Public Health Methodologies        Biostatisticsdrrkb@hotmail.com
Data• Data is a collection of facts, such as values or  measurements.                          OR• Data is information tha...
Statistics    Statistics    is    the    study    of    the    collection, summarizing, organization, analysi    s, and in...
Vital statistics    Vital                statistics                 is    collecting, summarizing, organizing, analysis,  ...
Biostatistics    Biostatistics is the application of statistical    techniques to scientific research in health-    relate...
Descriptive Statistics    The term descriptive statistics refers to    statistics that are used to describe. When    using...
Inferential or Analytical Statistics Inferential statistics are used to draw conclusions and make predictions based on the...
Primary & Secondary Data• Raw or Primary data: when data collected  having lot of unnecessary, irrelevant & un  wanted inf...
Ungrouped & Grouped Data• Ungrouped data: when data presented or observed individually. For  example if we observed no. of...
Variable    A variable is something that can be    changed, such as a characteristic or value. For    example age, height,...
Types of Variable    Independent variable: is typically the    variable representing the value being    manipulated or cha...
Categories of DATA9/3/2012          Dr. Riaz A. Bhutto   12
Quantitative or Numerical data    This data is used to describe a type of    information that can be counted or expressed ...
Quantitative or Numerical data (cont.)This data is of two types1. Discrete Data: it is in whole numbers or values and   ha...
Qualitative or Categorical dataThis is non numerical data as                Male/Female, Short/TallThis is of two types1. ...
Measures of Central Tendency &       Variation (Dispersion)9/3/2012       Dr. Riaz A. Bhutto   16
Measures of Central Tendency    are quantitative indices that describe the    center of a distribution of data. These are•...
Mean  Mean or arithmetic mean is also called AVERAGE and  only calculated for numerical data. For example• What average ag...
Median• It is central most value. For example what is  central value in 2, 3, 4, 4, 4, 5, 6 data?• If we divide data in tw...
Mode• is the most frequently (repeated) occurring  value in set of observations. Example• No mode  Raw data:       10.3 4....
Measures of Dispersionquantitative indices that describe the spread of  a data set. These are• Range• Mean deviation• Vari...
Range    It is difference between highest and lowest    values in a data series. For example:           the ages (in Years...
Mean Deviation    This is average deviation of all observation    from the mean                                           ...
Mean Deviation Example  A student took 5 exams in a class and had scores of 92, 75, 95, 90, and 98. Find the mean deviatio...
• 2nd step find mean deviation                                                   Deviation from   Absolute value of       ...
Variance• It is measure of variability which takes into  account the difference between each  observation and mean.• The v...
Variance (cont.)• The Variance is defined as:• The average of the squared differences from the  Mean.• To calculate the va...
Example: House hold size of 5 families was recorded as following:                   2, 5, 4, 6, 3       Calculate variance...
Standard Deviation• The Standard Deviation is a measure of how  spread out numbers are.• Its symbol is σ (the greek letter...
Example    You and your friends have just measured the heights of your                       dogs (in millimeters):• The h...
Your first step is to find the Mean:                                   Answer:             Mean = 600 + 470 + 170 + 430 + ...
Now, we calculate each dogs difference from the Mean:      To calculate the Variance, take each difference, square it, and...
And the Standard Deviation is just the square root of Variance, so:           Standard Deviation: σ = √21,704 = 147.32... ...
