What is the "quality" of a measurement and how can we determine it?

What are "accuracy" and "precision" of measurement?

Acuracy and precision

The Quality of a measurement is it’s ability to properly describe the various amounts of substances in the environment. The degree of quality help us understand how good an assessment of quantity is compared to other similar assessments, The quality of one measurement is normally expressed in terms of its accuracy, or how fine, sharp, exact each one outcome is, and its precision, or how trustworthy, reliable, consistent, repeatable such measurement outcomes are.

The accuracy of measurement is determined by the identifiable separating distance between markers in one of several "scales of measurement" that offer a continuous reference to sequences of increasing value. These uniform sequences of markers are typically presented as visual “tick marks" and numbers etched in measuring devices, rulers or yardsticks, tapes, and as angle-dial markings for swinging needle-pointers in weighting scales, or in a diversity of digital-numeric displays in newer measurement devices, machines and tools.

Depending on their degree of accuracy, scales are identified within broad degrees of coarse or fine capabilities, as described in the previous chapter.

The degree of accuracy is established by the certainty with which some specific size can be attributed to the substance being measured. The degree of precision normally indicates the degree of trust on a measurement, dictated by the confidence given to instruments and procedures during repeated measurements. In general terms, the degrees of accuracy can be between "estimated-or-loose, rough" for most casual situations, to "medium", to "fine" or even "very fine/ultra-high, tight", for industrial or scientific applications. The precision of measurement tools can be stated from "very loose" unreliable untrustworthy, to "reasonably helpful" and trustworthy for practical uses and even "very tight" highly reliable and trustworthy, for critical and delicate situations. Measurement instruments are devices created to facilitate measurement activities by easing the comparison between the objects being measured, against the size of "official", widely recognized, unchanging objects (or events). To maintain consistency around the world, selected highly reliable and stable objects or events of reference, called "standard units of measurement" and procedures are defined and maintained by recognized institutions to remain uniquely reliable through time and available for eventual comparison, validation and re-validation (i.e. calibration, described ahead) of various other measuring devices or processes.

Call the animated illustration of accumulating and counting standard units of weight - grams in the metric system, where the units (grams) are being counted and grouped in multiples of 5 and 10 to configure an increasing scale. Practical instruments, like the scales for weighting are artifacts that make it easy to evaluate the weight of an object by comparing it to a count of these standard units of measurement in a scale. Call the scale and balance and turn ON power of its TOTAL WEIGHT display to observe weighting standard reference and non-standard common items using instruments called the scale and the balance. To support trustworthy accuracy and precision through time and space, standard units of measure are carefully made and maintained by recognized standards measurement organizations. The validity of readouts of measuring instruments everywhere, it is normally required for them to be "calibrated" that is, to insure that each time the instruments are used, they will recognize and be true to the actual, officially recognized standards. Calibration provides periodic verification, adjustment and validation as necessary, typically required by human activities, such as in industrial, commercial and scientific operations, to verify that the instrument properly recognizes official standard units (or certified copies of them) at all times.The image and the activities below illustrate the effect of applying different, gradually more accurate scales over the greater or lesser accuracy of a measurement:

Figure 1.1 Increased degree of ACURACY in measurement scales

In the following activities, different levels of "loose" and "tight" scales of measurement (sharpness) are displayed. The precision (trust) on each measurement, will depend on the specific procedures and instruments selected.

HANDS ON Examples of gradual increase of accuracy offered by different scales:CATEGORICAL/nominal/classification scales (Sorting by color), (Sorting Animals) ORDINAL scales (Grouping balls by size), (Ordering containers by size) INTERVAL AND RATIO scales (Grouping students by height), (Grouping students by test scores)

Tinthe real world and through time, two predominant groups of standard units of measurement have been developed and used around: a) the Metric (base-10) or Decimal, MKS (Meters, Kilograms, Seconds) system, andb) the English (Feet, Pounds, Seconds) system.

Call the Measuring Tool Size display to observe the sizing of open gap width of common mechanic wrenches in the most common Metric (meters, Kilograms) and English (feet, pounds) systems, by using (clicking and dragging) the tick-marked ruler or the (yellow) length-strips provided, focusing and zooming in, as needed, to view image details closer, more clearly.

