dr. ameer kadhim hussein m.b.ch.b.ficms (com.)

Biostatistics

Presentation of data

DR. AMEER KADHIM HUSSEIN

M.B.CH.B.FICMS (COM.)

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).

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.

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.

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.

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.

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.

Criteria For proper graph

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.

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.

Tabular and Graphical Presentation of data

Qualitative Data

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.

FREQUENCY DISTRIBUTION

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

FREQUENCY DISTRIBUTION

Frequency Results

3 poor

3 good

2 Very good

2 excellent

10 Total

RELATIVE FREQUENCY AND PERCENT

FREQUENCY DISTRIBUTION

Percent

frequency

Relative

frequency Results

30% 0.3 poor

30% 0.3 good

20% 0.2 Very good

20% 0.2 excellent

100% 1 Total

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.

BAR GRAPH

0%

10%

20%

30%

PoorGood

Very goodExcellent

30% 30%

20% 20%

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.

PIE CHART

30%

30%

20%

20%

Poor

Good

Very good

Excellent

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.

CROSS-TABULATIONS

Total

Group

Gender Control Case

40 10 30 Male

60 40 20 Female

100 50 50 Total

Table: Distribution of case and control groups by gender

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 ).

Quantitative Data

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

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 = 1 + 3.322 (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.

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.

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.

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.

THE FREQUENCY DISTRIBUTION

91 78 93 57 75 52 99 80 97 62

71 69 72 89 66 75 79 75 72 76

104 74 62 68 97 105 77 65 80 109

85 97 88 68 83 68 71 69 67 74

62 82 98 101 79 105 79 69 62 73

The following are the heart rate of 50 patients

1. Number of classes :

(K) = 1+3.322 Log 50

= 1+3.322 (1.69)

= 1+ 5.64 = 6.64 6

2. Width of class interval

W = R/K

= 109 – 52 /6 = 57/6 = 9.5 10

ANSWER

Frequency, cumulative frequency, relative frequency

and cumulative relative frequency distribution of

heart rate of 50 patients

Cumulative

relative

frequency

Relative

frequency

Cumulative

frequency

Frequency Class

interval

0.04 0.04 2 2 50-59

0.3 0.26 15 13 60-69

0.62 0.32 31 16 70-79

0.76 0.14 38 7 80-89

0.9 0.14 45 7 90-99

1 0.1 50 5 100-109

1 50 Total

Example: The following are the hemoglobin values

(g/100ml) of 30 children receiving treatment for hemolytic anemia.

10.0 8.7 6.7 7.8 8.9 10.8

9.7 9.9 8.5 7.5 9.0 10.0

9.1 9.1 8.4 10.6 10.2 8.5

8.6 9.7 9.7 9.6 10.2 11.4

12.2 9.4 9.3 8.4 8.2 9.2

Order the sample observations by size,

6.7 7.5 7.8 8.2 8.4 8.4

8.5 8.5 8.6 8.7 8.9 9.0

9.1 9.1 9.2 9.3 9.4 9.6

9.7 9.7 9.7 9.9 10.0 10.0

10.2 10.2 10.6 10.8 11.4 12.2

No. of classes = 1+ 3.322 (Log10 30) 6

Width = (12.2 – 6.7) / 6 1

Cumulative

relative

frequency

Relative

frequency

Cumulative

frequency Midpoint Frequency

True class

limits

0.033 0.033 1 7 1 6.5 -7.5

0.2 0.167 6 8 5 7.5 - 8.5

0.567 0.367 17 9 11 8.5 - 9.5

0.867 0.300 26 10 9 9.5-10.5

0.967 0.100 29 11 3 10.5 - 11.5

1 0.033 30 12 1 11.5 - 12.5

1 30 Total

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.

HISTOGRAM

0

2

4

6

8

10

12N

o. o

f ch

ildre

n

Hemoglobin values (g/100ml)Fig ( ) Hemoglobin values of children receiving

treatment for hemolytic anemia

6.5 7.5 8.5 9.5 10.5 11.5 12.5

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.

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.

SCATTER DIAGRAM

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).

Money spent this week

$0.00

$5.00

$10.00

$15.00

$20.00

$25.00

Mon. Tues. Wed. Thurs. Fri.

Day

Am

outn

of $

LINE GRAPH

Calories burned while running

0

20

40

60

80

100

120

140

160

180

200

220

240

30 60 90 120

150

180

210

240

270

Hours

Cal

orie

s

PICTORIAL PRESENTATION

Small pictures or symbols are used to present data.

For example: picture of no horn on road near a hospital.

1. PICTOGRAM

PICTORIAL PRESENTATION

These maps are prepared to show the geographical distribution of

frequencies of a characteristic.

2. MAP DIAGRAM OR SPOT MAP

Thank you