Chapter 2:Strategies for Understanding the Meanings of Data · 2/9/2017 · Dr. Ahmed Jaradat, AGU Chapter 2:Strategies for Understanding the Meanings of Data. Learning Outcomes:

Key Words

Frequency Tables

Pie Chart, Bar Chart, Line Chart

Stem and Leaf

Histogram, Polygon, Shapes

Cross Tabulation

Scatter Diagram

Parameter, Statistic

Mean (Average), Median, Mode, Percentiles

Range, Variance, Standard Deviation, Coefficient of Variation

Box–and-Whisker Plots

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Dr. Ahmed Jaradat, AGU

Chapter 2:Strategies for Understanding

the Meanings of Data

Learning Outcomes:

After studying this chapter, you will:

1. Understand how data can be appropriately organized and

displayed.

2. Understand how to reduce data sets into a few useful,

descriptive measures.

3. Be able to calculate and interpret measures of central

tendency, such as the mean, median, and mode.

4. Be able to calculate and interpret measures of dispersion,

such as the range, variance, and standard deviation.

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Ahmed Jaradat, AGU 2

Qualitative (Categorical) and quantitative variables are:Graphed

Charted

Tabled and

Statistically summarized

in very different ways

3

Descriptive Statistics:

Organizing and Summarizing Data

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Grade

SexFemale 6 31 18 29 33

Male 9 14 20 11 10

GroupA 5 19 18 18 25

B 10 26 20 22 18

Total

Data Summarization and Presentation Qualitative Data:

1. Tables

1. Frequency Table

2. Relative Frequency Table

3. Percent Frequency Table

4. Cross Tabulation

2. Graphs

1. Bar chart

a. Simple Bar Chart

b.Clustered Bar Chart

c.Stacked Bar Chart

2. Pie Chart

Quantitative Data:

1. Tables1. Frequency Table

2. Relative Frequency Table

3. Percent Frequency Table

4. Cumulative Frequency Table

5. Cumulative Relative Freq. Table

6. Stem and Leaf Display

7. Cross Tabulation

2. Graphs1. Line Graph

2. Histogram

3. Frequency Polygon

4. Cumulative Frequency Polygon

5. Scatter Diagram

6. Box and Whisker Plot

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5

Summarization and Presentation of Qualitative Data:

Frequency Tables

Smoking Status Frequency

Ever Smoked Cigarettes 3222

Stop Smoked Cigarettes 748

Currently Smoked

Cigarettes1274

Total 5244

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Frequency distribution of Smoking Status of 5244 persons

Relative

Frequency

0.614

0.143

0.243

1.000

Percent

Frequency

61.4

14.3

24.3

100.0


Simple Bar Chart

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7

0

500

1000

1500

2000

2500

3000

Ever Smoked

Cigarettes

Stop Smoked

Cigarettes

Currently

Smoked

Cigarettes

Nu

mb

er

of

Pe

rso

ns

Smoking Status

Male

Femal

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0

200

400

600

800

1000

1200

< 18 18-25 25-30 30-40 >40

Nu

mb

er

of

pe

rso

ns

Age

Ever Smoked Cigarettes

Stop Smoked Cigarettes

Currently SmokedCigarettes


Clustered (Grouped) Bar Chart

8

0

200

400

600

800

1000

1200

1400

1600

1800

< 18 18-25 25-30 30-40 >40

Nu

mb

er o

f P

ers

on

s

Age

Currently Smoked Cigarettes

Stop Smoked Cigarettes

Ever Smoked Cigarettes

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Stacked Bar Chart

Pie Chart

Summarization and Presentation of

Quantitative Data: Frequency Tables

Grade

Limits

Number of

Students

40-49 9

50-59 6

60-69 45

70-79 38

80-89 40

90-100 43

181

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Relative

Frequency

0.05

0.03

0.25

0.21

0.22

0.24

1.00

Percent

Frequency

4.97

3.31

24.86

20.99

22.10

23.76

100.00

Cumulative

Frequency

9

15

60

98

138

181

Cumulative

Percent Freq.

