Biostatistics Presentation of data DR. AMEER KADHIM HUSSEIN M.B.CH.B.FICMS (COM.)

Transcription

1 Biostatistics Presentation of data DR. AMEER KADHIM HUSSEIN M.B.CH.B.FICMS (COM.)

2 PRESENTATION OF DATA 1. Mathematical presentation (measures of central tendency and measures of dispersion). 2. Tabular presentation. 3. Graphical presentation. 4. Pictorial presentation. (Map chart).

3 TABULAR PRESENTATION Presentation of data in tables make them into a compact, concise and readily comprehensible form. They can display the characteristics of data more efficiently than the raw data.

4 TYPES OF TABLES 1.Simple Table including one variable (quantitative or qualitative) and the corresponding frequency. 2. Cross tabulation is a tabular method for simultaneously summarizing the data for two categorical variables.

5 CRITERIA FOR PROPER TABLE 1.Simple. 2.Understandable and self explanatory (all symbols should be explained in details in a foot note,each row or column should be labeled clearly, units of the data should be clearly mentioned,the title should be clear, precise, and should answer the questions, what? where? and when? and totals should be shown. 3.The title should be separated from the body of the table by lines or spaces. 4.Avoid too much ruling. 5.If the data are not original, their source should be mentioned as a foot note or in the title.

6 GRAPHICAL AND PICTORIAL PRESENTATION The use of diagrams or pictures to describe the distribution or characteristics of one or more sets of data in a compact and readily comprehensible form. They can provide a better visual presentation of characteristics of data than tabular presentation.

7 Criteria For proper graph 1. Vertical and horizontal scales should be clearly labeled and units identified. 2. Keep graphs as simple as possible avoid too many bars or lines two or three is appropriate more than four is probably too many. 3. Graphs are designed to provide a snapshot of the results use tables for details. 4. Avoid presentation of numbers in the body of a graph.

8 Tabular and Graphical Presentation of data Qualitative Data: Tabular presentation include: 1. Frequency distribution. 2. Relative frequency distribution. 3. Percent frequency distribution. 4. Cross tabulation. Graphical presentation include: 1.Bar chart. 2. Pie chart.

9 Tabular and Graphical Presentation of data Quantitative data Tabular presentation include: 1. Frequency distribution. 2. Relative frequency distribution. 3. Cumulative frequency. 4. Cumulative relative frequency. Graphical presentation include: 1. Histogram. 2. Frequency polygon. 3. Scatter diagrams. 4. Line graph.

10 Qualitative Data

11 FREQUENCY DISTRIBUTION Frequency: It determines the number of observations falling into each category. Relative frequency: It determines the proportion of observation in the particular class relative to the total observations. A relative frequency distribution is a tabular summary of a set of data showing the relative frequency for each class. The percent frequency of a class is the relative frequency multiplied by 100.

12 FREQUENCY DISTRIBUTION Example: A sample of 10 students were examined by certain teacher and the results of examination was as below: 1. good 2. very good 3. good 4. excellent 5. poor 6. very good 7. good 8. poor 9. excellent 10. poor

13 FREQUENCY DISTRIBUTION Results poor good Very good excellent Total Frequency

14 RELATIVE FREQUENCY AND PERCENT FREQUENCY DISTRIBUTION Results poor good Very good excellent Total Relative frequency Percent frequency 30% 30% 20% 20% 100%

15 BAR GRAPH A bar graph is a graphical device for depicting qualitative data. On the horizontal axis we specify the labels that are used for each of the classes. A frequency, relative frequency, or percent frequency scale can be used for the vertical axis. Using a bar of fixed width drawn above each class label, we extend the height appropriately. The bars are separated to emphasize the fact that each class is a separate category.

16 BAR GRAPH 30% 30% 30% 20% 20% 20% 10% 0% Poor Good Very good Excellent

17 PIE CHART The pie chart is a commonly used graphical device for presenting relative frequency distributions for qualitative data. First draw a circle; then use the relative frequencies to subdivide the circle into sectors that correspond to the relative frequency for each class. Since there are 360 degrees in a circle, a class with a relative frequency of 0.25 would consume 0.25(360) = 90 degrees of the circle.

18 PIE CHART 20% 20% 30% 30% Poor Good Very good Excellent

19 CROSS-TABULATIONS Cross-tabulation : is a tabular method for simultaneously summarizing the data for two categorical variables. Steps for Constructing a Cross-tabulation 1. Put the categories of one variable at the top of each column, and the categories of the other variable at the beginning of each row. 2. For each row and column combination, enter the number of observations that fall in the two categories. 3.The bottom of the table gives the column totals, and the right-hand column gives the row totals.

