 11. Descriptive Statistics Types of descriptive statistics: (Data Presentation) • Organizing Data – Tables • Simple table • Frequency Distribution table • Contingency table • Correlation table – Graphs • Bar Chart • Pie chart • Histogram • Frequency Polygon • Line diagram • Stem and Leaf Plot • Box Plots
- 12. Simple Table State Population State A 5,000 State B 70,000 State C 30,000 State D 150,000 Table (1) Population of some states in country X Source: Census of country X, 2000
- 13. Frequency Distribution table Table (2) Age distribution of study population Age group Frequency Percentage 0-4 years 15 30 5-9 years 20 40 10-14 years 5 10 ≥15 years 10 20 Total 50 100
- 14. Contingency table Table (3) Association between Sex and smoking status among study population Sex Smoking + Smoking - Total Male 80 6 86 Female 70 4 74 Total 150 10 160
- 15. Age Weight 1 month 2 months 3 months 6 lbs 10 lbs 14 lbs Correlation table
- 16. Bar chart • Consist a set of vertical or horizontal bars • Same width • Height of each bar represent the frequency of each specific category • Equal space between bars • Purpose of the use of bar chat is to compare the categories of the same variable Simple vertical bar chart Simple horizontal bar chart 0 2 4 6 8 10 12 14 16 18 illitrate primary middle high graduate 0 5 10 15 20 illitrate primary middle high graduate
- 17. Bar chart Multiple bar chart Component bar chart 0 2 4 6 8 10 12 14 16 illitrate primary middle high graduate urban rural 0 5 10 15 20 illitrate primary middle high graduate urban rural
- 18. Pie chart illitrate primary middle high graduate • A circle containing 360 degrees • Pie chart is the best adapted for illustrating the problem of hoe, the whole is sub-divided into segments • Segments can be colored or shaded differently for greater clarity
- 19. Histogram • A special type of bar graph showing frequency distribution • It consists of a set of columns with no space between each of them • The area under each column represents the frequency of each class • If the data have been grouped into unevenly spaced intervals, a histogram is the most suitable kind of diagram
- 20. Frequency Polygon • A special kind of line graph connecting midpoints at the tops of bars or cells of histogram • Total area under the frequency polygon is equal to that of histogram
- 21. Line Diagram 0 10 20 30 40 50 60 70 80 90 Jan Feb March April May June July August Sept Oct Nov Dec DHF incidence during 2007, in X hospital • Most commonly used for showing changes of values with the passage of time
- 22. Stem and leaf plot • It resembles with the histogram and has the same purpose (range of data set, location of highest concentration of measurements, presence or absence of symmetry)
- 23. Box plot
- 24. Descriptive Statistics • Summarizing Data – Central Tendency (or Groups’ “Middle Values”) • Mean • Median • Mode – Variation (or Summary of Differences Within Groups) • Range • Standard Deviation • Variance • Coefficient of variation
- 25. Measures of Central Tendency • Statistic : A descriptive measure computed from the data of a sample • Parameter : A descriptive measure computed from the data of a population • Most commonly used measures of central tendency: Mean, Median, Mode
- 26. Mean • also called 'Average' • obtained by adding all the values in a population or a sample • dividing by the number of values that are added Formula of the mean : For a finite population: μ = ∑ xi / N : For a sample : x = ∑ xi / n Eg. Mean age (year) of the following 9 subjects 56, 54, 61, 60, 54, 44, 49, 50, 63 x = ∑ xi / n = 56+54+61+60+54+44+49+50+63 / 9 = 54.55 year Properties of the mean • Uniqueness • Simplicity • Being influenced by extreme values
- 27. Exercises Mean Class A--IQs of 13 Students 102 115 128 109 131 89 98 106 140 119 93 97 110 Class B--IQs of 13 Students 127 162 131 103 96 111 80 109 93 87 120 105 109 Σ x = 1437 Σ x = 1433 x bar= Σ x = 1437 = 110.54 x bar = Σx = 1433 = 110.23 n 13 n 13
- 28. Mean 1. Means can be badly affected by outliers (data points with extreme values unlike the rest) 2. Outliers can make the mean a bad measure of central tendency or common experience All of Us Bill Gates Mean Outlier Income in the U.S.
