Statisticians have it legibly inscribed in their books that in any experiment conducted on a popuplation or on a sample of the population, the test of normality must almost always validate your work.
That is to say, majority of the observations (about 95% of them) should span three (3) standard deviation units on either side of the graph; half of the remaining 5%, each, should occupy the ends of the graph.
(The standard normal graph is bell-shaped! If you still can’t visualize, picture a cone sitting on its circular base.)
The 95% observations for majority means that in any study of a continuous variable of a population or sample, ninety-five percent(95%) of the population will be within a certain range of values for that continuous variable. Only few or very few of the population will be at the extremes, representing ‘exceptional’ values.
To simplify it, if you are to conduct a class exercise on students of a particuar class, majority of students will score around 40-69, very few will score 70-100, and very few will score 0-39 (yeah! It is an exceptional range , isn’t it?)
What really does account for these variations in the marks obtained by these students who were taught by the same teacher in the same class at that same time (assuming they were all in class?) Does the difference stem from the fact that we all understand differently? Or, perhaps, we read different books?
Well, I think a fact is a fact! Maybe teaching methods will be different, but the final result should be the same: we are all to understand right!
As a student statistcian, my curiosity spurred me on…
After mid-semester examinations, I did a post hoc anaylsis on quite a number of students (n=10) on what they thought or knew about Area Under Curve (AUC) for plasma concentration-time curve.
Five of them said same things, three of them said they did not know, and the remaining two also said same things but differently from the other five.
“Area under curve gives the total concentration of drug in your body.” Response from the five students.
“Area under curve gives the average concentration of drug in the body during a period of time.” Response from the two students.
“No idea.” Response from the three students.
When a plasma concentration-time curve is drawn for a particular drug administered extravascularly, a bell-shaped graph is obtained. To be able to apply the test of normality to any trial, the continuous variables studied must be fairly constant. In other words, the variable must not change so rapidly in the course of the experiment.
In the concentration-time curve, two processes act concurrently: Absorption and Elimination. The latter is dependent on the former. In that, the fraction eliminated is high if the amount absorbed is also high.
The time-axis gives the period our experiment is supposed to span. If we are assuming a period of 24hrs, then the Area Under Curve gives a certain value measured over 24hrs.
The process of absorption marked (+) because we are increasing blood concentration and elimination marked (-) because we are losing can be akin to these values, if we are assuming these values arbitrarly for the 24 hour period: +10, -5, +15, -7, +9, -4.
Since those two aforementioned phases occur simultaneously and differently (in terms of rate), then we can as well assume that the value obtained at the end of the 24 hour period gives us the average or mean concentration of the drug present in the blood. Does it make sense?
So in short, AUC gives or measures the AVERAGE CONCENTRATION of a drug sample over a PERIOD OF TIME. Omitting the time factor would mean that the concentrations at time t= 0 and t= 10 hours will give same areas under the curve. And that is veritably not true.
What then is the significance of AUC?
The plasma therapeutic concentration of Theophylline is quoted as 10-20 ug/ml. Assuming at the end of our calculation for AUC we obtained say, 12ug/ml, then this value is within the therapeutic range and hence therapeutic effects will still be observed during the 24 hour period for that particular administered dose (the initial starting dose). That means that the dose will be given once daily.