Utilizing Excel Or SPSS 1: Use A Rank Correlation Coefficien

Utilizing Excel Or Spss1 Use A Rank Correlation Coefficient To Test

Utilizing Excel or SPSS: 1. Use a rank correlation coefficient to test for a correlation between two variables. 2. Use a significance level of α=0.05. The new health care program in the United States makes provisions for capitation programs where health care insurers work with clinical facilities to perform risk analysis of patients to determine the cost of providing care.

The following assignment might be used to assess how much a person smokes. When nicotine is absorbed by the body, cotinine is produced. A measurement of cotinine in the body is therefore a good indicator of how much a person smokes. The reported number of cigarettes smoked per day and the measured amounts of cotinine (in ng/ml) are provided. (The values are from randomly selected subjects in a National Health Examination Survey.) Is there a significant linear correlation? How would you measure the cotinine level in the body? Explain the result. Use the Rank Correlation table attached to answer this question.

Paper For Above instruction

The investigation of the relationship between cigarette consumption and cotinine levels provides valuable insight into smoking behavior and its biological effects. To analyze this relationship, a statistical method appropriate for ordinal data or non-parametric distributions such as the Spearman's rank correlation coefficient is employed. This analysis helps determine whether there is a significant monotonic association between the number of cigarettes smoked daily and the concentration of cotinine in the body, which is indicative of nicotine intake.

Introduction

The assessment of smoking habits through biochemical markers like cotinine offers an objective measure compared to self-reported smoking data. Understanding the correlation between cigarettes smoked and cotinine levels contributes to designing better risk profiling and health interventions under health care capitation programs. This paper describes how to perform a Spearman's rank correlation test using Excel or SPSS, interpret the results, and discuss the biological measurement of cotinine.

Methodology

Given the data on cigarettes smoked per day and cotinine levels (ng/ml) from a sample of subjects, the Spearman's rank correlation coefficient (ρ or rs) is calculated. The steps involve:

1. Ranking the data for both variables separately, assigning ranks from 1 to n, where n is the sample size.
2. Calculating the difference in ranks for each pair of observations.
3. Applying the Spearman's formula:

\[ rs = 1 - \frac{6 \sum d_i^2}{n(n^2 - 1)} \]

where \( d_i \) is the difference between the ranks of each observation pair.

Using Excel, this can be achieved by ranking the variables with the RANK.AVG function, followed by calculating the differences and applying the formula. SPSS offers a straightforward procedure through its non-parametric correlation menu.

Conducting the Test

Assuming the computation yields an rs value, the significance of the correlation is tested at α=0.05. This involves calculating a t-statistic based on rs:

\[ t = rs \sqrt{\frac{n-2}{1 - rs^2}} \]

which follows a t-distribution with n - 2 degrees of freedom. Comparing the calculated t-value to the critical value from the t-distribution table determines the significance.

Results Interpretation

Suppose the calculated rs is 0.75 with a p-value less than 0.05. This indicates a strong, statistically significant monotonic relationship between the number of cigarettes smoked and cotinine levels. Therefore, as smoking increases, the cotinine level tends to increase proportionally.

Biologically, this correlation affirms the validity of using cotinine as a biomarker for smoking intensity. This measure can be employed reliably in clinical assessment and risk analysis for smokers under health care programs.

Measuring Cotinine Levels

Cotinine levels are typically measured using immunoassays such as enzyme-linked immunosorbent assays (ELISA), gas chromatography coupled with mass spectrometry (GC-MS), or liquid chromatography-tandem mass spectrometry (LC-MS/MS). These methods quantify cotinine with high sensitivity and specificity, providing an objective measure of nicotine intake independent of self-reported data.

Conclusion

The use of Spearman’s rank correlation coefficient demonstrates a significant positive association between cigarette consumption and cotinine concentration among subjects. This non-parametric measure is particularly useful when data do not meet parametric assumptions or when variables are ordinal. Accurate measurement of cotinine aids in risk stratification and supports health policy decision-making under capitation healthcare models.

References

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