In the fascinating world of measurement, understanding the difference between error and mistake is akin to deciphering the subtle dance between precision and human fallibility. Errors, akin to playful imps, often creep into our measurements slyly, causing deviations from the true value due to imperfections in tools or techniques. They are the mischievous gremlins lurking in scientific experiments, adding an unexpected twist to the results. On the other hand, mistakes, those curious slip-ups, emerge from the quirks of the human mind, leading us astray through miscalculations or misjudgments. While errors can be tamed and understood through careful analysis and calibration, mistakes remind us of the delightful unpredictability of human endeavors. Navigating this interplay between errors and mistakes becomes an art, where scientists wield their knowledge and intuition to unravel the mysteries of the universe while embracing the charming unpredictability that comes with every measurement.
Aims/Objectives
- Define error and sensitivity requirements
- Differentiate between absolute error and relative error
- Differentiate between Systematic Error and Random Error
- Calculate Relative Error and Percentage Relative Error
- Define least weighable quantity and least measurable quantity.
- Identify permissible error in weighing and measuring.
- Calculate the least weighable quantities using the sensitivity requirement and permissible error.
What is an Error?
Error refers to the discrepancy between a measured or observed value and the true or theoretically correct value. It quantifies the accuracy of a measurement or prediction. The true value is the average of the infinite number of measurements, and the measured value is the precise value. 
Mathematically, error () can be expressed as:
E = Measured Value − True Value
For instance, consider a laboratory scale calibrated to measure the weight of an object. Let’s say the true weight of the object is 100 grams. If the scale reads 100.20 grams, the absolute error can be calculated as:
E = 100.20 g − 100.00 g = 0.20 g
In this example, the absolute error is 0, indicating that the measurement deviates from the true value by 0.20 grams. Scientists use various techniques, including error analysis, to understand and minimize errors, ensuring the precision and reliability of their experiments and research findings. A common way to express error in measurement is using a plus or minus symbol e.g. ± 0.2 g. When a measurement is presented as 100 g ± 0.2 g it does not mean a mistake, but rather due to experimental limitations there is uncertainty of ± 0.2 g in the measured value. Therefore, the measured value may fall anywhere between 99.80 g to 100.20 g.
Types of Error
In the realm of measurements, errors can be categorized into different types, each with specific characteristics and sources. Understanding and minimizing these types of errors are crucial in scientific research, pharmacy and various fields where accurate measurements are essential. Scientists employ error analysis techniques to identify and mitigate these inaccuracies, ensuring the reliability and validity of their experimental results.
Let us look at what some of these errors are:
Absolute Error and Relative Error
The Absolute Error is the difference between the desired measurement and measured value.
Absolute Error = Measure Value – Actual/Desired Value
Relative Error is the quotient of the Absolute Error and the Measured Value. Since the desired measurement, is not achievable, the best we can do is use the measured value.
The Percentage Error is the Relative Error shown as a percentage.
Let us review this example:
A pharmacy technician desires to weigh 140 mg of Precipitated Sulphur on a top loading balance, but ends up weighing 125 mg when checked on a more accurate prescription balance. What is the percentage error associated with this measurement?
Did you notice anything special about the Absolute Error and Relative Error?
Absolute error is the numerical difference between the measured or observed value and the true or accepted value providing a straightforward measure of how far off a measurement or calculation is from the true value. Relative error on the other hand is is the ratio of the absolute error to the magnitude of the true value. It provides a standardized way to represent the error, making it easier to compare the accuracy of different measurements or calculations, especially when dealing with values of varying magnitudes.
Absolute error is in the same units as the measured or observed value, while relative error is expressed as a percentage (%). Absolute error does not consider the magnitude of the true value, whereas relative error takes the magnitude into account, making it useful for comparing errors in values of different sizes. Absolute error represents the numerical discrepancy, while relative error gives a standardized view of the error relative to the true value’s magnitude.
Accuracy and Precision
Accuracy
Accuracy refers to the closeness of a measured value to the true or accepted value of a physical quantity. It is an essential aspect of scientific measurements and experiments. Accurate measurements are crucial for ensuring the reliability and validity of chemical analyses and experiments.
Accurate measurements are free from systematic errors, which are consistent and predictable deviations from the true value. Achieving accuracy in chemistry involves calibrating instruments, using high-quality equipment, and following precise experimental procedures. Accurate results provide a trustworthy basis for scientific conclusions, ensuring that the data obtained reflect the true nature of the substances or processes being studied. Accurate measurements are fundamental for making reliable predictions, formulating medicines and protecting the population.
Precision
Precision pertains to the reproducibility and consistency of measurements. It reflects the closeness of individual measurements to each other when the same quantity is measured under the same conditions. Precise measurements are essential for obtaining reliable and consistent results in experiments. Instruments and techniques that yield precise measurements are crucial for ensuring the accuracy of chemical analyses, formulations, and scientific investigations. Precision in chemical measurements is often expressed in terms of significant figures, indicating the number of digits known with certainty in a measurement.
