In order to be a good scientist, you have to make sure that your data is worthwhile. But how can you be sure of that? This lesson goes over many of the techniques you can use to be sure that your data is both accurate and precise.
Let's say that you are conducting research in the field - perhaps you're measuring the spirals on snails. Or maybe you've been tasked with finding out the relative mass to volume ratios of a number of rocks. Whatever the nature of the field work, chances are, you're going to have to use some sort of measurement to finish your work. Simply reporting back that 'the snails are big' or 'the rocks are bigger' just won't cut it. Such measurement helps to make sure that science is objective and repeatable. Luckily, from calipers to mass scales, you've got no shortage of tools to help to do that. Still, there's a problem. Even the most well-intentioned scientists can sometimes make mistakes. Minimizing those mistakes is one of the reasons that maintaining good measurements is so important to scientists.
Let's say you are out there measuring snail shells. Now, you could use a ruler and get a reasonably accurate measurement, probably within a few millimeters. But that's not really good enough, is it? No, that's why you use calipers, which allow you to measure to a fraction of a millimeter. That said, such precise measurements are only good if the equipment is properly calibrated. Calibration refers to the process of making sure that the equipment is set to properly measure for data. For a set of calipers, that may mean making sure that the tiny gears of the mechanism are clear and clean. For a balance, it could be as simple as hitting the tare button until the mass reads zero. In any event, it is far better to calibrate an instrument before performing fieldwork. Otherwise, you may have to start over, or at the least try to adjust all previous data.
Accuracy and Precision
In fact, adjusting data is generally not a good idea. This is because data does not exist just as a number. Instead, data must be accurate and precise. You sometimes hear those words used interchangeably, but the truth is that there is a great deal of difference. Accuracy refers to the proximity of a value to a target. For example, if you took a measurement of a 100-gram weight and then found that the balance measured it as 100.5 grams, 100.25 grams, 99.0 grams and 99.5 grams, the data would be pretty close to accurate. While I'd still tare that scale out again, the numbers are still pretty accurate for 100 grams. If you had taken a mass of the 100 gram weight and gotten 50.0 grams as a mass, that would be inaccurate.
Still, the above numbers may have been pretty accurate, but they lacked precision. Precision refers to the closeness of the measurements to each other. Let's say that you massed the weight on a different balance. Just like before, you took its mass four times. However, this time, the balance read 90.0 grams each of the four times! The scale is precise, but it is inaccurate.
Sometimes, it's not just how you measure the numbers, but how you record them. Try this, for example. 10 * 10 = 100. However, 10.4 * 10.4 = 108.16. That's a difference of more than eight percent! Yet, had you just rounded, that's the difference that you would have ended up with. How can we make sure that data is kept to a consistent and useful amount of precision? We can do this through the use of significant figures. Significant figures make sure that recorded data is kept to a certain level of precision.
The term 'significant figures' is a bit of a misnomer, as it's not that the other digits are any less important. It just refers to the numbers that are not used for spacing purposes. Therefore, 0.000001 and 0.1 have the same number of significant digits: one. The zeroes for spacing are not significant figures. However, the numbers 0.00001 and 0.00101 have different numbers of significant figures. The first number has one, while the second one has three. Zeroes that space between non-zero figures are significant. So, what does all of this mean? Say you were to limit data in a given set to three significant figures. The numbers in question were 0.123, 0.004539 and .1. The first one is pretty easy - the number is the same. For the second one, we keep all the spacing zeroes, then cut it off after the third non-zero number. Finally, for the third one, we don't just write 0.1. Instead, we make sure that it is exactly the point in question. If it is, we record it as 0.100, since that is precisely the point in question.
In this lesson, we looked at ways that scientists can be sure that their measurements are reliable. We started with ensuring that instruments are properly calibrated. We then discussed the differences between the concepts of accuracy and precision. Finally, the importance of significant figures was discussed as a way to make sure that both accuracy and precision were maintained.
- caliper: tool that allow you to measure to a fraction of a millimeter
- calibration: the process of making sure that the equipment is set to properly measure for data
- accuracy: refers to the proximity of a value to a target
- precision: refers to the closeness of the measurements to each other
- significant figures: numbers that ensure that recorded data is kept to a certain level of precision
If taking a measurement of 100 grams and the weight reads 90 grams, then the accuracy is off.
Do what's necessary to prepare to reach the following goals:
- Discuss the importance of accuracy in measurements
- Understand the process of calibration
- Compare accuracy and precision
- Use significant figures to maintain accuracy