20 CROSS-TABULATIONS Table: Distribution of case and control groups by gender Gender Case Group Control Total Male Female Total

21 CLUSTERED BAR GRAPHS Clustered bar graphs are useful for comparing two categorical variables and are often used in conjunction with cross-tabulations. (we can use frequency or relative frequency ).

22 Quantitative Data

23 THE FREQUENCY DISTRIBUTION To group a set of observations, we select a set of contagious, non overlapping intervals, such that each value in the set of observation can be placed in one, and only one, of the interval, and no single observation should be missed. The interval is called: Class interval

24 THE FREQUENCY DISTRIBUTION Number of class interval : Too few intervals are not good because information will be lost. Too many intervals are not helpful to summarize the data. A commonly followed rule is that number of class interval should be not fewer than 6 and not more than 15. The specific guidance to decide the number of classes is (Sturges formula). k = (log n) k= number of class intervals. n= number of observations in the set. The result should not be regarded as final, but can be regard as guide only. The number of class intervals obtain by sturges rule can be increase or decrease for convenience and clear presentation.

25 THE FREQUENCY DISTRIBUTION Range: It is the difference between the largest and the smallest observation in the data set. The Width of the interval (w): Class intervals generally should be of the same width, but sometimes this is impossible to do. Width of class interval can be obtain by the following formula: W= Width of the class interval, R= Range, K= Number of class intervals. To make the summarization more comprehensible, the class width may be 5 or 10 or the multiples of 10.

26 THE FREQUENCY DISTRIBUTION Frequency: It determines the number of observations falling into each class interval. Relative frequency: It determines the proportion of observation in the particular class interval relative to the total observations in the set. Cumulative frequency: This is calculated by adding the number of observation in each class interval to the number of observations in the class interval above, starting from the second class interval onward. Cumulative relative frequency: This calculated by adding the relative frequency in each class interval to the relative frequency in the class interval above, starting also from the second class interval onward.

27 THE FREQUENCY DISTRIBUTION Cumulative frequency and cumulative relative frequency distributions are used to facilitate obtaining information regarding the frequency or relative frequency within two or more contagious class intervals. The Mid-interval (midpoint): It can be computed by adding the lower bound of the interval plus the upper bound of it and then divide by 2.

28 The following are the heart rate of 50 patients

29 ANSWER 1. Number of classes : (K) = Log 50 = (1.69) = = Width of class interval W = R/K = /6 = 57/6 =

30 Frequency, cumulative frequency, relative frequency and cumulative relative frequency distribution of heart rate of 50 patients Class interval Frequency Cumulative frequency Relative frequency Cumulative relative frequency Total 50 1

31 Example: The following are the hemoglobin values (g/100ml) of 30 children receiving treatment for hemolytic anemia Order the sample observations by size, No. of classes = (Log 10 30) 6 Width = ( ) / 6 1

32 True class limits Frequency Midpoint Cumulative frequency Relative frequency Cumulative relative frequency Total 30 1

33 HISTOGRAM A common graphical presentation of quantitative data is a histogram. The variable of interest is placed on the horizontal axis. A rectangle is drawn above each class interval with its height corresponding to the interval s frequency, relative frequency, or percent frequency. Unlike a bar graph, a histogram has no natural separation between rectangles of adjacent classes. To draw the histogram, the true classes limits should be used. They can be computed by subtracting 0.5 from the lower limit and adding 0.5 to the upper limit for each interval.

34 No. of children Hemoglobin values (g/100ml) Fig ( ) Hemoglobin values of children receiving treatment for hemolytic anemia

35 FREQUENCY POLYGON Another form of graphical presentation of frequency distribution of quantitative variables. It is similar to the histogram, but instead of using rectangles to present data, the midpoint of the top of each rectangle are plotted, and connected together by straight lines.

36 SCATTER DIAGRAM A scatter diagram is a graphical presentation of the relationship between two quantitative variables. One variable is shown on the horizontal axis and the other variable is shown on the vertical axis. The general pattern of the plotted points suggests the overall relationship between the variables.

37 SCATTER DIAGRAM

38 Amoutn of $ LINE GRAPH A line graph is used to show trend of events with passage of time and show how frequency of particular event change over time. Time could be (Seconds - Minutes - Hours Days - Weeks - Months Years - Decades - Centuries etc). $25.00 Money spent this week $20.00 $15.00 $10.00 $5.00 $0.00 Mon. Tues. Wed. Thurs. Fri. Day

39 Calories LINE GRAPH Calories burned while running Hours

40 PICTORIAL PRESENTATION 1. PICTOGRAM Small pictures or symbols are used to present data. For example: picture of no horn on road near a hospital.

41 PICTORIAL PRESENTATION 2. MAP DIAGRAM OR SPOT MAP These maps are prepared to show the geographical distribution of frequencies of a characteristic.

42 Thank you