The levels of the Homeland Security Advisory System are listed.
Severe High Elevated Guarded Low
What data set level of measurement is this? Ordinal, Nominal, Interval, or Ratio?
Two Plus Two Equals Four, But Not Always
Believe it or not, sometimes 2 + 2 does not equal 4. It depends on what type of measurement scale you are using. There are four types of measurement scales – nominal, ordinal, interval, and ratio. Only in the last two categories does 2 + 2 = 4. Let me explain.
All the nominal scale does is name or classify. Each number merely represents a category or individual. For example, numbers on baseball or football uniforms are only nominal. Having the number "1" on your uniform does not necessarily mean you are "numero uno" (the best) in your sport. Social security numbers are also nominal. All they do is name or classify the individual.
The ordinal scale has all the qualities of the nominal scale plus the ability to rank objects according to some attribute. If you ranked all the members of a group according to height, "1" would be the tallest, "2" the second tallest and so on. However, the intervals between these rankings are not necessarily equal. If the tallest people were 5'11", 5'8" and 5'7", respectively, the interval between the first two ranks would be 3 inches, while the interval between the last two is only 1 inch. Ranking in various sports and beauty contests are also only ordinal scales.
An interval scale combines the qualities of the previous scales with equal intervals. The best example would be a centigrade (Celcius) thermometer. The change in heat between 0ºC and 10ºC is the same as between 10ºC and 20ºC. But watch out! 20ºC is not twice as hot as 10ºC! Why? Interval scales have arbitrary zeros (just because we decided to call it zero), rather than absolute (true) zeros. At 0ºC water freezes, but that does not mean that there is no heat.
In contrast, the ratio scale has all the qualities of the previous scales plus an absolute (true) zero, as with a Kelvin thermometer. At 0ºK, theoretically there is no heat. You have nothing of what you are measuring, therefore the zero is true or absolute. However, 0ºK = -273ºC. Since one degree indicates the same heat change in both scales, we can see what happens when we compare them.
20ºC = 293ºK
10ºC = 283ºK
0ºC = 273ºK
-273ºC = 0ºK
Thus 20oC is not twice as hot as 10oC! Although this may seem confusing, it becomes very clear when you switch to the Kelvin scale – 293oK definitely does not even look like it is twice as hot as 283oK. Only with a ratio scale – with a true zero – can you correctly use the concept of multiples. Length, height, and weight are ratio scales. Therefore, you can correctly say that "A yard is three times longer than a foot" or "A 200-pound man weighs twice as much as a 100-pound woman."
If you are having some trouble understanding this, it is probably because most of you have only used ratio scales in school. Mathematics courses typically deal only with scales that have true zeros and equal intervals.
How does this relate to psychology? Most psychological tests are only ordinal measures! Let's say that three different people score 60, 40 and 20 on a test of extraversion (having outgoing personality traits). Because it is an ordinal scale we can correctly say that 60 is the most extraverted (rank #1), 40 is the second most, and 20 is the third most or least extraverted.
Notice that the difference between 60 and 40 is 20, and the difference between 40 and 20 is also 20. However, a 20-point difference in one part of the scale may not have the same meaning as a 20-point difference in another part of the scale. Thus the same difference of 20 points may not reflect the same underlying difference in extraversion, because we don't know if the intervals are equal. It is not an interval scale.
Likewise, even though 20 x 2 = 40 and 20 x 3 = 60, we cannot correctly say that the person with a score of 60 has three times the extraversion as the person with 20 or that the person with a score of 40 has twice as much. We cannot compare scores in terms of multiples, because the scale has no true or absolute zero. It is not a ratio scale.
Again, most psychological tests – and almost all tests used in our schools (including mine) – are only ordinal measures. These tests allow ranking of people according to various attributes — personality traits or knowledge in specific subject areas. However, if someone gets a score twice as great as yours, it does not mean that person knows twice as much as you do.
I hope this helps you to figure it out for yourself.
To determine the level of measurement for the data set provided, we need to understand the characteristics of each level.
Nominal level is used for data that can be categorized or classified, such as names or categories. There is no inherent order or rank to the categories.
Ordinal level is used when data can be ranked or ordered, but the differences between the categories are not equal. For example, if we have a dataset with three categories (e.g., small, medium, large), we can arrange them in order but the difference between small and medium may not be the same as the difference between medium and large.
Interval level is used for data that has order and the intervals between the values are equal. However, there is no meaningful zero point. Temperature is an example of an interval level measurement because the differences between 10 and 20 degrees Celsius are the same as the differences between 20 and 30 degrees Celsius.
Ratio level is similar to interval level but with a meaningful zero point. In addition to having order and equal intervals, ratio level data can be measured or compared in terms of ratios. For example, height and weight are measured at ratio level because they have an absolute zero point and the ratios between two measurements are meaningful (e.g., someone who weighs 200 pounds weighs twice as much as someone who weighs 100 pounds).
In the given data set "Severe High Elevated Guarded Low," the categories can be ranked or ordered, which suggests an ordinal level of measurement. However, it is important to note that without any further information about the specific numerical values associated with each category, we cannot definitively determine the level of measurement.
To be certain about the level of measurement, we would need additional information, such as numerical values or thresholds associated with each category.