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Rank Correlation and Statistical Essay


Abstract

This study seeks to establish whether the relationship between the numbers of cigarettes smoked and the level of cotinine in the body is linear. Data of randomly selected subjects from National Health Examination Survey in the United States is the basis of this study. The methodology involves determining the strength of the relationship using Spearman’s rank correlation.

Data analysis is by use of SPSS, and the interpretation of the output of the analysis is given in the body of the paper under the analysis and result section. The researcher uses Wilcoxon’s Ranks test to verify the nature of the relationship between these variables. The null hypothesis of the study argues that the relationship between the concentration of cotinine in the body, and the number of cigarettes smoked is linear.

On the other hand, the alternative hypothesis argues that the relationship between the number of cigarettes smoked and the level of cotinine in the body is nonlinear. If the test statistic obtained is less than the level of significance (0.05), it means that the null hypothesis is not true and the researcher should reject it for the alternative hypothesis. This quest forms the essence of the study.

Introduction

Healthcare programs in the USA make provisions for the capitation of programs that facilitate collaborations between health insurers and clinical facilities to perform risk analysis of patients to help healthcare stakeholders determine the cost of care delivery (Ezzati, Lopez, Rodgers, & Christopher, 2004).

This report seeks to determine whether the rate of smoking correlates with risk of developing cancer by computing the concentration of cotinine in the body (Visweswara, 2007).

The study uses values from randomly selected subjects in the National Health Examination Survey (Carver & Nash, 2009: Lehman & Romano, 2005). This study seeks to determine whether there is a significant linear correlation between the number of cigarettes smoked and the level of cotinine in a smoker’s body.

Data analysis and Results

Table 1. Test Statisticsb,c
Y – X
Z -2.981a
Asymp. Sig. (2-tailed) .003
Monte Carlo Sig. (2-tailed) Sig. .000
95% Confidence Interval Lower Bound .000
Upper Bound .221
Monte Carlo Sig. (1-tailed) Sig. .000
95% Confidence Interval Lower Bound .000
Upper Bound .221
a. Based on negative ranks.
b. Wilcoxon Signed Ranks Test
c. Based on 12 sampled tables with starting seed 2000000.

The mean number of cigarettes smoked per subject was 14.58, while the mean concentration of nicotine level in the body of a subject was 175.2050ng/ml. Wilcoxon’s ranks test was useful in determining the relationship between these two variables (Wickham, 2012).

The null hypothesis to be tested argues that the relationship between the level of cotinine in a smoker’s body and the number of cigarettes smoked is linear (Watkins, Scheaffer, & Cobb, 2010: DiClemente, Salazar, & Crosby, 2013).

Conclusion

The test statistic obtained is less than the level of significance, which is approximately about 1.96. The results of the analysis reject the null hypothesis, while it verifies the alternative hypothesis (Lehman, 2005). The test statistic value, -2.981, is less than the level of significance.

Hence, this result rejects the null hypothesis and supports the position that the numbers of cigarettes smoked do not determine the level of cotinine in the body and, thus, some factors external to this study are involved (Boyle, Gray, Henningfield, Seffrin, & Zaton’ski, 2010: Weinberg & Abramowitz, 2002: “Introduction to Hypothesis Testing,” 2006).

This condition indicates an opportunity for a research to investigate on the external factors that lead to an increase in the risk of cancer associated with cigarette smokers.

References

Boyle, P., Gray, N., Henningfield, J., Seffrin, J., & Zatonski, W. A. (2010). Tobacco: Science, Policy and Public Health. Oxford : Oxford University Press.

Carver, R. H., & Nash, G. J. (2012). Doing Data Analysis with SPSS Version 18.0. Boston : Cengage Learning.

DiClemente, R. J., Salazar, L. F., & Crosby, R. A. (2013). Health Behavior Theory for Public Health: Principles, Foundations, and Applications. Burlington, MA: Jones & Bartlett Learning.

Ezzati, M., Lopez, A. D., Rodgers, A. A., & Christopher, F. J. (2004). Comparative Quantification of Health Risks: Global and Regional Burden of Disease. Geneva: World Health Organization.

Introduction to Hypothesis Testing. (2006, July 13). Retrieved from sjsu:

Lehman, A. (2005). mp For Basic Univariate And Multivariate Statistics: A Step-by-step Guide. Chapel Hill: University of North Carolina.

Lehman, E. L., & Romano, J. P. (2005). Testing Statistcial Hypotheses. Berkeley: Springer.

Visweswara, R. K. (2007). Bostatistics: A Manual of Statistical Methods for Use in Health, Nutrition and Anthropology. Delhi: K Visweswara Rao.

Watkins, A. E., Scheaffer, R. L., & Cobb, G. W. (2010). Statistics: From Data to Decision. John Wiley & Sons. Inc: Hoboken.

Weinberg, S. L., & Abramowitz, S. K. (2008). Statistics Using SPSS: An Integrative Approach. Cambridge : Cambridge University Press.

Wickham, C. (2012, October 17). Stat 411/511: Wilcoxon Rank Sum. Web.

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IvyPanda. (2019) 'Rank Correlation and Statistical'. 22 December.

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