Accuracy and precision

1. To learn how to use a balance to weigh objects. 2. To determine the accuracy of various lab glassware as well as the precision obtainable when using each of these. II. BACKGROUND: If a person goes into a restaurant and orders a cup of coffee, how much coffee will be given to the person? Will the coffee arrive in a large, earthenware mug or a delicate, china cup? Do all coffee cups hold a cup of coffee? If, on the other hand, another person is following a recipe that called for a cup of coffee, how much coffee will that person use? Will there be a difference in how the coffee is measured in these two situations? Recording numerical data is an important part of scientific research.

The reliability of these data can influence the conclusions drawn from the experiment. Although “accuracy” and “precision” are used interchangeably in common speech, in scientific language, they mean two different things. The “true value” of any number is a philosophical idea which we take as a given/known thing; for example, scientists say that exactly 100. 0000 mL of water weigh exactly 100. 0000 g at 4° C (theoretically 99. 823 g at 20°C – room temperature). An “error” in data is the numerical difference between the measured value and the true value.

An “accurate” result is one that agrees closely with the true value (has less error); for 100 mL of water, a weight of 100. 001 g is more accurate than 100. 009 g, and that is more accurate than 100. 01 g. “Precision,” on the other hand, refers to agreement among a group of data, but says nothing about their relationship to the true value. Three measurements of 100. 009, 100. 008, and 100. 007 g might be more precise than three measurements of 100. 009, 100. 002, and 99. 995 g, and yet may not be more accurate. In the above example, which of these methods of measuring coffee is the most accurate?

If a measuring cup is used, will that always measure exactly one cup of coffee? Why or why not? What factor(s) could be sources of error in the user’s measurement? Which of these methods of measuring coffee would be the most precise? Why? There is a variety of glassware here in the Biology Lab – beakers, graduated cylinders, Erlenmeyer flasks, volumetric flasks – that could be used for a lab exercise in which students would be required to measure 100 mL of distilled water (dH2O). Because these various types of lab glassware are designed for different purposes, their accuracy and precision vary.

Certain types of glassware are manufactured with greater precision than other types and/or yield more accurate measurement of volume. Knowledge of the relative accuracy and/or precision of the various types of glassware can aid in determining the appropriateness of a piece of glassware for a desired use. For example, if a student needs several identical 100 mL samples, which measuring utensil should be chosen? Why?

When a scientist comes up with an answer to a question like the preceding one that might be right yet needs to be tested to see if it is true, this is called a hypothesis (hypo = under, beneath; thesis = an arranging). Any testable answer to the previous question such as, “I think that the ___ glassware is more precise (or more accurate),” is a hypotheses. Once a scientist has formed an hypothesis, it is then necessary to figure out how that hypothesis can be tested.

The scientist would need to decide what to do (procedure/methods) and what data are appropriate to gather to uphold or disprove the hypothesis. At times, scientists may end up gathering “negative” data that actually disprove their hypotheses.

For this glassware, what could be done – what steps could be followed – to find out if the ___ glassware really is the most precise/accurate? Is it enough to use one piece of glassware or should several kinds/styles be tried? Is it enough to take one reading on each piece of glassware or should several tests/trials be performed on each piece? If a person places a desired amount of water into a piece of glassware, how will that person know if the container is correctly filled?

How will (s)he know the container is filled the same amount every time? When viewed from the side, the surface of the water in a transparent glass container is a characteristic shape that is a clue to solving this dilemma. Because of water’s affinity for glass (glass is hydrophilic, hydro = water, philio = brotherly love), the edges of the water’s surface will creep up the walls of the container slightly. Especially in small-diameter glassware, the surface of the water is, thus, noticeably curved. This curved surface of the water is called a meniscus (Figure 1) (menisc = a crescent). Glassware is designed such that the correct way to measure an amount of water June 19, 2011 38 Figure  1.

Meniscus is to line up the BOTTOM of the meniscus with the top of the line on the glassware, or to determine how much is there, by looking at where the bottom of the meniscus falls in comparison to the lines on the glassware. By lining up the bottom of the meniscus with the top of the line in question, a person can come closer to filling the container with the same amount every time. Unlike the beakers we will be using in this lab, the buret pictured in Figure 1 is read from the top, down. Note that the bottom of the meniscus in Figure 1 is at 27. 53 mL, (NOT at 27. 4, etc. ). However, if what looks like 100 mL

of dH2O is put in a container, how will the experimenter know if it is really 100 mL or how close to 100 mL it really is? By what means can one determine how much water is actually in the container? How might knowing the true value of the weight of water aid in this determination? It is possible to make use of a chemical property of substances called density to determine the accuracy of these volumes. At a given temperature, a given volume of a substance weighs a given amount – density is weight per volume. For water at 25° C (77° F), 1. 00 mL should weigh 0. 99707 g or 100 mL should weigh 99. 707 g.

Thus, determining the weight of the “100 mL” of water can show how close the volume really is. What about the weight of the container? How can one obtain the weight of just the water? Do all containers of the same type weigh the same amount? How would any differences in container weights affect the procedure used in this experiment? In science, it’s not enough to do the experiment, look at the data, and decide if the numbers are close enough to each other to be considered the “same. ” Rather, some kind of statistical analysis must be done.

If a given container is filled only once, and the weight was, say, 98. 87 gm, how will the experimenter know if the container was filled wrong or if it was manufactured wrong? It is, thus, important to obtain at least three measurements for each item being tested. To help evaluate these numbers, it is necessary to need to employ a couple of statistical concepts.

The mean or average (X) of a set of data is the total of the values of those data divided by the number of data points. This is expressed mathematically as: X = (xi)/n.  means sum, xi means all the individual values, and n means the number of items. In the examples above, (100. 009 + 100. 008 + 100.007) ? 3 = 100. 008 g average, and (100. 009 + 100. 002 + 99. 995) ? 3 = 100. 002 g average.

Thus, the second set of data is more accurate – closer to the theoretical value of 99. 707. The closer the mean of a group of numbers is to the true value, the more accurate that group of numbers is. The standard deviation, s, is a measure of the central tendency or dispersion of the data, in other words, a measure of how far from the mean the data are scattered. This is expressed mathemat ical ly as . In the above examples, (100. 009 - 100. 008)2 = 0. 0012 = 1 ? 106 (100. 008 - 100. 008)2 = 0. 0002 = 0 ? 106