1. Graphical Presentation Dr. Amjad El-Shanti MD, PMH,Dr PH University of Palestine 2016

2. Definition of Graph The graph is a method of presenting statistical data in visual form. Most graphs are drawn using Cartesian (Rectangular) coordinates as shown in the following figures. X and Y are called Scale Lines.

3. Types of Graphs: There are many varieties of graphs. The use of a particular type is dependent upon the data and upon the purpose for which the graph is constructed. A- Graphs drawn using Cartesian coordinates: 1. Line Graph 2. Frequency Polygon 3. Histogram 4. Bar Graph 5. Scatter Plot B- Pie Chart C- Stem-and Leaf Display (Stem-Plot) D- Statistical Maps E- Pictograms

4. Rules for Construction of Graphs: 1.The simplest type of graph consistent with its purpose is the most effective. No more lines or symbols should be used in a single graph than the eye can easily follow. 2.Every graph should be self-explanatory. Therefore, it should be correctly labeled as to title, source, scales, and explanatory keys or legends. As a rule the title includes information as to:  The nature of the data  The geographical location  The period covered These elements of the title customarily appear in the order given above. 3.The position of the title for a graph is one of personal choice. In published graphs, however the title is commonly placed below the graph. 4.When more than one variable is shown on a graph, each should be clearly differentiated by means of legends or keys.

5. Rules for Construction of Graphs: 5.The diagram or graph generally proceeds from left to right and from bottom to top. 6.No more coordinate lines should be shown than are necessary to guide the eye. 7.Scale lines should be drawn heavier than other coordinate lines. 8.The lines of the graph itself should be heavier than either coordinate or scale lines. 9.Frequency or percentage is generally represented on the vertical scale, with method of classification on the horizontal. 10.Footnotes, if any, should be placed under and to the right of the graph. 11.Each scale must have a scale a scale caption (scale or axis title) indicating the units used. The X-axis scale caption should be centered directly beneath the x- axis. The y-axis scale caption should be placed at the top or to the left of the Y axis. 12. Zero point should be indicated on the scale (Y axis), otherwise a misleading comparison may result. If however, lack of space makes it inconvenient to use zero point line a scale break may be inserted to indicate its omission.

6. The Line Graph This type of graph is particularly suitable to represent certain observation over time period. The time points may be hours, days, weeks, months, seasons, years, …etc. Each observation is presented by a single point whose abscissa is the time at which the observation was taken and whose ordinate is the value observed and then each two points are joined by a single line.

7. The Line Graph Example: YearCrude Birth Rate Per 1000 Population 199750 199851 199953 200055 200152

8. The Line Graph Example: Figure (1) Crude birth rate of Gaza Strip. 1997-2001

9. The Frequency Polygon This type of graph is suitable to present of quantitative continuous variables whether from simple or complex frequency distribution tables. The method used for drawing this graph is that each category in the table is represented on the graph by one point whose abscissa is the mid-point of the interval and whose ordinate is the frequency or percentage of that interval and then every consecutive points are joined by a straight line. The polygon is a representation of the shape of the particular distribution. Since the area under the percentage distribution (entire polygon) must be 100%. It is necessary to connect the first and last midpoints with the horizontal axis so as to enclose the area of the observed distribution. This is accomplished by connecting the first observed midpoint with the midpoint of a “ fictitious preceding” class having zero observations and by connecting the last observed midpoint with the midpoint of a “fictitious succeeding” class having zero observations.

10. The Frequency Polygon Examples: Age in YearsSexMid-point of interval MalesFemales 20-32(20+30)/2=25 30-55(30+40)/2=35 40-78(40+50)/2=45 50-43(50+60)/2=55 6960-24(60+70)/2=65 Total2122

11. The Frequency Polygon Example: Figure (2): Distribution of a group of subjects by age and sex

12. Frequency Curve This type of graph is used under the following conditions: 1.It is used with quantitative continuous variables. 2.Simple frequency distribution table or complex frequency distribution table. 3.The width of intervals should be as small as possible. 4.The number of categories in the table should be large. The graph is drawn according to the same principles used in the frequency polygon except that, the points are not joined by straight lines but a smooth curve is drawn to pass along these points. The final shape of the frequency curve is very important in statistical analysis because curves of different shapes have specific formulae to describe these curves and specific types of statistical analysis are based on these formulae.

