When it comes to measurement in research. There are some rules and concepts a student needs to be aware of that are not difficult to master but can be tricky. Measurement can be conducted at different levels. The two main levels are categorical and continuous.
Categorical measurement involves counting discrete values. An example of something measured at the categorical level is the cellphone brand. A cellphone can be Apple or Samsung, but it cannot be both. In other words, there is no phone out there that is half Samsung and half Apple. Being an Apple or Samsung phone is mutually exclusive, and no phone can have both qualities simultaneously. Therefore, categorical measurement deals with whole numbers, and generally, there are no additional rules to keep in mind.
However, with continuous measurement, things become more complicated. Continuous measurement involves an infinite number of potential values. For example, distance and weight can be measured continuously. A distance can be 1 km or 1.24 km, or 1.234. It all depends on the precision of the measurement tool. The point to remember now is that categorical measurement often has limit values that can be used while continuous has an almost limitless set of values that can be used.
Since the continuous measurement is so limitless, there are several additional concepts that a student needs to mastery. One, the units involved must always be included. At least one reason for this is that it is common to convert units from one to the other. However, with categorical data, you generally will not convert phone units to some other unit.
A second concern is to be aware of the precision and accuracy of your measurement. Precision has to do with how fine the measurement is. For example, you can measure something the to the tenth, the hundredth, the thousandth, etc. As you add decimals, you are improving the precision. Accuracy is how correct the measurement is. If a person’s weight is 80kg, but your measurement is 63.456789kg, this is an example of high precision with low accuracy.
Another important concept when dealing with continuous measurement is understanding how many significant figures are involved. The ideas of significant figures are explored below.
Significant figures are digit that contributes to the precision of a measurement. This term is not related to significance as defined in statistics related to hypothesis testing.
An example of significant figures is as follows. If you have a scale that measures to the thousandth of a kg, you must report measurements to the thousandths of a kg. For example, 2 kg is not how you would report this based on the precision of your tool. Rather, you would report 2.000kg. This implies that the weight is somewhere between 1.995 and 2.004 kg. This is really important if you are conducting measurements in the scientific domain.
There are also several rules in regards to determining the number of significant figures, and they are explained below
- All non zeros are significant
- Example-123 are all non-zeros and thus are all significant in this case
- A zero is significant if it is between two significant numbers
- example-1023. The 0 is in between 1 and 2 and is thus significant
- Zeros are significant if it is at the end of a number and to the right of the decimal
- Example 2.00: Here, the 0’s are to the right of the decimal, which makes them significant
Each of the examples discussed so far has been individual examples. However, what happens when numbers are added or multiplied. The next section covers this in detail
Significant Figures in Math
When adding and subtracting measurements, you must report the measurement results with the less precise measurement.
- 115kg – 16.234kg = 98.766kg, but the least precise measurement is 115kg, so we round the answer to 99 kg. This is because our precision is limited to one’s place.
When multiply or dividing measurements report results with the same number of significant figures as the measurement with the fewest significant figures
- example 1
- 16.423 m / 101 m = 0.16260396 m
This number is too long. The second number, 101, has three significant figures, so our answer will have 3 significant figures, 0.163m. The zero to the left of the decimal is insignificant and does not count in the total.
- example 2
- 8.0 cm * 3.208 = 25.664 cm2 or 26cm2 the first number has two significant digits, so the answer can only have two significant figures, which leads to an answer of 26cm2.
Finally, there are rules for converting units as well. To convert units, you must know the relationship that the two units have. For example, there are 2.54 cms per inch. Often this information is provided for you, and simply apply it. Once the relationship between units is known, it is common to use the factor label method for conversion. Below is an example.
To solve this problem, it is simply a matter of canceling the numerator of one fraction and the denominator of another fraction because, in this example, they are the same. This is shown below.
Essentially there was no calculation involved. Understanding shortcuts like this saves a tremendous amount of time. What is really important is that this idea applies to units as well. Below is an example.
In the example above, we are converting inches to meters. We know that there is 2.54cm in 1 inch. We set up our fractions as shown above. The inches cancel because they are in the numerator of one fraction and the denominator of another. The only unit left is cm. We multiply across and get our answer. Since 24.0cm has the fewest number of significant figures are the answer will also have three significant figures, and that is why its 61.0cm
There can be problems with following the rules of significant figures. For example, if you want to convert meters to centimeters. There can be a problem.
The answer should only have three significant figures, but our answer has one significant figure. We need to move two zeros to the right of the decimal.
This is done with scientific notation as shown vbelow.
This simple trick allows us to keep the number of signifcant figures that we need without hhanging the value of then umber.
Below is an example of how to do this with a really small number that is a decimal.
This post explains some of the rules involved with numbers in scientific measurement. These rules are critical in terms of meeting expectations for communicating quantitative results.