Posted: November 6th, 2022

Biostatics
Given that a lot of students have trouble at first with applying the correct scales (nominal, ordinal, ratio, interval) to certain variables, I wanted to add a Discussion here and have you think about variables that you encounter in your work place (or elsewhere) and see if you can identify what scale those variables may fit into. Now, the examples we use in our notes and in the assignment are more straight-forward, but other variables may be more complicated (such as the APGAR measurement). We can discuss what it is that may make some variables more complicated where they don't fit so nicely into the definition of one of the four scales and see if perhaps some variables may fit in more than just one scale, and what factors affect their "dual-scale" application. Remember not to confuse the definition of a variable with the "frequency" or the "number of..." a variable (which is a descriptive of a variable describing how many times that variable exists, such as how many medical gloves you count, or how many medals one has).

Consider what variables you work with on a daily basis and see what you come up with. Students? Help out your fellow students in using the definitions and resources under our Module and in the text to see if we can reasonably identify correct scales for the variables that we come up with, and let's see how much we can discover about the variables we encounter every day!

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First, lets remember our continuous vs. discrete variables (from Class Notes):

Discrete Variable: Consists of separate, indivisible categories. No value can exist between 2 neighboring categories. Commonly restricted to whole numbers.

Continuous Variable: There are an infinite number of possible values that fall between any 2 observed values. It should be rare to obtain identical measurements for 2 different individuals, & the intervals must be defined by boundaries.

Next, remember our questions for identifying scales (from your Commentary):

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Nominal Scale is remembered as a “name” or a “label” assigned to the variable. The name of the variable does not represent a numeric value, has no natural order, and is a discrete variable: The distance between 2 variables cannot be measured and cannot be multiplied.
Ordinal Scale is remembered as having a natural “order” to the variables. They are also discrete variables, often represented as a nominal value, or name, but does have a natural order to it as the example represents: 1st, 2nd, 3rd place; room #12, Room #13, Room #14, etc..
Interval Scale and Ratio scales are continuous variables: There is a numeric distance between 2 adjacent variables which can be measured and also can be multiplied. The main difference between interval and ratio scales is that for interval scales, there is an arbitrary “0” point. That means that if the value is “0” it doesn’t mean that the value is non-existent. The value does hold meaning. For example, temperature: If it is “0” degrees outside, that does not mean that the temperature is non-existent. If the temperature is -15 degrees. That does not mean that temperature has been taken away. Temperature still exists at the ‘0’ point and as negative values.
But, for a ratio scale, the “0” point is absolute. Given a value of “0” means that the value is no more. For instance, time. If you set a stop watch for one minute and the watch winds down to “0,” that means that the time is up. There is no “0” o’clock. If a distance value of “0” is given, then no forward progress has been made
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Biostatistics
Continuous variables
i. Happiness
ii. Level of performance
iii. Income level
Discrete Variables
i. Gender
ii. Place of residence
iii. Arrival time
Measurement of Variables
Nominal Scale
A nominal scale is a naming scale. In most cases an ordinal scale can be used to measure discrete values such as gender, arrival time, and place of residence. For instance, when you consider gender it presumed that there are only male and female which means the nominal scale can either classify gender as male or female. And in this case we can make statistical inference on the number of men and women for example in a class. Also, arrival time can be considered as morning, evening or lunch time which is also a common variable measured by the nominal scale. Moreover, place of residence is nominal measured as city, suburbs, or village (Kampn, 2019).
Ordinal Scale
An ordinal scale is used to order variables. The scale is used to measure how much is better than the other. Variables such as level of performance, and happiness can be measured using the ordinal scale (Ono, 2019). In this case, the level of happiness can be varied between very happy and less happy about a certain event or situation. Also, the level of income is ordered from higher incomes to lower income generating nations. In this case, such variables have a sense of distance between each other which makes it easier to order them. Consequently, these variables can be varied over an ordinal scale to determine the exact position a certain person or individual holds.

References
Kampen, J. K. (2019). Reflections on and test of the metrological properties of summated rating, Likert, and other scales based on sums of ordinal variables. Measurement, 137, 428-434.
Ono, Y. (2019). The ordinal scale on lexicostatistical data in Ainu dialects: Towards a new interdisciplinary research among the humanities and statistics. 北方人文研究, 12, 89-110.