Errors in Pharmaceutical Analysis

 Chapter 2

 Errors in Pharmaceutical Analysis

 Introduction

•  These errors may be predictable or unpredictable. Depending on the nature and source, errors have been classified and discussed as below. Two major categories of errors are known as absolute error and relative errors. The difference between the experimental mean and a true value is known as 'absolute error'. Sometimes a term 'relative error' is used in analysis. The relative error is the value found by dividing the absolute error by the true value. 

Source and Type of Errors

• In pharmaceutical analysis, it is generally accepted that results of analysis are subject to errors. The variations or differences in the results are caused by errors of various sources and these errors are of different nature. Depending on the nature of errors which affects the accuracy or precision of a measured quantity, they are classified as two main classes: 

• 1 Determinate Errors

• These are ascertainable errors that can be either avoided or corrected. The error may be constant as in the case of weighing with uncalibrated weights or in measuring a volume using burette or pipette. Such measurable determinate errors are categorized as systematic errors. The determinate errors arise due to,

• (a) Instrumental errors: These errors are caused by faulty equipment's or low-quality equipment's which do not perform well.

• (b) Personal errors: These errors occur by persons who are handling the method of analysis. The error may be resulted due to carelessness or ignorance and even by unskilled persons. This error is also called operative error.

• (c) Chemical errors: These errors are resulted by using chemicals and reagents with impurities or contaminants which may interfere with the reactions, thus affects the results.

• (d) Errors in the methodology: This is a most serious error in analysis as the error arises due to faulty method, e.g. co-precipitation of impurities, slight solubility of precipitate, incomplete reactions etc. Errors of this category are usually detectable and can be eliminated to a large extent.

• 2. Indeterminate Errors

• Indeterminate errors are often called accidental or random errors. They are revealed by small differences in series of measurements made by the same analyst under identical conditions. They cannot be predicted and hence cannot be eliminated. Such accidental errors will follow a random distribution pattern and the mathematical laws of probability can be applied to get net conclusion regarding the results.

• 1. Very large errors are unlikely to occur.

• 2. Smaller errors occur with greater frequency than large errors, and

• 3. The errors on positive and negative side occur with equal probability. 

Methods to Minimize Errors

• Errors can be minimized by understanding the source and type of errors thoroughly. The predictable errors can be minimized by correcting the factor directly whereas the unpredictable errors can be minimized by following the standard protocols and good laboratory practices (GLP) strictly.

• Some of the methods to minimize the errors are discussed as follows: 

• 1. Instrumental Errors: 

• These errors can be minimized by checking thoroughly the equipment used for the analysis before starting of any analysis. Proper calibration equipment used for the analysis before starting of any analysis. Proper calibration should be performed to ensure the performance of equipment's. Faulty equipment's should be corrected by experts and rechecked for accuracy of results. If the performance is not satisfied, then replacement should be done.

• 2. Personal Errors: Skilled persons should be employed or the knowledge of the operator to perform analysis is to be ensured prior to analysis. Regular reporting and monitoring of analysis can be done.

Accuracy and Precision

• The term 'accuracy' refers to the agreement of experimental value with the true value and it is usually expressed in terms of error. Accuracy is also described as degree of agreement between a measured value and the accepted true value. In scientific experiments since no measurement is completely accurate, the true value is not known within certain limits. It is simply taken as a value that has been 'accepted' and is generally a mean calculated from the results of several determinations from many laboratories using different techniques. Precision is defined as, "the degree of agreement between various results of the same quantity". In other words, it is the reproducibility of result. For example, if a result of an analysis is 6.18 when it was performed for the first time. If the analysis is repeated four times, and the values obtained are 6.17, 6.19, 6.18 and 6.17, then the precision is calculated by comparing the values with each other. The closeness of the values decides the precision of the method.

Significant Figures 

• In analysis, it is important to understand the term 'significant figures. While recording the values measured in analysis, some errors do happen if the figures are not properly recorded. The number of significant figures can be defined as, "the number of digits necessary to express the results of a measurement consistent with the measured precision". Each digit denotes the actual quantity that it specifies. The proper manner of expressing a result or observations is to retain such number of figures that all are known with certainty except the last.

• It should be clear that, zeroes are employed to denote the significant part of measurement to denote tens, hundreds, thousands etc. or merely to locate the decimal point. Thus, zeroes within a number like 25.05 and 1350 are significant as they express the exact quantity while zeroes in figures like 0.0234 only show the magnitude of the other digits. For example, in quantities 1.2670 g and 1.0056 g the zeroes are significant, but in the quantity 0.0035 kg the zeroes are not as important; the zeroes in 0.0035 kg serve only to locate the decimal point; this is omissible by the use of proper units like 03.5 g. Thus, in 1.2570 g and 1.0056 g there are five significant figures.

• The digits of a number which are needed to express the precision of measurement must be retained. When a volume is between 15.7 ml and 15.9 ml should be written as 15.8 ml and not as 15.80, since the latter would indicate that the value is between 15.79 ml and 15.81 ml. If a weight is to the nearest of 0.1 mg, e.g. 3.280-0 g; it should not be written as 03.280 g.

Rounding Off Figures

• In number of observations or measurements or in calculations, sometimes data is spread in large numerical. It is necessary for accuracy and in calculations that rounding off the figures is done. In rounding off the quantities, the correct number of significant figures should be retained, e.g., when adding 128.12+ 6.018+ 0.2678, it should be written as 128.12 +6.00 +0.27. Likewise, in multiplication or division, a similar rounding off the figures are carried out as in multiplication of 1.12 x 2.301 x 0.5786, the values used for calculations are 1.12 x 2.30 x 0.58. The rounding off the figures thus is essential to curtail lengthy and tedious calculations.

• It is very common in analytical work to get dissimilar results, and no analysis is complete until all the results are collected, calculated and properly reported. In quantitative analysis, when numerical data and results are collected, it is generally observed that the results obtained by various methods or of series of determinations differ among themselves to a varying extent. There is a general tendency to find an average value of a series of measurements to be taken as the true value. It should be always remembered that the average value may not be the true value.

• It is therefore, necessary to know, what the true value is so that the average value so obtained can be compared with it. Furthermore, in most analyses, the ultimate result of analysis is important from an accuracy and reliability point of view. To understand this, it is necessary to know the various terms used in analysis.