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Datos y análisis

Data analysis

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- An introduction to Medical statistics (L2 presentation of data) By Dr. Basma M. Hani Lecturer of Public Health Faculty of Medicine Benha University
- DEFINITION It is a process of putting collected data in a concise and comprehensive form (table or graph or mathematical form)so that the eyes can grasp it easy. presentation of data 2
- The main methods of presentation of data are: A. Tabular presentation. B. Graphical presentation. C. Mathematical presentation (Numerical or Parameters). presentation of data 3
- presentation of data 4
- - Characteristics of the tables : A table can be simple or complex. The tables should be numbered. A brief title must be given to each table. The headings of the columns or rows should be clear and concise. presentation of data 5
- - Characteristics of the tables : The data must be presented according to its importance. Table should not be too large. A vertical arrangement is better than a horizontal one. presentation of data 6
- presentation of data 7
- Some examples of tabulation are(types):- • Simple tables • Frequency distribution tables • Cumulative frequency distribution tables presentation of data 8
- 9 presentation of data
- presentation of data 10 The data is first split into convenient groups or class intervals and the number of items which occur in each group (Frequency) is shown in the adjacent column.
- The following figures are the ages of patients admitted to a hospital with gastroenteritis. Construct a frequency distribution Table, regarding their age distribution. 8, 24, 18, 5, 12, 4, 3, 3, 2, 3, 23, 9, 18, 16, 1, 2, 3, 5, 11, 31, 9, 11, 11, 7, 19, 6, 9, 5, 16, 20, 4, 3, 3, 3, 10, 3, 2, 1, 6, 9, 3, 7, 14, 8, 1, 4, 6, 4, 15, 22, 2, 1, 4, 7, 1, 12, 3, 23, 4, 19, 6, 2, 2, 4, 14, 2, 2, 21, 3, 2, 9, 3, 2, 1, 7, 19. presentation of data 11 Age (class interval) Number of patients (frequency) 0 – 4 35 5 – 9 18 10 – 14 11 15 – 19 8 20 – 24 6 Table 2: Age distribution of gastroenteritis patients
- In constructing frequency distribution tables: Determine the largest and smallest numbers in the given set of data i.e. range. divide the range into a convenient number of class intervals having the same size. Determine the number of observations falling into each class interval. presentation of data 12
- ◙ Shows the total number of observations either less or more than a given level of the variable. ◙ Includes: * Ascending distribution tables. * Descending distribution tables. presentation of data 13
- presentation of data 14 a) Ascending cumulative frequency tables:
- presentation of data 15 b) Descending cumulative frequency tables:
- presentation of data 16
- presentation of data 17
- Criteria of a graph The graph must be simple and legible. Not more than 3, preferably only 2, elements should be compared in a single graph. The graph should be a simple summary of tabulated data. presentation of data 22
- Types of graphs 1. Bar charts. 2. Histogram. 3. Frequency polygon. 4. Line diagrams. 5. Pie (Circular) chart. 6. Pictogram. presentation of data 19
- Bar charts are ways of presenting a set of numbers by the length of a bar – the length of the bar is proportional to the magnitude to be represented. Bars may be vertical or horizontal. presentation of data 20 1. Bar charts
- The bars are usually separated by appropriate spaces, the bars should be of the same width. A suitable scale must be chosen to present the length of the bars. presentation of data 21
- Vertical Bar charts horizontal Bar chartspresentation of data 22
- presentation of data 23 0 10 20 30 40 50 60 70 80 90 100 Percentage(%) U. R. Residence 0 10 20 30 40 50 60 70 80 90 100 Percentage(%) U. R. Residence Males Females 0 10 20 30 40 50 60 70 80 90 100 Percentage(%) U. R. Residence Males Females Simple Multiple Component
- Figure 3.3 Simple bar chart (shows one variable in one group )of hair color of children receiving Malathion in nit lotion study presentation of data 24
- Figure 3.4 Multiple (Compound) bar chart of hair color by sex for children Shows :- One variables in >one group Or More than one variable in one group presentation of data 25
- Component Bar Chart: The bars are divided into two or more parts which are distinguished from each other by coloring, shading or stippling. Each part representing a certain item and proportional to the magnitude of that particular item. presentation of data 26
- Figure 3.6 A component bar chart of hair color by sex presentation of data 27
- 2. Histogram. 0 2 4 6 8 10 12 14 16 18 20 10 20 30 40 50 60 70 80 Age (Years) % of the population 28 presentation of data
- It’s a pictorial diagram representing the frequency distribution table. As bar chart but with no gaps. Can represent only one variable. presentation of data 29
- Table(4): Grouped frequency distribution for birth weight of 30 infants presentation of data 30
- Figure 3.8 Histogram of the grouped birth weight data in Table 4 presentation of data 31
