Please help to my Statistics question?

Question

I'm getting confused about this things:

1. My teacher said that Nominal,Ordinal,Interval and Ratio has their own appropriate measures of location. for example: For Nominal the appropriate measures of location is Mode while in Ordinal is Median and can sometimes be mode. He also cited some examples for guidance, but I still am having a hard time on identifying them. For example, my teacher gave "Religion" as an example for  and since the appropriate measures of location of the Nominal is Mode, he cited that you can have "many Religion" thus, Mode. (Mode is the highest frequency, or has more frequency) Now the question is.. how do I determine the appropriate measures of location? Like, what's the easiest way to determine them? Can you cite also an examples for me to clearly understand them? Thank you so much!

Answer 1

Dear Paige,

I empathize with your difficulty on this. Your teacher has thrown a lot of word names at you, without apparently walking you through definitions aimed at your general level. Even I, with an excellent technical background, have trouble seeing why this particular set of word names was selected for this discussion.

But anyway -- "nominal" means something with a name (only) = non-numeric. Thus, for religions: Judaism, Christianity, Animism, Buddhism, etc. are all examples. So if you started lumping people together by religion, and had say 5 Animists, 3 Christians, 3 Jews, and 1 Buddhist, what could you say about the "trend" ("Measure of Location" to your teacher)? You couldn't graph these data as an x-y plot, religions aren't numbers! You could make a bar graph, with each bar labeled with one religion, and the height of the bar = the number of people of that religion. The only thing (bar) that would stand out would be the highest bar, representing the Mode of the data (more people are this religion than any other). There couldn't be a Median for the data, because there's nothing to allow you to reasonably assign any particular order to the bars in the bar graph, so that everyone represented by a bar to the left should be grouped together, and everyone represented by a bar to the right should be grouped together.

 

Anything else you can assign a name but not a number to the categories, would also be Nominal: examples might be people's moods, the colors of paint, what instrument is playing, what street do you live on. Note that there may be values associated (for example, 1085 Wal-mart Dr. -- your local Dollar Tree!) but the category (Wal-mart Dr.) is still just a name.

 

On the other hand, if you have Ordinal data (that is, numbers, they can be numbers with identical units), you can start grouping them together. Depending on what you want to show ("What's the most popular speed for cars to be travelling?" vs. "For what speed are an equal number of cars moving slower vs. faster?") you may pick as your statistic of choice ("Measure of Location") either the mode (the former example) or the median (the latter example) (and don't ever forget to include your units!).

 

Now, for Interval data (don't know what's intended here, perhaps an timed interval between repetitive events?) if that's a measured time value, then you may treat these as pure numbers, and deal with them like the Ordinal data. For some purposes, a value other than either the mode or median may be most useful for interval data! This is because a "long" interval is associated with a "rare" event -- and one extremely long interval, in the midst of a series of short intervals, severely reduces the total number of events that took place over your sampling period -- i.e., it has a large effect on the overall average rate of the events.

 

For Ratio data, that's always numbers, so you can, again, either pick mode or median as "Measure of Location", with the same caution as for Interval data.

 

When you get a little more into science, you'll also commonly find other types of data which have number values and directions associated (for example) -- that is, vectors (particularly in physics). They have their own special rules -- you can't treat the values without the associated directions. So if the molecules in a container are moving randomly around inside, they may have substantial average speed and kinetic energy, but the overall average direction is "zero". But worry about that when you get to it!

 

There are also times when we could use either qualitative (Nominal) or quantitative (Ordinal) values to describe -- examples might include musical tone pitch (notes of the scale, or frequencies?), sound intensity (perceived loudness, or acoustic amplitude?), color ("blue", vs. a Lab* measurement (that stands for Luminosity, a = red vs. green, b = blue vs. yellow) ), relative perceptibility of any stimulus in general ("very salty", vs. 0.26 g salt/ml), etc. Frequently the quantitative method is used for science purposes, since it's more exact and the data can be more completely statistically treated.

 

Hope this gets you started!

--S