The following displays Using a Ruler (1) and Using a Ruler (2) allow for the measurement of physical size of various small objects and toys. The ruler instrument in each display offer two different interval/ratio scales tick-marked on each of its two edges, one in centimeters (Metric System) and the other in inches (English System). Call the display to measure and record on a sheet of paper the height and width in both centimeters and in inches of each object presented.

Different types of rulers and measuring tapes (flexible) can also be used to measure sizes of real physical objects and toys accessible to the learner.The caliper (or Vernier, displayed in the Accuracy and Precision activity - image below) can also be used to evaluate small but critical straight-line distances of objects to evaluate their accurate sizes. The caliper relies on the sliding movement of tightly fitting solid feelers and indicator parts. Through its mechanism, the caliper produces clearer, unambiguous (accurate), and more consistent (precise) measurements of distance.

Observe and use the caliper in the Accuracy-and-Precision activity to measure and record, as accurately as possible the size of the various small objects shown with it. If available to the learner, a real physical caliper could be used to experience the abilities of these devices to provide more accurate and precise measurements of real useful objects.Measure each once with the ruler, and then with the caliper, to appreciate its visual and/or mechanical advantages.

QUESTIONS: 1.- Which instrument (ruler or caliper) is more likely to be accurate (exact)? Why?

2.- Which instrument (ruler or caliper) is more likely to be more precise (consistent, same reading each time)? Why? 3.- What would it take for a ruler to become a more accurate and precise instrument?DOING AND RECORDING MEASUREMENTS

Gross and fine measurement

In practice and in general, the degree of quality of measurements can be simplified to be within one of two major groups: Gross, or fine.

Gross measurement is looser, and most likely to be less accurate, less precise, and likely of relatively lower quality. Gross measurement includes rough measurement, guessing, estimation, and can be done using simpler or no auxiliary instruments and/or procedures.

Fine measurement is tighter, more accurate, precise and of higher quality. Fine measurement would require better quality instruments and/or procedures.

REPRESENTATION/EXPRESSION OF QUANTITY As stated in the INTRODUCTION chapter, in addition to its meaning as a verb describing the action of determining how big, or small things are, the word measurement can also refer to a noun (or a "thing") meaning the surrogate (borrowed) representation: images, sounds, physical objects, and symbols (namely numbers formated with punctuation symbols and reference units,) that can be used to describe the magnitude, size, or quantity of things measured. The important role that these representations play in mathematics was also highlighted in the introductory section: they can allow us to perceive, understand, manipulate, and communicate about our environment more effectively and efficiently.

With the widening range of choices of tools and methods available for the collection, representation, storage, processing, and communication of information, it is becoming increasingly important that we learn about, and become proficient in how to take advantage of these choices to view, analyze, and manipulate quantities in the environment. The mounting pressures to become effective and competitive in the workplace, makes it imperative for us to always understand, use and if not available, create better tools and instruments and methods of measurement.

In this section, some of the most common forms and tools of measurement are described. Simpler practical situations are also offered through simulated illustrative interactive displays. The most common forms of representation of quantity are:

Analog (concrete, iconographic, visual, auditory or perceptually explicit mimicked forms), or symbolic/digital/numeric (abstract, orthographic, implicit, interpretable symbol-coded objects)

Positive (forward) or negative (opposing) for directional or locational effects

Integer (whole units) or fractional (using smaller component parts of a whole-unit)

Physical (tangible) or virtual (intangible, most likely, computer-generated)

Analog and digital representations

As described in more detail in Chapter 5 ahead, analog representations use look-alike, mimicking images, pictures, objects, sounds or movements that imitate, resemble, suggest or insinuate instinctively the form, size or magnitude of the objects or actions represented. Analog representations tend to be more natural, intuitive, and, in general, easier for our natural (animal) senses (particularly the eyes) to perceive. Digital and other number representations on the other hand consist primarily of encoded shapes and symbols that encode and need to be "decoded" to mean the magnitudes being described.