Part I: Nonparametric Methods
A sign test is a nonparametric method used in statistics for comparison of a single sample with a hypothesized value. The test is commonly used in situations where a paired t-test is traditionally applied. In the study, a sample of n patients is used in determining the preference for central nervous system saturation. The main objective of conducting the test was to determine whether a difference in preferences between the central nervous system saturation and the time of oxygen admission existed. Sign test was explored in paired data whereby central nervous system saturation data from ten patients was collected on admission and 6 hours after admission to an Intensive Care Unit (ICU). A plus and a minus sign were used to record the preference data. The plus sign was used when the difference between the time of admission and 6 hours after admission was positive while the minus sign was used when the difference was negative (Walley, 2011).
On the other hand, the sign test is commonly used where the researcher had initially placed study hypotheses. From the study, the null hypotheses suggested that there could be no effect of 6 hours of ICU treatment on central venous oxygen saturation treatment. The null hypotheses suggested that the difference between the time of admission and time after 6 hours would be zero. The sign test method used was to achieve 50% of the differences below zero (negative) and the other 50% above zero (positive). The results indicated otherwise because only 2 differences recorded a minus sign and this led to a 0.11 probability of occurrence in case the null hypothesis was true. From the normal distribution table, the P value of 0.02 was observed from the paired t-test conducted. The two tests provided different results that concluded that, for sign test the differences should be independent of one another while for t-test the differences should follow a normal distribution (Mendenhall & Beaver, 2003).
Part II: Cancer Case Scenario
Various regression and correlation constructs were used in the scenario. Firstly, the study used P-value and r-value for hypotheses test and correlation of coefficient respectively. The following correlation values used to find the relationship between variables by determining the preference of the results observed. In addition, the correlations determined the association between the measure of adiposity (BMI, WHR) and serum estradiol. To determine the relationship between various variable, an X-Y graph should be constructed. These forms the regression constructs of the study. The linear regression of (Y, X) is equivalent to (r2, P).
In analyzing the cancer case scenario, the sign test would be the most appropriate followed by the hypothesis test (the t-test). To start with, I would get the difference between BMI and serum estradiol values from the excel sheet to determine the data preference. Using a null hypothesis that states that, there is a crude association between the two measure of adiposity (BMI and WHR) and serum estradiol. If more than 50% of total people tested show negative results, the null hypothesis is true. From table 1, the positive signs exceeded the negative signs showing that the null hypothesis is false. This indicates a crude association between either measure of adiposity (BMI, WHR) and serum estradiol. The following method is recommendable because it avoids complex calculations and easily arrives at the answer. Secondly, I would carry out a t-test to determine P-values and r-values. The following constructs will be used because the study compares only two variables at a time. Only 49 out of 151 samples tested had negative nalues. This is a probability of (49/151) = 0.3245. Thus; P = 0.3425. From the normal distribution table, r = 0.633 (Ahsanullah & Nevzorov, 2013). The following results show aa lack of correlation between the measure of adiposity and serum estradiol.
Ahsanullah, M., & Nevzorov, V. B. (2013). An introduction to order statistics. Amsterdam:
Mendenhall, W., & Beaver, R. J. (2003). Introduction to probability and statistics (11th ed.).
Pacific Grove, CA: Thomson-Brooks/Cole.
Walley, K. R. (2011). “Use of central venous oxygen saturation to guide therapy”, Critical Care
Research Laboratories. Vol. 184, No. 5.