Accuracy and Precision
Accuracy is achieved by comparing measured results to the true or accepted value, not necessarily by taking their average. Precision, on the other hand, refers to the consistency and reproducibility of measured values. The closer the results are to each other, the more precise the measurements. However, the closeness of these precise measurements to the reference or desired value determines accuracy. In essence, high precision means the measurements are consistent and have low variability, while low precision indicates that the measured values vary widely. It’s crucial to note that highly precise measurements do not guarantee accuracy; accuracy also depends on how close these precise measurements are to the true or accepted value.
In pharmacy, measurements are inherently not entirely accurate due to the limitations of the instruments used. It’s crucial to acknowledge these limitations and evaluate the degree of error when compounding medications. Pharmacists and pharmacy technicians should be fully aware of these constraints and practice in a way that does not exacerbate these errors.
Errors in Compounding and Dispensing
When pharmacists or pharmacy technicians measure liquid volumes or weigh solid portions, two key concepts come into play: the apparent weight or volume of what has been measured and the potential excess or deficiency in the actual quantity obtained. Determining whether there is more or less than the intended amount is crucial. Additionally, understanding the allowable error is vital. According to the USP (United States Pharmacopeia), a maximum error of 5% is permitted when weighing and measuring substances, ensuring a 95% accuracy level.
The selection of measuring devices holds significant importance in pharmacy practice. Pharmacy technicians must have a deep understanding of which type of device to choose based on the required accuracy level. The choice of device depends on the acceptable margin of error, emphasizing the need for careful consideration during the selection process. Accurate measurements are paramount in pharmaceutical preparations, and the proper choice of measuring devices plays a fundamental role in maintaining the integrity and safety of medications.
When measuring liquids, it’s crucial to differentiate between volumetric and non-volumetric devices. Non-volumetric tools are suitable for holding substances but should never be relied upon for precise measurements, especially when dealing with small quantities. According to the United States Pharmacopeia (USP) guidelines:
For Metric Graduated Cylinders (such as measuring cylinders), the minimum measurable quantity should be 20% of the total measurable capacity of the cylinder. For instance, if you’re using a 100 mL measuring cylinder, the smallest accurate measurement achievable would be 20 mL.
This implies that any volume measurement below 20 mL cannot guarantee an accuracy level of 95%. Using appropriate measuring devices is paramount in ensuring the accuracy and reliability of pharmaceutical preparations.
Example: To determine the least measurable quantity using a 500 mL measuring cylinder, you apply the guideline that the minimum measurable quantity is 20% of the total measurable capacity of the cylinder.
For a 500 mL measuring cylinder:
20% × 500 mL = 0.2 × 500 mL = 100 mL
Therefore, the least measurable quantity using a 500 mL measuring cylinder is 100 mL.
Let us review another example
Using a graduated cylinder, a pharmacist measured 40 mL of a liquid. On subsequent examination, using a narrow-gauge burette, a more accurate device, it was determined that the pharmacist had actually measured 36 mL. What was the percentage error in the original measurement? Is it acceptable?
Pharmaceutical products are meticulously prepared with a minimal margin of error due to several key reasons. Firstly, official compendia standards permit a tolerance of ± 5% for most formulas. This standard ensures a balance between precision and practicality, allowing for efficient production while maintaining a high degree of accuracy. 
Additionally, heightened accuracy is imperative for potent drugs with greater toxicity potential. Even a slight error in dosage could have severe consequences, making precision crucial in such cases. This stringent accuracy requirement extends to all extemporaneously compounded products, emphasizing the universal need for precise pharmaceutical preparations.
In pharmaceutical weighing, different scales and balances are utilized, each with specific degrees of precision assigned to them. One crucial metric is the Sensitivity Requirement (SR), representing the load that causes a change of one division on the index plate of a balance. This sensitivity requirement, such as the 6 mg SR of a class III balance, serves as a benchmark to determine the percentage error in a given weighing. By adhering to these stringent standards and utilizing precise instruments, pharmaceutical products are prepared with utmost accuracy and reliability.
Percentage error may be defined as the maximum potential error x 100 and divided by the desired quantity.
Example
The maximum potential error in weighing is ± 6 mg for a total weight of 130 mg, what is the percentage error? Is the level of error acceptable based on established standards?
Least Weighable Quantity
The least weighable quantity is the smallest amount that can be measured on a balance with a known sensitivity to maintain a desired level of accuracy; this is known as the least weighable quantity (LWQ). The smallest or least weighable quantity of a substance (LWQ) that can be weighed on the balance must be determined using the following equation:
Calculating the least weighable quantity
On a prescription balance with an SR of 6 mg and with an acceptable error of no greater than 5%, what is the least weighable quantity for this prescription balance?
Let us review another example:
The Class III prescription balance has a sensitivity requirement of 6 mg. What % of error would result in weighing 50 mg of a drug on the balance?
Summary
Accurate weighing and measuring in pharmacy are paramount for ensuring patient safety, efficacy of medications, and compliance with prescribed dosages. Precision in compounding and dispensing medications is crucial to avoid adverse reactions and achieve the desired therapeutic outcomes. Choosing the right equipment, such as calibrated balances and measuring devices, is essential. Properly calibrated instruments guarantee accurate measurements, preventing dosing errors that could lead to serious consequences. Pharmacists and pharmacy technicians must meticulously select and use these tools, adhering to established guidelines and standards. By doing so, they ensure the formulation of precise dosages, contributing significantly to the overall quality of healthcare delivery and patient well-being.