Measuring Measurement

How accurate are you in measuring quantities? This is the question that our professor wants us to ponder last Wednesday. For all we know, measurement is very important in our everyday living. From the simple way of measuring the right amount of food we're about to consume in every meal to measuring the pixel size of our uploads, we are very dependent on measurement. As a student studying physics, the accurate and reliable way of measurement is a fundamental thing to master. In fact, as our professor said, the meticulous way of measurement in physics sets it above from other disciplines with the likes of chemistry, biology, etc.

However, measuring is not as ordinary as we think it would be. The way of measurement that our professor wants us to learn is more than using a ruler or any measuring device in measuring quantities. Since measuring devices and humans have some flaws in their selves, we cannot guarantee a perfectly accurate kind of measurement that we want to attain. However, through the use of some techniques that our professor shared to us, we can somehow reach a considerable accuracy that will significantly help us attaining the data that we need.

Our discussion last Wednesday started with the introduction of the concepts of scientific notation, rounding off values, and significant figures. Since we already tackled these concepts since in my freshman level in high school, I found no problem dealing with them.The discussion eventually tackled the central topic which is the order of approximation.  The first order of approximation deals with the use of significant figures and their operations (e.g. addition, subtraction, multiplication and division). The second order of approximation deals with “Best Estimates”. The second order of approximation is commonly used in measuring irregular or fluctuating quantities. From these, terms like expectation value and uncertainty were introduced. Expectation value ‹Q› is the average of the trials obtained while uncertainty “gives the idea of the range of values where the actual value can fall”. Best estimate Qbe of a quantity is given by Qbe=‹Q› ± ΔQ. The third order of approximation is the Statistical approach. We didn’t tackle much of the third order of approximation because it deals with higher math which are not yet appropriate for us in the moment.  My professor gave us activity sheet regarding the first and second order of approximation. We accomplished half of the activity and left the other half to be considered as homework.

The second part of the discussion deals with error in measurement. Errors in measurement are an inevitable thing. It denotes “how far a measured value is with respect to a reference value”. There are two types of error with respect to a reference value. The first one is “uncertainty” (also called random error) or error with respect to the mean of the data. The other one is “deviation” or error with respect to a standard or accepted value. Uncertainty and deviation may be recorded in two different ways: either absolute error or relative error. Absolute error is the “actual absolute difference between the quantity and the reference value” while relative error is a “number that describes how large the error value is compared to the reference value. Absolute error has the unit of the quantity involved while relative error is usually reported as percentage.

At the third part of the discussion, we discussed the issues about the precision, accuracy, acceptability, and practicality of measurement. Our professor explained to us the difference between being “precise” and being “accurate” by showing some illustrations of darts placed in different manner on the target. Darts that are closer to one another and located at the bull’s eye represent both accuracy and precision. Those that are close from one another but far from the bull’s eye represent precision only while those at the bull’s eye but a bit far from one another represent accuracy. However, those that are neither close from one another nor near from the bull’s eye are considered neither precise nor accurate. From these representations, we can define accuracy as the closeness of the values (represented by the location of darts) to the standard value (represented by the bull’s eye). Precision, on the other hand, can be defined as the closeness of the measured values to each other.

Uncertainty and deviation has indirect relationship with precision and accuracy, respectively. The “lower the uncertainty of a given set of data, the more precise the measurement is.” Similarly, the lower the deviation of the given set of data, the more accurate the measurement is.

Is the data measured should be considered? This is the question that can be answered by the parameter of acceptability. From our discussion, the acceptability of the given measurement has something to do with the relative values of deviation and uncertainty of the given measurement.  A measurement can be accepted when the “uncertainty is small enough and the deviation is smaller than the uncertainty”.

The other condition that must also be considered is “practicality”. The most practical measurement will be the “one that yield a maximum error value that is within the specified margin.”

At the last part of our discussion, we tackled error propagation. Error propagation says that error propagates when an unknown quantity is measured by means of computation of given quantities and not by directly measuring the unknown quantity with a specific device. Since the individual quantity has in itself an uncertainty value, then the uncertainty value will only combine with one another once different operations are applied to them. In other words, as the principle of maximum pessimism states, “ the error of computed quantities must be greater than or equal to the individual quantities used to obtain it”. There are different approaches on adding, subtracting, dividing, or multiplying the uncertainties in best estimates.

Our professor once again gave us activity sheet about the lessons above and homework as well.

Reference:Physics 101.1 Handout