Data from a cross-sectional study of patients with malignant melanoma are shown

Question

Data from a cross-sectional study of patients with malignant melanoma are shown below. For a sample of 400 patients, the site of the tumour and its histological type were recorded.

Carry out an appropriate statistical analysis that examines the relationship between the type of melanoma and where it is situated, and comment on the significance of these variables.

SITE Tumour type Head and Neck Trunk Extremities Total Hutchinson’s melanotic freckle 22 2 10 34 Superficial spreading melanoma 16 54 115 185 Nodular 19 33 73 125 Indeterminate 11 17 28 56 Total 68 106 226 400

Explanation / Answer

here we use chi-square test for examines the relationship between the type of melanoma and where it is situated with

Null hypothesis H0: there is no relationship between the type of melanoma and where it is situated,

alternate hypothesis H1: relationship between the type of melanoma and where it is situated,

and ch-square=sum( O-E)2/E=65.81 with (r-1)(c-1)=(4-1)*(3-1)=8 df

critical chi-square(0.05,8)=15.51 is less than calcuated chi-square=65.81, so we fail to accept H0 and conclude that there is relationship between the type of melanoma and where it is situated,

follwoing information has been generated using ms-excel

observed(O) Expected(E) E (O-E) (O-E)2 (O-E)2/E 22 34*68/400 5.78 16.2200 263.0884 45.5170 2 34*106/400 9.01 -7.0100 49.1401 5.4540 10 34*226/400 19.21 -9.2100 84.8241 4.4156 16 185*68/400 31.45 -15.4500 238.7025 7.5899 54 185*106/400 49.025 4.9750 24.7506 0.5049 115 185*226/400 104.525 10.4750 109.7256 1.0498 19 125*68/400 21.25 -2.2500 5.0625 0.2382 33 125*106/400 33.125 -0.1250 0.0156 0.0005 73 125*226/400 70.625 2.3750 5.6406 0.0799 11 56*68/400 9.52 1.4800 2.1904 0.2301 17 56*106/400 14.84 2.1600 4.6656 0.3144 28 56*226/400 31.64 -3.6400 13.2496 0.4188 sum 400.00 400.00 0.00 801.06 65.81

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