- 29. Median • The middle value of the data set which is arrayed from the lowest to the highest. • 50% < Median > 50% • For the series of odd numbers, median is the middle value. • For even numbers, median is the average of two middle values. Formula: ( n + 1) / 2 th value Properties of Median • Uniqueness • Simplicity • Median can avoid the effect of skewed distribution
- 30. eg. Median age (year) of the following 9 subjects 56, 54, 61, 60, 54, 44, 49, 50, 63 Ordered array → 44, 49, 50, 54, 54, 56, 60, 61, 63 ( n + 1) / 2th value → (9 + 1) /2 = 10/ 2 = 5th value 5th value is 54, so median is 54
- 31. Median Median = 109 (six cases above, six below) Class A--IQs of 13 Students 89 93 97 98 102 106 109 110 115 119 128 131 140
- 32. Median Median = 109.5 109 + 110 = 219/2 = 109.5 (six cases above, six below) If the first student were to drop out of Class A, there would be a new median: 89 93 97 98 102 106 109 110 115 119 128 131 140
- 33. Median 1. The median is unaffected by outliers, making it a better measure of central tendency, better describing the “typical person” than the mean when data are skewed. All of Us Bill Gates outlier
- 34. Median 2. If the recorded values for a variable form a symmetric distribution, the median and mean are identical. 3. In skewed data, the mean lies further toward the skew than the median. Mean Median Mean Median Symmetric Skewed
- 35. Mode • Value most frequently occurring in a set of data • More than one mode present • Can be used for the categorical data. eg. Modal age (year) of the following 9 subjects 56, 54, 61, 60, 54, 44, 49, 50, 63 54 is modal age
- 36. Mode 1. It may give you the most likely experience rather than the “typical” or “central” experience. 2. In symmetric distributions, the mean, median, and mode are the same. 3. In skewed data, the mean and median lie further toward the skew than the mode. Median Mean Median MeanMode Mode Symmetric Skewed (Rt)
- 37. Measures of dispersion • Dispersion: synonyms → variation, spread, scatter • Range: The difference between the largest and smallest value in a set of data and poor measure of dispersion. R = xL - xS eg. The range of ages (year) of the following 9 subjects 56, 54, 61, 60, 54, 44, 49, 50, 63 R = xL - xS = 63 – 44 = 19
- 38. Range • The spread, or the distance, between the lowest and highest values of a variable. • To get the range for a variable, you subtract its lowest value from its highest value. Class A--IQs of 13 Students 102 115 128 109 131 89 98 106 140 119 93 97 110 Class A Range = 140 - 89 = 51 Class B--IQs of 13 Students 127 162 131 103 96 111 80 109 93 87 120 105 109 Class B Range = 162 - 80 = 82
- 39. Standard Deviation • Standard deviation: s for sample : σ for population • It measures how each observation in the data set differs from the mean • The square root of the variance reveals the average deviation of the observations from the mean. s.d. = √ variance
- 40. Standard Deviation 1. The larger s.d. the greater amounts of variation around the mean. For example: 2. s.d. = 0 only when all values are the same (only when you have a constant and not a “variable”) 3. Like the mean, the s.d. will be inflated by an outlier case value.
- 41. Variance • An average measure of squared deviation of observations from the mean. • The larger the variance, the further the individual cases are from the mean. • The smaller the variance, the closer the individual scores are to the mean. Mean Mean
- 42. Variance • Variance is a number that at first seems complex to calculate. • Calculating variance starts with a “deviation.” • A deviation is the distance away from the mean of a case’s score. variance (𝑠2) = Ʃ (x – x ) 2 n−1
- 43. The coefficient of variation • To compare the dispersion in two sets of data. • Express the standard deviation as a percentage of mean. • Useful in comparing the relative variability of different kinds of characteristics or with different unit. CV = 𝑠 𝑥 * 100 = ( ) %
- 44. Descriptive Statistics Summarizing Data: Central Tendency (or Groups’ “Middle Values”) • Mean • Median • Mode Variation (or Summary of Differences Within Groups) • Range • Standard Deviation • Variance • Coefficient of variation – …Wait! There’s more
- 45. Normal Distribution • Symmetrical distribution of data • Normal curve or Gaussian distribution • The shape of curve depends on mean and SD Properties of normal distribution • Symmetrical, belled shape • Usually not touch to the base line • Mean, Median, Mode are the same • Area under the curve, ± 1 SD = 68.26% ± 2 SD = 95.46% ± 3 SD = 99.74%
- 46. Skew Distribution • If a graph (histogram or frequency polygon) of distribution is asymmetric, the distribution is said to be skewed. • Right or positively skewed : if the graph extends further to the right, long tail to the right. • Left or negatively skewed : if the graph extends further to the left, long tail to the left. Skewed (Rt)Skewed (Lt)
- 47. Kurtosis • Is the measure of the degree to which a distribution is peaked or flat in comparison to normal distribution whose graph is characterized by bell- shaped appearance. • Mesokurtic : Kurtosis measure = 0 • Leptokurtic : Kurtosis measure > 0 • Platykurtic : Kurtosis measure < 0
- 48. Curve Name 8/29/2018 48 Mesokurtic (Normal) Leptokurtic Platykurtic
- 49. Descriptive Statistics • Now you are qualified use descriptive statistics! • Questions?
- 50. Thank you!