Data Analysis: Basic Statistics Analysis was performed on an anonymized database of medical patients from a particular doctor’s office. The data set contained four categorical variables and two continuous variables that could be used for hypothesis testing.  A summary of the variables presented in the data set, along with descriptive statistics, are presented in Figure 1. Figure 1: Descriptive Statistics of Variables in Database

QUESTION

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Data Analysis: Basic Statistics

Analysis was performed on an anonymized database of medical patients from a particular doctor’s office. The data set contained four categorical variables and two continuous variables that could be used for hypothesis testing.  A summary of the variables presented in the data set, along with descriptive statistics, are presented in Figure 1.

Figure 1: Descriptive Statistics of Variables in Database

Z-Test on Proportion of Smokers

A hypothesis test was run on the proportion of smokers in the data set to understand if the population proportion is bigger than 60%.  This right tailed test was conducted with an alpha value of 0.05, allowing for 5% Type I error in the test.  The null hypothesis, H0, was p = 0.6; the alternative hypothesis, Ha, was p > 0.6.

The proportion of smokers found in the sample data was equal to 68%.  The z-score for this proportion is found by using the formula .

The critical z-value for a right tailed test with significance level of 0.05 is 1.645.  Since the test statistic is less than the critical value, there is insufficient evidence to reject the null hypothesis, and we cannot conclude that the proportion of smokers in the population is greater than 60%. The p-value for this test was 0.082 which is greater than the significance level of 0.05.  This is further evidence that null hypothesis should not be rejected; the null hypothesis is rejected when the p-value is less than the significance level.

T-test on Medication Use

A final test was conducted to understand if patients who had experienced a fracture took more medications than patients who did not have a fracture.  The null hypothesis for this test was that the average number of medications taken were the same between the groups regardless of having experienced a fracture; the alternative hypothesis was that the average number of medications in patients who experienced a fracture was different than the average number of medications taken by patients who had not experienced a fracture.  This is a two tailed test.

Excel was used to perform the test, and summary statistics are shown in Figure 2.

Figure 2: Summary Statistics for T-Test

The confidence interval for this test can be calculated using the following formulas:

For a 95% confidence interval with 16 degrees of freedom, the critical value used was 2.12, and the confidence interval was found to be [-1.66, 2.75].  Since zero is in the confidence interval, and the test statistic is less than the critical value, and the p-value of 0.61 was higher than the significance level of 0.05, we failed to reject the null hypothesis that the average medications taken by patients who had experienced a fracture was higher than patients who did not have a fracture.

ANSWER

Statistical Analysis of Medical Patient Data: Smoking Proportion and Medication Use

Introduction

In this analysis, a dataset from a doctor’s office containing medical patient information was examined. The dataset consisted of categorical and continuous variables subjected to hypothesis testing. This essay focuses on two statistical tests conducted to explore the proportion of smokers and the difference in medication use between patients with and without fractures. Descriptive statistics and test results are presented to provide insights into the findings.

Z-Test on Proportion of Smokers

The first test aimed to determine if the proportion of smokers in the population was greater than 60%. The null hypothesis (H0) assumed a proportion of smokers equal to 60%, while the alternative hypothesis (Ha) suggested a proportion greater than 60% (Dahiru, 2011). With an alpha value of 0.05, corresponding to a 5% Type I error, the critical z-value for a right-tailed test was determined as 1.645.

After analyzing the sample data, it was found that the proportion of smokers was 68%. To calculate the z-score, the formula for proportions was utilized. Comparing the test statistic to the critical value, it was observed that the z-score was lower than the critical value. Consequently, there was insufficient evidence to reject the null hypothesis (Large Sample Tests for a Population Proportion, n.d.). Additionally, the p-value obtained from the test was 0.082, higher than the significance level of 0.05. This further supported the decision not to reject the null hypothesis, as the p-value did not fall below the specified significance level.

T-Test on Medication Use

The second test aimed to assess whether patients who experienced fractures consumed a significantly different number of medications compared to those without fractures. This was a two-tailed test, with the null hypothesis stating that the average number of medications taken by both groups was the same (Suresh & Chandrashekara, 2012). The alternative hypothesis suggested a difference in the average medication use between the two groups.

The analysis was performed using Excel, and summary statistics were obtained. To establish a 95% confidence interval with 16 degrees of freedom, a critical value of 2.12 was used. The calculated confidence interval was [-1.66, 2.75]. Notably, since zero fell within the confidence interval and the test statistic was lower than the critical value, the null hypothesis was not rejected. Furthermore, the obtained p-value of 0.61 exceeded the significance level of 0.05. Hence, it was concluded that there was insufficient evidence to support the claim that patients who experienced fractures consumed a significantly different number of medications compared to those without fractures.

Conclusion

In conclusion, the statistical analysis of the medical patient data focused on the proportion of smokers and medication use. For the proportion of smokers, the null hypothesis was not rejected, indicating that there was insufficient evidence to suggest a proportion greater than 60%. Similarly, for medication use, no significant difference was found between patients with and without fractures. These findings demonstrate the importance of rigorous statistical analysis in drawing reliable conclusions from medical datasets. Further research and exploration can provide deeper insights into the factors influencing these variables and inform medical decision-making processes.

References

Dahiru, T. (2011). P-Value, a true test of statistical significance? a cautionary note. Annals of Ibadan Postgraduate Medicine, 6(1). https://doi.org/10.4314/aipm.v6i1.64038 

Large Sample Tests for a Population Proportion. (n.d.). https://saylordotorg.github.io/text_introductory-statistics/s12-05-large-sample-tests-for-a-popul.html 

Suresh, K., & Chandrashekara, S. (2012). Sample size estimation and power analysis for clinical research studies. Journal of Human Reproductive Sciences, 5(1), 7. https://doi.org/10.4103/0974-1208.97779