13. Frequency Curve Examples: Age in YearsSexMid-point of interval MalesFemales 20-32(20+30)/2=25 30-55(30+40)/2=35 40-78(40+50)/2=45 50-43(50+60)/2=55 60-6924(60+70)/2=65 Total2122

14. Frequency Curve Example: The previous table on age and sex can be drawn as follows Figure (3): Distribution of a group of subjects by age and sex

15. The Histogram This type of graph is suitable to represent data from a simple frequency distribution table for quantitative continuous variables. Each category in the table is represented by a bar the height of which corresponds to the frequency or percentage of the category but the width of the bar depend on the width of the interval itself. It will be noted that the final picture of the histogram will have no space between the consecutive bars also the bars are not necessarily of the same width.

16. The Histogram Examples: Age in YearsNumber of patients 0 -4 5 -10 10 -18 15 -8 20 - 256 Total46

17. The Histogram Examples: Number of patients Age in Years Figure (4): Distribution of a group of subjects by age

18. The Bar Chart This type of graph is the most suitable to represent data of three types of variables namely: A.Quantitative Discrete B.Qualitative Ordinal C.Qualitative Nominal Usually this graph is drawn for data presented in the form of simple or complex frequency distribution. The method used in this graph is to:  Represent each category in the frequency table by means of a rectangle or bar.  The height of this bar corresponds to the frequency or percentage of that category.  The width of the bar is chosen in such a way that all bars have the same width.  Another important feature of the bar chart is that a space must be left between every two consecutive bars and the width of this space must be constant. N.B.  The space between the bars is usually ½ - 1 width of the bar itself.  If we are dealing with qualitative –nominal variables then the bars could be drawn on the graph in a descending or ascending order of magnitude.

19. The Bar Chart Examples 1: Simple Frequency Distribution Table Marital StatusFrequency Single5 Married8 Divorced4 Widowed2 Total19

20. The Bar Chart Examples 1: Figure (5): Distribution of a group of subjects by marital status

21. The Bar Chart Examples 2: Complex Frequency Distribution Table Marital StatusSex MalesFemales Single57 Married88 Divorced43 Widowed22 Total1921

22. The Bar Chart Examples 1: Figure (6): Distribution of a group of subjects by marital status and sex

23. The Scatter Diagram When two quantitative variables such as blood pressure and weight have been measured on the same set of individuals, a simple and effective way of describing them is the scatter diagram. The scatter diagram uses two perpendicular axes one for each variable. Each individual’s X (first variable value) and y (2 nd variable value) measurements are plotted as a point on the diagram. The X value plotted on the horizontal scale. The Y value on the vertical scale. For example for the data below, the first individual’s weight is 67 kg, his blood pressure is 114 mmHg. The marked point in the figure corresponds to this individual's weight and blood pressure. Weight (kg)6769858374819792114 SBP (mmHg)11490889611392103123125

24. The Scatter diagram Weight (kg)6769858374819792114 SBP (mmHg)11490889611392103123125 Figure (7): Scatter diagram of weight and systolic blood pressure for a group of individuals

25. The Scatter Diagram From the scatter diagram we can often see whether the two variables X and Y are related. In the figure for example, we notice a tendency for high blood pressure and high weights to be associated.

26. The Pie Chart This type of graph can be used with all types of variables in simple or complex frequency distribution tables. And these are the rules for drawing pie chart: 1.A pie or circle is drawn using a suitable radius. 2.The pie is divided into a number of sectors equal to the number of categories in the table so that each sector will represent one category from the table. 3.The starting line for sub-division of the circle is usually taken as 12 o’clock radius. 4.The sub-division of the pie is usually in a clockwise direction. 5.The angle of the sector representing a particular category can be determined as follows: Sectoral angle= Frequency of each category X 360 Total frequency

27. The Pie Chart Examples 1: Angle for single= 20 x360 = 100⁰ 72 Angle for married= 30 x360 = 150⁰ 72 Angle for widowed= 10 x360 = 50⁰ 72 Angle for divorced= 20 x360 = 60⁰ 72 Total = 100+150+50+60= 360⁰ Marital StatusFrequency Single20 Married30 Divorced10 Widowed12 Total72

28. The Pie Chart Examples 1: Marital StatusFrequency% Single2028 Married3041 Divorced1014 Widowed1217 Total72100 Figure (8): Distribution of a group of subjects by marital status

29. The Pie Chart N.B. If we are using the pie chart to represent qualitative nominal variables then we can arrange the sectors of the pie in a descending order of magnitude.