Base line BP:120,145, 130,160,152,143,126.
After 4 week:122,142,135,158,155,140,130.
A clinical trial is planned to compare an experimental medication to lower blood pressure. a pilot study is conducted involving 7 subjects.The objective was to see how BP changes over time without medication.Is there any statistical significant difference in BP over time. Run test at a 5%level of significance.
To determine if there is a statistically significant difference in blood pressure (BP) over time without medication, we can use a statistical test called the paired t-test. This test compares the mean difference between two related samples (in this case, the baseline and after 4 weeks BP measurements) to determine if the difference is statistically significant.
Here is how you can perform the paired t-test to analyze the data:
Step 1: Calculate the difference between the baseline and after 4 weeks BP measurements for each subject. This will give you a new set of data representing the change in BP for each subject.
Baseline BP: 120, 145, 130, 160, 152, 143, 126
After 4 weeks BP: 122, 142, 135, 158, 155, 140, 130
Difference = After 4 weeks BP - Baseline BP
Difference: 2, -3, 5, -2, 3, -3, 4
Step 2: Calculate the mean and standard deviation of the differences.
Mean difference = sum of differences / number of differences
Standard deviation of differences = square root of [(sum of (difference - mean difference)^2) / (number of differences - 1)]
Mean difference = (2 - 3 + 5 - 2 + 3 - 3 + 4) / 7 = 1.14 (rounded to two decimal places)
Standard deviation of differences = √[(0.96^2 + 4.14^2 + 3.86^2 + 1.14^2 + 2.86^2 + 5.14^2 + 2.14^2) / 6] = 2.26 (rounded to two decimal places)
Step 3: Calculate the t-value using the formula:
t = (mean difference - hypothesized difference) / (standard deviation of differences / √number of differences)
In this case, the hypothesized difference is 0 since we want to determine if there is a significant difference in BP over time without medication.
t = (1.14 - 0) / (2.26 / √7) = 1.14 / 0.854 = 1.33 (rounded to two decimal places)
Step 4: Determine the critical t-value from the t-distribution table or using statistical software. Since the test is to be run at a 5% level of significance (α = 0.05) with 6 degrees of freedom (7 subjects - 1), the critical t-value is approximately 2.447 (two-tailed test).
Step 5: Compare the calculated t-value to the critical t-value.
Since the calculated t-value (1.33) is less than the critical t-value (2.447), we fail to reject the null hypothesis. This means that there is not enough evidence to conclude that there is a statistically significant difference in blood pressure over time without medication.
In conclusion, based on the results of the paired t-test, there is no statistical significant difference in blood pressure over time without medication.