Figure 3.1 Estimation of pH: precision and accuracy. Summary of data from Table 3.1. Group A (open bar) pH = 8.0 ± 1.453 (mean ± St. dev). Group B (shaded bar) pH = 8.59 ± 0.223. Closed circles indicate raw data values for each group.
So, you can have precision without accuracy, but you will never know how accurate you are without precision.
Errors in measurement
In all our experimental measurements, there will be various levels of accuracy and precision – as experimental pharmacologists, it is our responsibility to reduce as far as possible these potential sources of error in our observations. The problem is, however, no matter how hard we try, there will always be the possibility for error in our observations such that all measurements will have some degree of error.
The different sources of measurement error are as follows:
A blunder is where there is a gross mistake in recording data by, for example, recording the wrong value, misreading a scale. All blunders should be eliminated by recording data carefully. Blunders should not be included in the analysis of data.
An observer error may simply be an incorrect reading of a measurement or device. This is similar to a blunder but may be due to inexperience of the observer (e.g. recording the incorrect units of measurement; mg instead of g) or the incorrect recording of someone else's measurements. Such observational errors should be eliminated from any subsequent analysis unless the level of error can be accurately corrected.
A systematic error may occur if a machine is incorrectly calibrated. However, this may be compensated for if the degree of error is known. Systematic errors may be eliminated or corrected by the careful calibration of your equipment.
Random errors are positive and negative fluctuations in the data that are generally beyond the control of the experimenter. These may be unpredictable changes in ambient temperature, humidity, or lighting conditions or variations in human reaction time during manual measurement of time variables. The level of error may be reduced or even eliminated by taking repeated measurements (e.g. taking measurements in duplicate, triplicate, or more depending on the size of the error) to increase the accuracy of the reported, single, observation.
An instrumental error may occur if a piece of equipment is faulty and provides an incorrect reading. Generally, such issues are not apparent until after completion of the experiment. Such error data should be discarded.
So, the data we obtain from our experiments will always be a balance between our striving for accuracy and precision on one side against the possibility of an error in our measurements on the other side.
One method we may adopt to reduce error in our measurements and increase the precision of the data is to take repeated readings from the same sample. Unfortunately, however, such a process is often interpreted as producing independent observations, thereby increasing the number of samples in our data group(s). So, let us look at this more carefully and try to clear up any misunderstandings about this important issue.
Independent observations or duplicate/triplicate/quadruplicate? That is the question!
Example 3.2
Consider a simple experiment where you are trying to assess the effect of a drug or serum on the population growth of cells in culture. You carefully prepare two flasks containing equal volumes of identical growth medium, except that one flask also contains the drug or serum you are interested in. From your stock flask of cells in culture, you carefully remove an exact volume and add the aliquot to one of the flasks. As carefully as possible you repeat the process and add another aliquot to the second flask. The assumption here is that you have added the same number of cells to each flask so that the cell concentration in each flask is the same. You then leave the flasks to incubate. After a suitable incubation period (e.g. three days) you take four samples from each flask and estimate the cell concentration using a haemocytometer. This process is summarised in Figure 3.2.
Figure 3.2 Measurement of cell population in quadruplicate.
In this example, the cell population in each flask is measured in quadruplicate. This is a process whereby the precision of the final population value is improved by taking more than just one reading. It is important to note, however, that these are not independent readings as in each case the four samples are taken at the same time from the same flask. Consequently, the four values are averaged to provide a single value which is the best estimate of the population of cells in each flask, i.e. n = 1 for each flask. Such a process has often been erroneously misinterpreted as providing an n = 4, but this is incorrect simply because the four values for each flask are not independent. [See also Chapter 20, Example 20.3.]
Example 3.3
In contrast, consider a second, albeit similar, experiment. Here the initial set‐up is different in that six aliquots from the stock solution are placed in a multi‐well plate. Drug or serum is then added to three of the wells, the other three wells are the controls. All wells are then left to incubate for three days. At the end of the incubation period, four samples from each of these wells are placed on a haemocytometer and the cells were counted. This process is summarised in Figure 3.3, but note the important step of adding drug or serum to three samples independently prior to incubation.
Figure 3.3 Multiple estimates of cell population in quadruplicate.
In this latter example, the cell population from each initial aliquot is subsequently measured in quadruplicate to improve the precision of the final population value by taking more than just one reading. However, the fact that samples were taken from flask and drug or serum added prior to incubation now means that there are three independent wells containing medium alone or with drug or serum during the incubation period. Consequently, we now have three independent estimates of the cell population each of which has been estimated in quadruplicate, i.e. we now have n = 3 estimations of cell growth over the three days of incubation.
Note that the measurements in quadruplicate still only provide an n of 1 for each original aliquot, but the fact that we now prepared three aliquots means that we now have n = 3 for each flask. This is useful because we can now perform some meaningful analysis of the cell populations exposed to drug or serum compared with our control group.
Example
