Slide 3 - Data_Presentation

7/29/2019 Slide 3 - Data_Presentation

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Data Presentation

Dr. Atallah Rabi


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Summarizing Data

Frequency Table

Relative frequency Table

Bar ChartHistogram

Frequency Polygon

Cumulative frequency polygon Pie Chart


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Distribution of 50 patients at the surgicaldepartment of KAUH in May 2011 according totheir ageAge

(years)

Frequency %

20-


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Complex frequency distribution TableTable (III): Distribution of 20 lung cancer patients at the chest

department of KAUH and 40 controlsin May 2011 according tosmoking

Smokin

g

Lung cancerTotal

Cases ControlNo. % No. % No. %

Smoker15 75% 8 20% 23

38.3

3

Non

smoker 5 25% 32 80% 3761.6

7

Total 20 100 40 100 60 100


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Complex frequency distribution Table

Distribution of 60 patients at the chest department of KAUH

in May 2011 according to smoking & lung cancer

Smokin

g

Lung cancerTotal

positive negative

No. % No. % No. %

Smoker 15 65.2 8 34.8 23 100

Nonsmoker 5 13.5 32 86.5 37 100

Total 20 33.3 40 66.7 60 100


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Frequency polygon

Age

(years)

Sex Mid-point of

intervalMales Females

20 - 3 (12%) 2 (10%) (20+30) / 2 = 25

30 - 9 (36%) 6 (30%) (30+40) / 2 = 35

40- 7 (8%) 5 (25%) (40+50) / 2 = 45

50 - 4 (16%) 3 (15%) (50+60) / 2 = 55

60 - 70 2 (8%) 4 (20%) (60+70) / 2 = 65

Total 25(100%) 20(100%)


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Example of Frequency tables

Test

Score

Class

boundaries

Class Mark

(class Mid

Point)

Freque

ncy

0 - 19 -0.5 19.5 9.5 2

20 - 39 19.5 39.5 29.5 11

40 - 59 39.5 59.5 49.5 9

60 - 79 59.5 -79.5 69.5 11

80 - 99 79.5 99.5 89.5 8

100-119 99.5 119.5 110.5 7

120-139 119.5 139.5 129.5 2


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Frequency Tables

Class limitsare the largest or smallest numbers whichcan actually belong to each class. Each class has alower class limit and an upper class limit.

Class boundariesare the numbers which separateclasses. They are equally spaced halfway betweenneighboring class limits. For this example, theboundaries would be -0.5, 19.5, 39.5, 59.5, 79.5, 99.5,119.5, and 139.5.

Class marksare the midpoints of the classes. For thisexample, the class marks are 9.5, 29.5, 49.5, ....

Class widthis the difference between two classboundaries (or corresponding class limits). For thisexample, the class width is 20.0.


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Relative Frequency Table

Increased sample sizes require data to becondensed

frequency distribution:

summary table of data arranged into numericallyordered class groupings

value of individual observations are lost through thegrouping process

relative frequency: frequency / total count,expressed as proportion or percent independent of the size of the data set

used when comparing two data sets of different size


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Guidelines for constructing

frequency tables The classes must be "mutually exclusive"no element

can belong to more than one class.

Even if the frequency is zero, include each and everyclass.

Make all classes the same width. However, it is not amust. (open ended classes may be inevitable.)

Target between 5 and 12 classes, depending on therange and number of data points.

Number of classes (k) = 1 + 3.322*log(n) Keep the limits as simple and as convenient as possible

Interval width (H V LV)/k


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frequency table construction

determine the width of class intervals = range /number of classes

establish the boundaries of the classes classes must not overlap

must include the entire range of observations choose to facilitate interpretation

tally observations into appropriate classes

total the frequency for each class

calculate the relative frequency for each class calculate cumulative frequencies if needed


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Procedure for constructing a

frequency distribution1. Identify the high (H) and low (L) scores. Find the

range. Range = H - L.

2. Select a number of classes and a class width sothat the product is a bit larger than the range.

3. Pick a starting point a little smaller than L. Countfrom L by the width to obtain the classboundaries.

4. Observations that fall on class boundaries areplaced into the class interval to the right.

Note:1. The class width is the difference between the

upper- and lower-class boundaries.

2. There is no bestchoice for class widths, numberof classes, and starting points.


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Example

The hemoglobin test, a blood test given to diabetics during their periodiccheckups, indicates the level of control of blood sugar during the pasttwo to three months. The data in the table below was obtained for 40different diabetics at a university clinic that treats diabetic patients.

Construct a grouped frequency distribution using the classes 3.7 -


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Solution

Class Frequency com. Relative Cumulative Class

Boundaries f FrequencyFrequency Rel. Frequency MP

-------------------------------------------------------------------

4.0


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Important Characteristics of a

Table The title of the table is concise and is preceded by a

reference number. It clearly indicates what data are

tabulated and how these data are measured. When

appropriate, the number of cases represented by thedata is reported.

The sources of the data used are clearly cited. Only

original data are used without citation.

The table does not contribute to its own misinterpretation.All symbols and abbreviations are explained. The tables

rows and columns are clearly labeled. Row, column, and

grand totals are reported when appropriate.


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Data Presentation

Circle graphs(pie diagrams) show the

amount of data that belongs to each

category as a proportional part of a circle.

Bar graphsshow the amount of data that

belongs to each category as proportionally

sized rectangular areas.


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Example of frequencies

The table below lists the number of patients seen in a cliniclast week.

Friday 12

Saturday 42

Monday 15

Tuesday 23

Wednesday 35

Thursday 11

Describe the data using a circle graph and a bar graph


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Patients Seen Last Week


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Histogram

A bar graph representing a frequency distribution of aquantitative variable. A histogram is made up of thefollowing components:

1. A title, which identifies the population of interest.

2.A vertical scale, which identifies the frequencies in thevarious classes.

3. A horizontal scale, which identifies the variablex. Valuesfor the class boundaries or class marks may be labeledalong thex-axis. Use whichever method of labeling theaxis best presents the variable.

Note:

1. The relative frequency is sometimes used on the vertical scale.

2. It is possible to create a histogram based on class marks.


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Histogram

Vertical bar chart in which the bars are constructed atthe boundaries of each class. The rectangles or barsare the

same width,joined at the class boundaries, and their

height represents the frequency or relative frequency ofeach category

Classes of the variable listed along the horizontal axisall categories listed and evenly space

Frequencies or relative frequencies listed along thevertical axis scaled to accommodate the highestfrequency

Comparison Histogram: uses only relative frequencies


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Histogram showing duration of hospital

stay for 40 randomly selected patients.

0

1

2

3

4

5

6

7

8

9

10

Hospital stay (in days)

1 2 3 4 5 6 7 8 9 10


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0

5

10

15

20

25

30

35

40

45

50

Departmental units

Medical/Surgical ObstetricsPediatrics Critical care Psychiatric

Bar graph of registered nurses by

hospital departmental unit.


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Frequency Polygon

To draw a frequency polygon:

Place a dot above the midpoint of each

class interval

The height of dot corresponds to

frequency

Connects the dots by strait lines


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0

1

2

3

4

5

6

7

8

9

10

0 1 2 3 4 5 6 7 8 9 10 11


Frequency polygon showing duration of

hospital stay for 40 randomly selected

patients.


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0

10

20

30

40

50

60

70

80

90

100

0 1 2 3 4 5 6 7 8 9 10 11


Cumulative Relative Frequency polygon

showing duration of hospital stay among

40 randomly selected patients


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Line Graph

0

10

2030

40

50

60

1960 1970 1980 1990 2000Year

MMR/1000

Year MMR

1960 50

1970 45

1980 26

1990 15

2000 12

Figure (1): Maternal mortality rate ofJordan, 1960-2000


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Frequency polygon

Age Sex M-P

M F

20- (12%) (10%) 25

30- (36%) (30%) 35

40- (8%) (25%) 45

50- (16%) (15%) 55

60-70 (8%) (20%) 65

0

5

10

15

20

25

30

35

40

25 35 45 55 65Age

%Males Females

Figure (2): Distribution of 45 patients at (place) ,in (time) by age and sex


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Important Characteristics of a graph

The sources of the data used in the graph areclearly cited. Only original data are used withoutcitation.

The title of the graph is preceded by a figure

number for reference. The graphs name figurenumber and title usually appear below thegraph. The title of the graph is clear, concise,and descriptive.

Traditionally, graphs are read from the left to theright and from the bottom to the top. All legends,scales, scale labels, and keys are thereforeplaced accordingly.

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