CROSS TABLES TWO AND MULTIWAY GRAPHS

CROSS TABLES

TWO AND MULTIWAY GRAPHS

MARGINAL TABLE

Marginal table gives us the distribution of n observations among classes or subgroups of a single variable.

Example

Bithweight Frequency Relative Freq.(%)

<2500 gr 14 23.33

2500 gr 46 76.67

Total 60 100.00

The distribution of 60 infants according to their birthweights

CROSS TABLE

Cross table gives us the distribution of n observations among classes or subgroups of two or more variables simultaneously.

Cross table shows the relationship between these variables if it exists.

In these tables, generally there are two kinds of variables

•Dependent (output)variable

•Independent (input)variable

The easiest way to identify the independent variable and dependent variable is to ask the question

Which variable depends on which?

5 31 36

9 15 24

14 46 60

SMOKENot smoking

Smoking

Total

<2500 >=2500

BWT

Total

4 40 44

10 6 16

14 46 60

History ofhypertansion

Not present

Present

Total

<2500 >=2500

BWT

Total

4 9,1 40 90,9 44 100,0

10 62,5 6 37,5 16 100,0

14 23,3 46 76,7 60 100,0

History ofhypertansionNot present

Present

Total

Count % Count % Count %

<2500 >=2500

BWT

Total

5 13,9 31 86,1 36 100,0

9 37,5 15 62,5 24 100,0

14 23,3 46 76,7 60 100,0

SMOKENot smoking

Smoking

Total

Count % Count % Count %

<2500 >=2500

BWT

Total

>=2500

<2500

Pe

rce

nt

100

80

60

40

20

0Not smoking Smoking

63

37

86

14

>=2500

<2500

Pe

rce

nt

100

80

60

40

20

0Not smoking Smoking

63

37

86

14

36 1588 4990 3360,4 753,9

24 1790 4250 2799,7 630,9

60 1588 4990 3136,1 754,4

SMOKENot smoking

Smoking

Total

N Min Max Mean Std. Dev.

BWT

44 2300 4990 3349,3 638,5

16 1588 4360 2550,0 754,9

60 1588 4990 3136,1 754,4

History

of hypertansion

Not present

Present

Total

N Min Max Mean Std. Dev.

BWT

2436N =

SMOKE

SmokingNot smoking

BW

T

6000

5000

4000

3000

2000

1000

13

2436N =

SMOKE

SmokingNot smoking

ME

AN

±1S

D

5000

4000

3000

2000

SMOKE

SmokingNonsmoking

BW

T

6000

5000

4000

3000

2000

1000

2 6,7 28 93,3 30 100,0

3 50,0 3 50,0 6 100,0

5 13,9 31 86,1 36 100,0

2 14,3 12 85,7 14 100,0

7 70,0 3 30,0 10 100,0

9 37,5 15 62,5 24 100,0

History of hypertansionNot present

Present

Total

Not present

Present

Total

SMOKENot smoking

Smoking

Count % Count % Count %

<2500 >=2500

BWT

Total

30 2300 4990 3458,0 647,4

6 1588 4360 2872,5 1097,4

36 1588 4990 3360,4 753,9

14 2410 4250 3116,2 572,5

10 1790 2960 2356,5 412,0

24 1790 4250 2799,7 630,9

44 2300 4990 3349,3 638,5

16 1588 4360 2550,0 754,9

60 1588 4990 3136,1 754,4

History of hypertansion

Not present

Present

Total

Not present

Present

Total

Not present-

Present

Total

SMOKE

Not smoking

Smoking

Total

N Minimum Maximum Mean Std. Dev.

BWT

106 1430N =

SmokingNot smoking

Mea

n ±

1 S

D

5000

4000

3000

2000

1000

History of hypertans

-

+

SMOKE

SMOKE

SmokingNot smoking

BW

T

6000

5000

4000

3000

2000

1000

History of hypertans

+

-

106 1430N =SmokingNot smoking

BW

T6000

5000

4000

3000

2000

1000

History of hypertans

-

+

SMOKE

SMOKE

SmokingNot smoking

Mea

n B

WT

3600

3400

3200

3000

2800

2600

2400

2200

History of hypertans

-

+2357

2873

3116

3458

Male Female Male Female0-4 14,7 14,7 10,6 10,55-9 15,1 14,6 10,6 10,3

10-14 12,9 11,7 10,9 10,615-19 9,7 8,9 10,8 10,620-24 7,6 7,4 9,8 9,625-29 6,6 7,6 8,5 8,430-34 7,1 7,4 8,1 7,935-39 6,3 6,1 7 6,840-44 4,4 4,4 5,8 5,645-49 2,8 2,8 4,6 4,550-54 3,8 3,8 3,4 3,655-59 2,8 2,7 2,9 3,260-64 2,8 3,3 2,8 3,065-69 1,6 1,8 2,1 2,570-74 0,9 1,4 1,2 1,475+ 0,9 1,4 1 1,4

1965 1995

Population, Turkey in 1965 and 1995

Age

03691215

%

Male

Population Pyramid of Turkey, 1965

Female

0 3 6 9 12 15

%

75+ 70-74 65-69 60-64 55-59 50-54 45-49 40-44 35-39 30-34 25-29 20-24 15-19 10-14 5-9

0-4

Age

Population Pyramid of Turkey, 1995

75+ 70-74 65-69 60-64 55-59 50-54 45-49 40-44 35-39 30-34 25-29 20-24 15-19 10-14 5-9

0-4

Age

036912

%

Male

0 3 6 9 12

%

female

03691215

%

Male Female

0 3 6 9 12 15

%

75+ 70-74 65-69 60-64 55-59 50-54 45-49 40-44 35-39 30-34 25-29 20-24 15-19 10-14 5-9

0-4

Age

036912

Male

0 3 6 9 12

female

75+ 70-74 65-69 60-64 55-59 50-54 45-49 40-44 35-39 30-34 25-29 20-24 15-19 10-14 5-9

0-4

Age

Population Pyramid of Turkey, 1965

Population Pyramid of Turkey, 1995

SCATTER PLOTScatter plots illustrate the relationship between two characteristics when both are measured on a numerical scale.

The characteristic hypothesized to explain or predict or the one that occurs first (independent) is placed on x-axis. The characteristic or outcome to be explained or predicted or one that occurs second (dependent) is placed on y-axis. Each observation is represented by a small circle.

Example Ages and sistolic blood pressures of 10 patients are given in the following table:

Patients

1 2 3 4 5 6 7 8 9 10

Age, x 48 47 63 71 54

84 56 69 71

38

SBP, y 68 83 94 90 90

80 100

86 98

71

AGE

807060504030

SB

P

110

100

90

80

70

60x=48

y=68

AGE

5040302010

BW

T6000

5000

4000

3000

2000

1000SMOKE

AGE5040302010

BW

T

6000

5000

4000

3000

2000

1000

Smoking

Not smoking

SCATTER PLOT MATRIX

Y

X1

X2

HEAD CIRCUMFERENCE FOR AGE- GIRLS (TURKEY)

Hea

d C

ircu

mfe

renc

e

AGE (MONTHS)

Head Circumference