Statistical analysis of patient blood pressure measurements
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¶ … Probability
Summarizing Data and Probability
Blood Pressure Data
Patient ID
Systolic
Diastolic
1st Patient
2nd Patient
3rd Patient
4th Patient
5th Patient
6th Patient
7th Patient
8th Patient
9th Patient
Diastolic Blood Pressure Measurements
Mean
Mean is also referred to as average. This is obtained by adding up a set of tallies and thereafter dividing the resulting summation by the number of tallies. The general formula for obtaining mean is as follows:
Mean of the systolic blood pressure measurements
Mean of the diastolic blood pressure measurements
Median
The median is the middle value of an ordered set or list of numbers.
Median of the systolic blood pressure measurements
Ordered set is as follows:
90, 110, 120, 120, 130, 130, 150, 150, 160
Therefore, the median is 130
Median of the diastolic blood pressure measurements
Ordered set is as follows
40, 60, 60, 70, 80, 80, 90, 90, 110
Therefore, the median is 80
1. Standard Deviation
The standard deviation is calculated using the following formula:
i. Standard deviation for systolic blood pressure measurements
Patient ID
Systolic
x - µ
(x -µ )2
1st Patient
31.11111
2nd Patient
21.11111
3rd Patient
-18.8889
4th Patient
-8.88889
79.01235
5th Patient
1.
1.234568
6th Patient
21.11111
7th Patient
1.
1.234568
8th Patient
-8.88889
79.01235
9th Patient
90
-38.8889
Summation
1,160
3,889
Mean
= 3,889 / (9-1)
= 3,889 / 8
= 486.125
Standard deviation = ?486.125
= 22.05
ii. Standard deviation for diastolic blood pressure measurements
Patient ID
Diastolic
x - µ
(x -µ )2
1st Patient
34.44444
2nd Patient
90
14.44444
3rd Patient
60
-15.5556
4th Patient
80
4.
19.75309
5th Patient
70
-5.55556
30.8642
6th Patient
90
14.44444
7th Patient
80
4.
19.75309
8th Patient
60
-15.5556
9th Patient
40
-35.5556
Summation
Mean
75.55556
= 3,422.22 / (9-1)
= 3,422.22 / 8
= 427.7775
Standard deviation = ?427.7775
= 20.68
1. Variance
The variance is obtained by squaring the standard deviation. Therefore, the variance is obtained as (std. dev) 2.
i. Variance for diastolic blood pressure measurements
20.682 = 427.66
ii. Variance for systolic blood pressure measurements
22.052 = 486.20
Histogram and box plot for systolic blood pressure
0. Histogram
Bin
Frequency
85
0
1
1
4
0
3
More
0
Histogram and box plot for diastolic blood pressure
Bin
Frequency
40
1
60
2
80
3
2
1
More
0
Systolic
Diastolic
Min
90
40
Q1
60
Median
80
Q3
90
Max
Specific ways in which probability is used in clinical research
One specific way in which probability is used in clinical research on a daily basis is in making medical decisions centered on results from different radiologic diagnostic implements. In radiologic research, one often requires to make conclusions regarding the comparative performance of one analytical tool matched with a different one for the uncovering of a certain disorder of interest. Such clinical research relies, for most part, on probability theory and its applications (Joseph and Reinhold, 2002). The other specific way is in diagnosis, where the clinical researchers are vested in computing the probability that the condition of interest is present because of results of a certain clinical test. This probability hinges on how profound and precise that test is in diagnosing the condition and on the contextual rate of the condition in the population (Joseph and Reinhold, 2002). For clinical research trials to be successful, probability has to be applied in making decisions for the circumstances and situations that are pertinent to the research (Joseph and Reinhold, 2002).
The impact or importance of probability in clinical research and practice
Probability, which is part of statistical inference, enables one to make conclusions regarding the individualities of a population on the foundation of data gathered from a sample of subjects from that particular population (Joseph and Reinhold, 2002). Probability is significant and has a massive impact on clinical research and practice because just about all the statistical inferences characteristically perceived in the medical literature are founded on probability models. These probabilities link summary statistics computed by making use of the experiential data to approximations of parameter values in the population (Joseph and Reinhold, 2002). It is through probability that the researchers in clinical trials are able to select the most pertinent and useful data for the condition being considered.
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