- 32 presentation of data 3. Frequency polygon It is obtained by joining the mid-points of the histogram blocks
- presentation of data 33 4. line diagram:-Line diagram are used to show the trend of event with the passage of time. Fig.(3): Infant mortality rate in Egypt during the period from 1935-1985. 0 50 100 150 200 1935 1945 1955 1965 1975 1985 Year I.M.R.(per thousand)
- presentation of data 34 5. Pie (Circular) chart.The distribution of the component are based upon a percentage Fig.(1): Distribution of the studied sample according to their residence. Urban 60% Rural 40%
- presentation of data 35
- presentation of data 36
- 6. Pictogram.Pictorial illustrations showing relative and proportional sizes. presentation of data 37
- According to types of data:- 1-Tools to Summarize Categorical & Discrete Data Frequency Table(simple table). Bar Chart. Pie Chart. Pictogram. 2-Tools to Summarize Continuous Data: Frequency Distribution Table. Histogram, Frequency Polygon presentation of data 38
- Mathematical presentation:- Measures of central tendency and Measures of dispersion
- A-Measures of central tendency (Statistical averages) The word “average”: Is a value tending to lie centrally within a set of data arranged according to magnitude
- A-Measures of central tendency 1- Mid-range 2- The arithmetic mean 3-The median 4-the mode
- 1-Mid-range a-Ungrouped data =Largest + smallest 2 b-Grouped data =Lower limit of first interval + the upper limit of last interval 2
- 1-Mid-range - Used only with quantitative variables - Rapid, rough and easy - Not accurate
- Ungrouped data:Weights of 5 Persons is 43, 20, 40, 36, 19 Kg. Mid-range = (19+43)/2 = 31 Kg. - Used only with quantitative variables - Rapid, rough and easy. - Not accurate. presentation of data 44
- Example The following table include the weight of 14 children calculate the mid-range Mid-range=30+50 =40 Kg 2 Weight Frequency 30- 3 35- 5 40- 4 45-50 2 Total 14
- 2) The Arithmetic mean: Is the sum of the values in a set of data divided by the number of the values in the set. It is denoted by the sign X (called X bar). X= ∑x n X denotes any value of an observation ∑ means sum n means number of observations
- *The advantages of the mean 1- Easy to calculate 2- Easy to understand *The disadvantages of the mean is that sometimes may be affected by abnormal values in the distribuation
- Example The diastolic blood pressure of 5 individuals was 83, 75, 81, 79, 72 mmHg calculate the mean X= ∑x n =390 = 78 mmHg 5
- 3-The median It is the central value of a set of observations when those observations are arranged in order of magnitude
- A-Measures of central tendency To obtain the median a- The data is first arranged in an ascending or descending order of magnitude b- If the number of set is odd, the median is the value N+1 2 c- If the number of set is even, the middle values are N and N +1 and the mean of which is taken as median 2 2
- Example The diastolic blood pressure of 9 individuals was 83, 75, 81, 79, 71, 95, 75, 77, 84 calculate the median first we arrange the data 71, 75, 75, 77, 79, 81, 83, 84, 95 The number of set is odd Median= N+1 = 9+1 =5 2 2 So the median is value number 5 in the set of data=79
- Example The diastolic blood pressure of 10 individuals was 83, 75, 81, 79, 71, 95, 75, 77, 84, 90 calculate the median first we arrange the data 71, 75, 75, 77, 79, 81, 83, 84, 90, 95 The number of set is even so, the middle values are N =10 =5 and N +1= 10 +1 =6 2 2 2 2 The median is average of 5Th and 6Th observation=79+81 =80 2
- 4) The mode: - The mode is the most frequently occurring value in a series of data. - It may not exist; no modal. - It may be unimodal, bimodal, trimodal... etc.
- Example -2,3,4,4,5,4,7,7,7,9 what is the mode It has 2 modes 4 and 7 (bimodal) - 3, 5, 8, 10, 12, 15, 18 what is the mode - It has no mode
- B-Measures of dispersion 1-Range 2-Mean deviation (M.D.) 3-Variance = S2 4-Standard deviation (± S.D.)
- B-Measures of dispersion 1- The range is the difference between highest and lowest value It depends only on the 2 outlying values e.g. 30, 34, 32, 36, 28. Range = 36 – 28 = 8
- 2-Mean deviation (M.D.) :-Is the arithmetic mean of the numerical differences of all observation from the mean, regardless of sign around the mean. =∑(X - X ) n
- B-Measures of dispersion 3-Variance = S2 The sum of the squares of the deviation of each measurement in a series from the mean of the series, divided by the total number of the observation minus one (The degree of freedom). =∑(X -X ) 2 n-1
- B-Measures of dispersion 4-Standard deviation (± S.D.) it is the positive square root of the variance
- Example 2,3,4,5,6,7,8 calculate the range, mean deviation, variance and standard deviation 1- range = 8-2=6 2- mean deviation X =35/7= 5 Deviation from the mean=3,2,1,0,-1,-2,- 3 Mean deviation= 12/7= 1.71
- Example 3- Variance= ∑ squared deviation from the mean n-1 =9+4+1+0+9+4+1 =28/6=4.6 6 4- Standard deviation = is the positive square root of the variance =2.1
- 62 presentation of data

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