Stastical Testing of Cancer Patients in J&K and Rajasthan with Punjab

INTRODUCTION

The data is taken for cancer patients recorded by Max Super Speciality Hospital Bathinda. The authentic reason of the cancer is never recorded but by the old circumstances of Punjab, Haryana, Himachal Pradesh and Rajasthan, it seems to cause by the water impurities and mixture of polluted water and ground water. We are not able to recognise the causes of cancer till the date but perhaps it causes due to smoking, non shrubbery, drinking of liquor, impurities of water (solidity of the water), and soil mixture of fertilizers and many other reasons to cause the cancer. We are going to use only data of Max Super Speciality hospital customary in Punjab and comparative study between Punjab and other (J&K and Rajasthan), through Max Super Speciality hospital is customary in Punjab, and so patients of Punjab are higher than other states in it. We like to inform you the circumstances of Punjab is very decisive than other states regarding cancer patients.

Below is the comparative statistical survey of cancer patients of Punjab with J&K and Rajasthan in Max Super speciality Hospital, Bathinda.

The connotation test, student t-test is as follows:

W.S. Gosset (1876-1937) in the early 1900 worked on t- distribution theoretically. Gosset was employed by the Guinness and Sons, a Dublin under their own names. So Gosset adopted the pen name ―student‖ and published his findings under this name. So the t- distribution is commonly known as Student‘s t- distribution or t-distribution. The Student‘s t- distribution is used when the sample size is 30 or less and the population standard deviation is unknown. 1. The variable t- distribution ranges from minus infinity to plus infinity. 2. The constant c is actually a function of ν (pronounced as nu). So for a particular value of ν, the distribution of f (t) is completely specified. Thus f(t) is a family of functions, for each value of ν. 3. The variance of t- distribution is greater than 1, but approaches 1 as the number of degrees of freedom; therefore the sample size becomes large. Thus as the sample size increases, the variance of t- distribution approaches the variance of the standard normal distribution. For infinite value of ν, the t- distribution and normal distribution are exactly equal. Hence there is a widely practised rule of sample size n ˃ 30 may be considered as large and the standard normal distribution may appropriately be uses as an approximation to t- distribution. Where the latter is the theoretically correct functional form.

The t- table is the probability integral of t- distribution. It gives, over a range of values of ν, the probabilities of exceeding by chance values of t at different levels of connotation. The t- distribution has a different value for each degree of freedom. When the degree of freedom is infinitely large, the t- distribution is equivalent to normal distribution and probabilities shown in the normal distribution tables are applicable.

Student‘s t- distribution is generally used to test the connotation of the various results obtained from small samples. Testing difference between means of two samples: given two independent random samples of size n1 and n2 with means 1and 2, and standard deviations S1 and S2 we may interested in testing the hypothesis that the samples come from the same normal population. To carry out the test, we calculate the statistics as follows: Where 2 = mean of the second sample1 n1 = number of observations in the first sample n2 = number of observations in the second sample S = combined standard deviation. If the calculated value of t is ˃ t0.05 (t0.01), the difference between the sample means is said to be momentous at 5% (1%) level of connotation otherwise the data are said to be consistent with the hypothesis. Here in data of Max Super Speciality Hospital Bathinda, n1 = n2 =6, After calculation, we get And using all these values in the Student‘s t test, we get

Since the decisive value is ˂ the actual value So the hypothesis at 95% confidence is rejected and is momentous. Hence the Result of comparison is failed which is only because the patients are generally admitted to the nearest hospital that provides more facilities with basic requirements It is nature of human beings that more comfort and facility with minimum expenditure is preferred. Although the result is not according to the expectation but still there is need to study about the results of cancer as people are going to impinge on by cancer in Punjab, Haryana and Rajasthan at very high rate.

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Scholar of Mathematics, Sr. Assistant Professor, New Horizon College of Engineering, Bangalore