Question

Dentists make many people nervous (even more so than statisticians!). To see whether such nervousness elevates blood pressure, the blood pressure and pulse rates of 60 subjects were measured in a dental setting and in a medical setting ("The Effect of the Dental Setting on Blood Pressure Measurement," American Journal of \(P u b-\) lic Health \([1983]: 1210-1214)\). For each subject, the difference (dental-setting blood pressure minus medicalsetting blood pressure) was calculated. The analogous differences were also calculated for pulse rates. Summary data follows.

Short answer

The conclusion whether there is a significant difference in blood pressure or pulse rates between dental and medical settings can be drawn after statistical analysis and depends on the results of the t-test. The t-test results on the obtained sample data will provide a p-value, based on which the null hypothesis can be either accepted or declined.

Step-by-step solution

Understand the data

Here, we have data for 60 subjects for their blood pressure and pulse rate recorded in two different settings, Dental and Medical. We are given the difference values, i.e., dental-setting blood pressure minus medical-setting blood pressure, and likewise for pulse rates. To analyze this data, we will have to calculate the mean difference and standard deviation of difference, and use these values to perform the appropriate statistical test.

Calculating mean and standard deviation

First thing we need to do is calculate the mean difference and standard deviation of the difference. The mean difference is the total of all the differences divided by the count of values (60 in this case). The standard deviation, on the other hand, is a measure of how much these values vary from the mean value. We can calculate standard deviation using the formula \(\sqrt{\frac{\Sigma (x_i - \bar{x})^2}{N-1}}\) where \(x_i\) is each difference value and \(\bar{x}\) is the mean difference.

Hypothesis testing

Once we have the mean difference and standard deviation, we can perform a paired t-test to investigate whether there is a significant difference in blood pressure and pulse rates in Dental setting versus Medical setting. The null hypothesis assumes that there is no difference (mean difference is zero), and the alternative hypothesis assumes that there is a difference (mean difference is not zero).

Interpretation

After performing the statistical test, the results have to be interpreted correctly. If the p-value is less than the threshold (usually 0.05), then the null hypothesis is rejected, concluding that there is a significant difference in blood pressure or pulse rates between dental and medical settings. Alternatively, if the p-value is more than the threshold, then the null hypothesis is upheld, indicating that there is no difference between these two setting.