Question

Carpal tunnel syndrome is a common wrist complaint resulting from a compressed nerve. It is often the result of extended use of repetitive wrist movements, such as those associated with the use of a keyboard. Among the various treatments available, two are common: apply a splint or perform surgery. The splint treatment has the advantages of being noninvasive. simpler, quicker, and much less expensive. But do those advantages justify the splint treatment instead of the surgery treatment? A critical factor is the success of the treatment. In one randomized controlled trial. 156 patients were identified as having carpal tunnel syndrome, they were treated with either splinting or surgery, then they were evaluated one year later. Success was defined to be "completely recovered" or "much improved," and it was determined by using patient scores and other measured outcomes, such as the numbers of nights that patients awoke from symptoms. Among 73 patients treated with surgery and evaluated one year later. 67 were found to have successful treatments. Among 83 patients treated with splints and evaluated one year later. 60 were found to have successful treatments. These results are summarized in Table 9-1 (based on data from "Splinting vs Surgery in the Treatment of Carpal Tunnel Syndrome," by Gerritsen et al., Journal of the American Medical Association, Vol. 288, No. 10 (Links to an external site.)). It would really do you justice to read the actual article so you can see what is involved in publishing research.

Examining the results of the trials in Table 9-1, it appears that surgery is a better treatment because its success rate is 92%, compared to only 72% for the splint treatment. However, we should not form a conclusion based on those success rates alone. We should also take into account the sample sizes and the magnitude of the difference between the two rates. We should also consider the sampling distribution that applies. We need a procedure that takes all of these relevant factors into account.

Table 9-1 includes two sample proportions: 67/73 (for the surgery treatment group) and 60/83 (for the splint treatment group). In a journal article about the trial, authors claimed that "treatment with open carpal tunnel release surgery resulted in better outcomes than treatment with wrist splinting for patients with CTS (carpal tunnel syndrome)." Do the sample results really support the claim that surgery is better? Using the methods discussed in Chapter 9, determine whether the surgery treatment is significantly better than the splint treatment.

Table 9-1	Treatments of Carpal Tunnel Syndrome
		Treatment
		Surgery	Splint
Success one year after treatment		67	60
Total number treated		73	83
Success rate		92%	72%

Use the sample data from Table 9-1 and use a 0.05 significance level to test the claim that the success rate with surgery is better than the success rate with splinting.

What to submit for the assignment.

1. State the null and alternate hypothesis in the form of p₁ and p₂.
2. Identify the type of test (right/left) or two-tailed.
3. Use the technology of your choice to find and state the value of the test statistic, and either the critical or p-value. *Note – This is a 2 sample proportional Z test.
4. Provide an interpretation of the results.
5. Use the sample data from Table 9-1 to construct a 90% confidence interval estimate of the difference between the two population proportions. You can use the technology of your choice, or you can grind through the calculation by hand.
6. Provide an interpretation of the results for the confidence interval.

Answer 1

• Let,

         population proportion of success with surgery and population proportion of success with splinting

• The null and the alternative hypotheses are :-

         

• This is a right tailed test .

This is a 2 sample proportional Z test .

• Using an online calculator to compute the t-statistic and p-value we get the following result :

             Test-statistic value = 3.2006

             P- value = 0.00069

(link : https://www.socscistatistics.com/tests/ztest/default2.aspx , if you want to know the formula to calculate test statistic and p-value by hand, please let me know through the comments)

• Interpretation : Since p - value is less than 0.05 , we reject the null hypothesis and conclude that the sample data provides sufficient evidence to support hte claim .
• Using an online calculator to compute the 90% confidence interval we get :

          90% C.I = [ - 0.309306 , - 0.090694 ]

(link : https://www2.ccrb.cuhk.edu.hk/stat/confidence%20interval/CI%20for%202-proportions.htm , if you want to know the formula to calculate it by hand, please let me know through the comments)

• Interpretation : Since the interval does not include Zero, rather only includes negative values, we are 90% confident that the success rate for surgery is significantly greater than the success rate for splinting .