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Lec. biostatistics

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Lec. biostatistics

  1. 1. Public Health Methodologies Biostatisticsdrrkb@hotmail.com
  2. 2. Data• Data is a collection of facts, such as values or measurements. OR• Data is information that has been translated into a form that is more convenient to move or process. OR• Data are any facts, numbers, or text that can be processed by a computer.3/3/2012 Dr. Riaz A. Bhutto 2
  3. 3. Statistics Statistics is the study of the collection, summarizing, organization, analysi s, and interpretation of data.3/3/2012 Dr. Riaz A. Bhutto 3
  4. 4. Vital statistics Vital statistics is collecting, summarizing, organizing, analysis, presentation, and interpretation of data related to vital events of life as births, deaths, marriages, divorces, health & diseases.3/3/2012 Dr. Riaz A. Bhutto 4
  5. 5. Biostatistics Biostatistics is the application of statistical techniques to scientific research in health- related fields, including medicine, biology, and public health.3/3/2012 Dr. Riaz A. Bhutto 5
  6. 6. Descriptive Statistics The term descriptive statistics refers to statistics that are used to describe. When using descriptive statistics, every member of a group or population is measured. A good example of descriptive statistics is the Census, in which all members of a population are counted.3/3/2012 Dr. Riaz A. Bhutto 6
  7. 7. Inferential or Analytical Statistics Inferential statistics are used to draw conclusions and make predictions based on the analysis of numeric data.3/3/2012 Dr. Riaz A. Bhutto 7
  8. 8. Primary & Secondary Data• Raw or Primary data: when data collected having lot of unnecessary, irrelevant & un wanted information• Treated or Secondary data: when we treat & remove this unnecessary, irrelevant & un wanted information• Cooked data: when data collected not genuinely and is false and fictitious3/3/2012 Dr. Riaz A. Bhutto 8
  9. 9. Ungrouped & Grouped Data• Ungrouped data: when data presented or observed individually. For example if we observed no. of children in 6 families 2, 4, 6, 4, 6, 4• Grouped data: when we grouped the identical data by frequency. For example above data of children in 6 families can be grouped as: No. of children Families 2 1 4 3 6 2 or alternatively we can make classes: No. of children Frequency 2-4 4 5-7 23/3/2012 Dr. Riaz A. Bhutto 9
  10. 10. Variable A variable is something that can be changed, such as a characteristic or value. For example age, height, weight, blood pressure etc3/3/2012 Dr. Riaz A. Bhutto 10
  11. 11. Types of Variable Independent variable: is typically the variable representing the value being manipulated or changed. For example smoking Dependent variable: is the observed result of the independent variable being manipulated. For example ca of lung Confounding variable: is associated with both exposure and disease. For example age is factor for many events3/3/2012 Dr. Riaz A. Bhutto 11
  12. 12. Categories of DATA9/3/2012 Dr. Riaz A. Bhutto 12
  13. 13. Quantitative or Numerical data This data is used to describe a type of information that can be counted or expressed numerically (numbers) 2, 4 , 6, 8.5, 10.59/3/2012 Dr. Riaz A. Bhutto 13
  14. 14. Quantitative or Numerical data (cont.)This data is of two types1. Discrete Data: it is in whole numbers or values and has no fraction. For example Number of children in a family = 4 Number of patients in hospital = 3202. Continuous Data (Infinite Number): measured on a continuous scale. It can be in fraction. For example Height of a person = 5 feet 6 inches 5”.6’ Temperature = 92.3 °F9/3/2012 Dr. Riaz A. Bhutto 14
  15. 15. Qualitative or Categorical dataThis is non numerical data as Male/Female, Short/TallThis is of two types1. Nominal Data: it has series of unordered categories ( one can not √ more than one at a time) For example Sex = Male/Female Blood group = O/A/B/AB2. Ordinal or Ranked Data: that has distinct ordered/ranked categories. For example Measurement of height can be = Short / Medium / Tall Degree of pain can be = None / Mild /Moderate / Severe9/3/2012 Dr. Riaz A. Bhutto 15
  16. 16. Measures of Central Tendency & Variation (Dispersion)9/3/2012 Dr. Riaz A. Bhutto 16
  17. 17. Measures of Central Tendency are quantitative indices that describe the center of a distribution of data. These are• Mean• Median (Three M M M)• Mode9/3/2012 Dr. Riaz A. Bhutto 17
  18. 18. Mean Mean or arithmetic mean is also called AVERAGE and only calculated for numerical data. For example• What average age of children in years? Children 1 2 3 4 5 6 7 Age 6443246 Formula -- = ∑ X X ___ n Mean = 6 4 4 3 2 4 5 = 28 = 4 years 7 79/3/2012 Dr. Riaz A. Bhutto 18
  19. 19. Median• It is central most value. For example what is central value in 2, 3, 4, 4, 4, 5, 6 data?• If we divide data in two equal groups 2, 3, 4, 4, 4, 5, 6 hence 4 is the central most value• Formula to calculate central value is: Median = n + 1 (here n is the total no. of value) 29/3/2012 Median = (n + 1)/2 = 7 + 1 = 8/2 = 4 Dr. Riaz A. Bhutto 19
  20. 20. Mode• is the most frequently (repeated) occurring value in set of observations. Example• No mode Raw data: 10.3 4.9 8.9 11.7 6.3 7.7• One mode Raw data: 2 3 4 4 4 5 6• More than 1 mode Raw data: 21 28 28 41 43 439/3/2012 Dr. Riaz A. Bhutto 20
  21. 21. Measures of Dispersionquantitative indices that describe the spread of a data set. These are• Range• Mean deviation• Variance• Standard deviation• Coefficient of variation• Percentile9/3/2012 Dr. Riaz A. Bhutto 21
  22. 22. Range It is difference between highest and lowest values in a data series. For example: the ages (in Years) of 10 children are 2, 6, 8, 10, 11, 14, 1, 6, 9, 15 here the range of age will be 15 – 1 = 14 years9/3/2012 Dr. Riaz A. Bhutto 22
  23. 23. Mean Deviation This is average deviation of all observation from the mean - Mean Deviation = ∑ І X – X І _______ _ n here X = Value, X = Mean n = Total no. of value9/3/2012 Dr. Riaz A. Bhutto 23
  24. 24. Mean Deviation Example A student took 5 exams in a class and had scores of 92, 75, 95, 90, and 98. Find the mean deviation for her test scores.• First step find the _ mean. x = ___ ∑x n = 92+75+95+90+98 5 = 450 5 = 909/3/2012 Dr. Riaz A. Bhutto 24
  25. 25. • 2nd step find mean deviation Deviation from Absolute value of ˉ ˉ Deviation Values = X Mean = X Mean = X - X Ignoring + signs 92 90 2 2 75 90 -15 15 95 90 5 5 90 90 0 0 98 90 8 8 Total = 450 -- ∑ X - X = 30 _n= 5 Mean Deviation = ∑І X – X І _______ = 30/5 =6 n Average deviation from mean is 6 9/3/2012 Dr. Riaz A. Bhutto 25
  26. 26. Variance• It is measure of variability which takes into account the difference between each observation and mean.• The variance is the sum of the squared deviations from the mean divided by the number of values in the series minus 1.• Sample variance is s² and population variance is σ²9/3/2012 Dr. Riaz A. Bhutto 26
  27. 27. Variance (cont.)• The Variance is defined as:• The average of the squared differences from the Mean.• To calculate the variance follow these steps:• Work out the Mean (the simple average of the numbers)• Then for each number: subtract the Mean and square the result (the squared difference)• Then work out the average of those squared differences.9/3/2012 Dr. Riaz A. Bhutto 27
  28. 28. Example: House hold size of 5 families was recorded as following: 2, 5, 4, 6, 3 Calculate variance for above data. Step 1 Step 2 Step 3 Step 4 Deviation from ˉ Values = X ˉ ( X – X)² Mean = X ˉ Mean = X - X 2 4 -2 4 5 4 1 1 4 4 0 0 6 4 2 4 3 4 -1 1 ∑ = 10 Step 5 _ ∑ ( X – X )² Step 6 s² = _______ = 10/5 = 2 n S²= 2 persons²9/3/2012 Dr. Riaz A. Bhutto 28
  29. 29. Standard Deviation• The Standard Deviation is a measure of how spread out numbers are.• Its symbol is σ (the greek letter sigma)• The formula is easy: it is the square root of the Variance.i-e s = √ s²• SD is most useful measure of dispersion s = √ (x - x²) n (if n > 30) s = √ (x - x²) n-1 (if n < 30)9/3/2012 Dr. Riaz A. Bhutto 29
  30. 30. Example You and your friends have just measured the heights of your dogs (in millimeters):• The heights (at the shoulders) are: 600mm, 470mm, 170mm, 430mm and 300mm.• Find out the Mean, the Variance, and the Standard Deviation.9/3/2012 Dr. Riaz A. Bhutto 30
  31. 31. Your first step is to find the Mean: Answer: Mean = 600 + 470 + 170 + 430 + 300 = 1970 = 394 5 5 so the mean (average) height is 394 mm. Lets plot this on the chart:9/3/2012 Dr. Riaz A. Bhutto 31
  32. 32. Now, we calculate each dogs difference from the Mean: To calculate the Variance, take each difference, square it, and then average the result:9/3/2012 So, the Variance is 21,704. 32 Dr. Riaz A. Bhutto
  33. 33. And the Standard Deviation is just the square root of Variance, so: Standard Deviation: σ = √21,704 = 147.32... = 147 (to the nearest mm) And the good thing about the Standard Deviation is that it is useful. Now we can show which heights are within one Standard Deviation (147mm) of the Mean:• So, using the Standard Deviation we have a "standard" way of knowing what is normal, and what is extra large or extra small.9/3/2012 Dr. Riaz A. Bhutto 33

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