CROSS TABLES TWO AND MULTIWAY GRAPHS MARGINAL TABLE

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 The distribution of 60 infants according to their birthweights Bithweight Frequency Relative Freq. (%) <2500 gr 14 23. 33 2500 gr 46 76. 67 Total 60 100. 00

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?

History of hypertansion Not present Present Total BWT <2500 >=2500 4 40 10 6 14 46 Total 44 16 60

BWT <2500 >=2500 Total History of hypertansion Count % Not present 4 9, 1 40 90, 9 44 100, 0 Present 10 62, 5 6 37, 5 16 100, 0 Total 14 23, 3 46 76, 7 60 100, 0

100 80 60 63 40 37 20 14 0 Not smoking 100 86 63 Smoking 80 Percent <2500 >=2500 86 60 40 37 20 14 0 Not smoking Smoking <2500 >=2500

BWT History of hypertansion N Min Max Mean Std. Dev. Not present 44 2300 4990 3349, 3 638, 5 Present 16 1588 4360 2550, 0 754, 9 Total 60 1588 4990 3136, 1 754, 4

6000 5000 BWT 13 4000 3000 2000 1000 N= 36 Not smoking 24 Smoking SMOKE

MEAN± 1 SD 5000 4000 3000 2000 N= 36 24 Not smoking SMOKE Smoking

6000 5000 BWT 4000 3000 2000 1000 Nonsmoking SMOKE

BWT SMOKE History of hypertansion Not smoking Not present Present Total Smoking Not present Present Total <2500 Count % 2 6, 7 3 50, 0 5 13, 9 2 14, 3 7 70, 0 9 37, 5 >=2500 Count % 28 93, 3 3 50, 0 31 86, 1 12 85, 7 3 30, 0 15 62, 5 Total Count % 30 100, 0 6 100, 0 36 100, 0 14 100, 0 10 100, 0 24 100, 0

BWT SMOKE History of hypertansion Not smoking Not present Smoking Total N Minimum Maximum Mean Std. Dev. 30 2300 4990 3458, 0 647, 4 Present 6 1588 4360 2872, 5 1097, 4 Total 36 1588 4990 3360, 4 753, 9 Not present 14 2410 4250 3116, 2 572, 5 Present 10 1790 2960 2356, 5 412, 0 Total 24 1790 4250 2799, 7 630, 9 Not present- 44 2300 4990 3349, 3 638, 5 Present 16 1588 4360 2550, 0 754, 9 Total 60 1588 4990 3136, 1 754, 4

6000 5000 + 4000 3000 2000 1000 3600 2000 6000 30 6 14 10 Not smoking SMOKE 3458 5000 3200 3116 4000 3000 2800 BWT Mean BWT 3400 3000 1000 N = 30 6 14 10 Not smoking SMOKE History of hypertans + Mean ± 1 SD BWT 5000 History of hypertans - 2873 History of hypertans 2600 2400 2200 2357 Not smoking SMOKE Smoking 3000 2000 History of hypertans + 1000 Smoking Not smoking SMOKE + -

Population, Turkey in 1965 and 1995 Age 0 -4 5 -9 10 -14 15 -19 20 -24 25 -29 30 -34 35 -39 40 -44 45 -49 50 -54 55 -59 60 -64 65 -69 70 -74 75+ 1965 Male 14, 7 15, 1 12, 9 9, 7 7, 6 6, 6 7, 1 6, 3 4, 4 2, 8 3, 8 2, 8 1, 6 0, 9 1995 Female 14, 7 14, 6 11, 7 8, 9 7, 4 7, 6 7, 4 6, 1 4, 4 2, 8 3, 8 2, 7 3, 3 1, 8 1, 4 Male 10, 6 10, 9 10, 8 9, 8 8, 5 8, 1 7 5, 8 4, 6 3, 4 2, 9 2, 8 2, 1 1, 2 1 Female 10, 5 10, 3 10, 6 9, 6 8, 4 7, 9 6, 8 5, 6 4, 5 3, 6 3, 2 3, 0 2, 5 1, 4

Population Pyramid of Turkey, 1965 Age 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 Male 15 12 9 % 6 3 0 0 Female 3 6 9 % 12 1

12 Population Pyramid of Turkey, 1995 Age 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 Male 9 6 % 3 0 0 female 3 6 % 9 12

Population Pyramid of Turkey, 1965 15 Age 75+ 70 -74 6569 6064 5559 5054 4549 4044 3539 3034 2529 2024 1519 1014 5 -9 0 -4 Male 12 9 6 % 3 0 0 Female 3 6 9 % 12 15 Population Pyramid of Turkey, 1995 Age 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 Male 12 9 6 3 0 female 0 3 6 9 12

SCATTER PLOT Scatter 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: 1 Age, x SBP, y 2 3 4 Patients 5 6 7 8 9 10 48 47 63 71 54 84 56 69 71 38 68 83 94 90 90 80 100 86 98 71