4.97

8.29

33.15

54.14

76.24

100.00

Summarizing Biostatistics Final Grades 2013/2014 Using Tables

Summarization and Presentation of

STA231: Biostatistics, Academic Year 2013/2014

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GradeTotal Average

< 60 60-69 70-79 80-89 90-100

SexFemale 6 31 18 29 33 117 78.69

Male 9 14 20 11 10 64 72.77

GroupA 5 19 18 18 25 85 78.61

B 10 26 20 22 18 96 74.81

Total 15

8.29%

45

24.86%

38

20.99%

40

22.10%

43

23.76%181

100%76.6

Stem and Leaf Display:

Biostatistics Final Grades/ 2013-2014

11

Stem

4

5

6

7

8

9

10

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Leaf

115577799

111233

000000000000111223455556666666777777778899999

00001111112222333444444455556666677889

0000001122222222233333344556666678888999

0001111222222333444555566666788999

000000000

9

6

45

38

40

34

9

Line Chart:

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Temperatures in Manama, in Co, over a 12-hour period

Line graph

0

1

2

3

4

5

6

7

2010 2011 2012 2013 2014

Nu

mb

er

of

clin

icia

ns

Clinic 1

Clinic 2

Clinic 3

Number of Clinicians Working in Each Clinic During Years 2010-2014

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Biostatistics Dr.

Ahmed Jaradat, AGU

Use a bar graph if you are not looking for trends (or

patterns) over time; and the items (or categories) are not

parts of a whole

Use a pie chart if you need to compare different parts of

a whole, there is no time involved and there are not too

many items (or categories).

Use a line graph if you need to see how a quantity has

changed over time. Line graphs enable us to find trends

(or patterns) over time.

14

Choosing the Right Graph

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How to Choose between Tables, Figures,

and Text to Present Data

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Use Table Use Figure Use Text

To show many and precise

numerical values and other

specific data in a small space

To show trends, patterns, and

relationships across and

between data sets when general

pattern is more important than

the exact data values (What to

use: graphs, data plots)

When you don’t have extensive

or complicated data to present

To compare and contrast data

values or characteristics among

related items or items with

several shared characteristics or

variables

To summarize research results

(What to use: graphs, data plots,

maps, and pie charts)

When putting you data into a

table would mean creating a

table with 2 or fewer columns

To show the presence or

absence of specific

characteristics

To present a visual explanation

of a sequence of events,

procedures, geographic features,

or physical characteristics (What

to use: schematic diagrams,

images, photographs, and maps)

When the data that you are

planning to present is peripheral

to the study or irrelevant to the

main study findings

Histogram:

Biostatistics Final Grades/2013-2014

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Frequency Polygon

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Ahmed Jaradat, AGU

Frequency Polygon

Relative Frequencies of Serum Cholesterol levels for 2294 U.S. Males, 1976-1980

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19

Shapes of Histogram

Variable Variable

Symmetry:

A histogram is said to be symmetric, if when we draw a vertical

line down the center of the histogram, the two sides are

identical in shape and size:

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Skewness : A skewed histogram is one with a long tail

extending to either the right or the left:

20

Shapes of Histograms

Positively SkewedNegatively Skewed

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Bell Shape: A special type of symmetric Unimodal

histogram is one that is bell shaped:

Many statistical techniques require that the population

be bell shaped.

Drawing the histogram helps verify the shape of the

population in question

21

Shapes of Histograms

Bell Shaped

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Thus far we have focused on methods that are used to summarize the

data for one variable at a time.

Often one is interested in tabular and graphical methods that will help

understand the relationship between two variables.

Cross-tabulation and a scatter diagram are two methods for summarizing

the data for two (or more) variables simultaneously.

Cross-tabulation: is a tabular method for summarizing the data for two

variables simultaneously.

Cross-tabulation can be used when:

◦ Both variables are qualitative

◦ Both variables are quantitative

◦ One variable is quantitative and one is qualitative

The left and top margin labels define the classes for the two variables.

22

Cross-Tabulations and Scatter Diagrams

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Distribution of 60 patients at the chest department of Al-Salmaniya

hospital in May 2008 according to smoking & lung cancer

Smoking

Lung CancerTotal

Positive Negative

No. % No. % No. %

Smoker 15 65.2 8 34.8 23 100

Non Smoker 5 13.5 32 86.5 37 100

Total 20 33.3 40 66.7 60 100

23

Cross-Tabulations: Both Variables are Qualitative

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Cross-Tabulations:

One Variable is Quantitative and One is Qualitative

Age

(Years)

Sex

Male Female Total

20 -30 3 (12%) 2 (10%) 5

30 -40 9 (36%) 6 (30%) 15

40-50 7 (8%) 5 (25%) 12

50 -60 4 (16%) 3 (15%) 7

60 - 0 2 (8%) 4 (20%) 6

Total 25 (100%) 20 (100%) 45

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Both Variables are Quantitative

Height/cm

Weight/kg <150 150-160 >160 Total

< 50

50-69

70-89

90-109

≥110

Total

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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

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Scatter Diagram

Positive Correlation Negative Correlation No Correlation

Documents

Chapter 2:Strategies for Understanding the Meanings of Data · 2/9/2017 · Dr. Ahmed Jaradat, AGU Chapter 2:Strategies for Understanding the Meanings of Data. Learning Outcomes: