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# Lec. biostatistics

## on Mar 23, 2012

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## Lec. biostatisticsPresentation Transcript

• Public Health Methodologies Biostatisticsdrrkb@hotmail.com
• 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
• Statistics Statistics is the study of the collection, summarizing, organization, analysi s, and interpretation of data.3/3/2012 Dr. Riaz A. Bhutto 3
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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 numerically (numbers) 2, 4 , 6, 8.5, 10.59/3/2012 Dr. Riaz A. Bhutto 13
• 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
• 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
• 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• Median (Three M M M)• Mode9/3/2012 Dr. Riaz A. Bhutto 17
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• • 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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