Statistical Analysis on Enduring of Post Graduate Institute of Medical Education & Research, Chandigarh Due to Infected Loam Causes

The data is taken for cancer endurings recorded by Post Graduate Institute of Medical Education & Reseaarch, Chandigarh. The authentic reason of the cancer is never recorded but by the old scenario of Punjab, Haryana, Himachal Pradesh and Rajasthan, it seems to cause by the loam impurities and mixture of polluted loam and ground loam. We are not able to recognise the causes of cancer till the date but perhaps it causes due to smoking, non-veg, drinking of liquor, impurities of loam (hardness of the loam), and soil mixture of fertilizers and many other reasons to cause the cancer. We are going to use only data of Post Graduate Institute of Medical Education & Reseaarch, Chandigarh established in Punjab and comparative study between Punjab and other (HP, Haryana and Rajasthan). As Post Graduate Institute of Medical Education & Reseaarch, Chandigarh is established in Punjab, so endurings of Punjab are higher than other states in it. But we like to inform you the scenario of Punjab is very critical than other states regarding cancer endurings.

Below is the comparative statistical survey of cancer endurings of Punjab with HP, Haryana and Rajasthan in Post Graduate Institute of Medical Education & Reseaarch, Chandigarh.

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 significance. 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 significance of the various results obtained from small samples. 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 1 = mean of the first sample 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. and also D.F. (Degree of Freedom) = n1 + n2 – 2, If the calculated value of t is ˃ t0.05 (t0.01), the difference between the sample means is said to be significant at 5% (1%) level of significance otherwise the data are said to be consistent with the hypothesis. Here in data of Post Graduate Institute of Medical Education & Reseaarch, Chandigarh, n1 = n2 =6, After calculation, we get

1= 396, 2= 37, S1= 178.7106, S2= 13.9284,

And using all these values in the Student‘s t test, we get

Since the critical value is ˂ the actual value So the hypothesis at 95% confidence is rejected and is significant. Hence the Result of comparison is failed which is only because the endurings are generally admitted to the nearest hospital that provides more facilities with basic needs. 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 affect by cancer in Punjab, Haryana and Rajasthan at very high rate.

Wright, D.B.I. (2006). Comparing groups in a before-after design: When t test and ANCOVA produce different results. British Journal of Educational Psychology 76 (3), pp. 663-675. Yudkin, P.L. & Moher, M. (2001). Putting theory into practice: a cluster randomized trial with a small number of clusters. Statistics in Medicine 20 (3), pp. 341-349. Zar, J.H. (1999). Biostatistical analysis. 4th Edn. Prentice Hall International, London. Zimmerman, D.W. (1997). A note on interpretation of the paired-samples t test. Journal of Educational and Behavioral Statistics 22 (3), pp. 349-360. Zimmerman, D.W. (2004). Inflation of Type I error rates by unequal variances associated with parametric, nonparametric, and rank-transformation tests. Psicologica 25, pp. 103-133. Zimmerman, D.W. (2004). A note on preliminary tests of equality of variances. British Journal of Mathematical and Statistical Psychology 25, pp. 103-133.

small inter subject correlation. Journal of Statistical Computation and Simulation 74, pp. 691-696. Zimmerman, D.W. (2005). Increasing power in paired-samples designs by correcting the Student t statistic for correlation. Zimmerman, D.W. & Zumbo, B.D. (2009). Hazards in choosing between pooled and separate-variances t tests. Psicologica 30, pp. 371-390. Joffe S. & Miller F.G. (2012). Equipoise: Asking the right questions for clinical trial design. Nat Rev Clin Oncol 9: pp. 230-235. Meurer WJ, Lewis RJ, Berry DA (2012). Adaptive clinical trials: A partial remedy for the therapeutic misconception? JAMA 307: pp. 2377-2378.

Scholar of Mathematics, OPJS University, Churu, Rajasthan