8/27 Data analysis lecture Notes

To use ordinal variable and create a scale of comparison.

Compared to a nuclear bomb, it actually seems like a tiny, trivial thing.

But it'll be helpful for us. So I've gone on at some length about this idea that we need to know what our level of measurement is so that we aren't making any basic dumb mistakes like trying to find

the average for an ordinal variable.

And now I would like to talk out of the other side of my mouth and say, "Well, but sometimes I can't."

And you'd like to, right? If you've got an ordinal variable

that is acting like A scale level variable, that's good news, because now you can put it into tests and do math with it of the kind of appropriate scale level variables, and that is better, bigger, more

powerful tests and further arithmetic. So, when you got a scale like

ordinal variable,

this is a matter of judgment. And different instructors in a room like this will tell you a different thing, and different books by different authors will tell you a different thing.

For instance, in, my stats class I'm teaching this semester, I'm using a text that says you can treat an ordinal variable that just has ranks but not necessarily a step set

like it's a scale level variable. When you think it's like a scale, Albert.

Well, that is a little loosey-goosey for me, thanks very much.

I would rather be

more cautious. So for our purposes, let's follow this guideline.

We will allow ourselves to use an ordinal variable.

As though it were a scale variable. If it meets two conditions.

One, you need at least seven response categories.

Right. So in other words, if I asked, "What is your political orientation, left to right?

" one, liberal; two, moderate; three, conservative. I, I wouldn't, I'd say, don't you do it.

That's not, you haven't got enough gradation there for it to behave in a, a, a genuinely scale-like fashion.

But if you got at least seven, it generally will.

So if you said, "On a scale of one to seven, with one being most liberal and seven being most conservative, where would you place yourself?

" One, two, three, four, five, six, seven.

Alright, then you've met the condition, this first condition for, for saying, "Alright, I can treat that as ordinal.

" And it's ordinal and not scale because I'm not, I don't have a specific metric, right?

You're just saying, "You, give me your impression.

" How liberal or conservative are you? And I'm not, I can't, I wouldn't

bet a million dollars that the distance between one and two

on that scale is exactly the same as the distance between four and five on that same scale.

But long practice has convinced us that it, it gets more and more Regularly to be that way as you add

response categories, and by the time you're up to seven, it does act more or less that way.

Now, if you meet the second condition, then you're really pretty safe treating an ordinal variable as scale-like.

If in your sample, 'cause you only have 3, 000 people or 200 people, you don't have everybody in the world, but if your sample data shows a distribution of scores on that scale that's pretty

normal,

then you're okay too.

Up L curve. If you got small number here, whole bunch in the middle, small number there, right?

If it's normally distributed scores

and you got seven or more response categories, there's hardly anybody who'll give you any grief for treating that as a scale-like variable and putting it in a regression analysis.

I mean, even rather strict statisticians would be like,

That one's gonna act like a scale.

So let's use that cautious and rather strict guideline as our default rule, and then we'll see if once in a while we wanna bend the rule even further.

What you'll find is that we're going to use a lot of tests that have assumptions.

This is the term of art. What assumptions does this test make?

This test assumes normally distributed data, assumes scale level variable, and these tests are also pretty robust against violations of the assumptions.

you can bend the rules a little bit and you'll still be saying the right thing when you say I found a statistically significant finding.

Yeah, or didn't. You'll still usually be right, even if you bend the rules here and there in ways that I'll show you.

my own

disposition towards this sort of thing. Is that we should be rather rule-following authoritarian types, you know, we, in some part of your life, you may wanna be some kind of anarcho

hippie, but when you're trying to decide should I do this or not with statistical tests, I, I think it makes pretty good sense to, be a goody-goody and a, and a rule follower

and go by the bush.

Alright, so currently,

for a long time, the GSS had as its best measure of political orientation one called the Polycube, and it was in fact a seven point ordinal scale, and that's pretty good.

But they have added now Leftright, and so

it is

L E F T R G H T.

That's a funny way to spell, right? But that's what the name is.

And, let's see, I would show you the main and show me students and curricula systems too.

I haven't subscribed just yet. What? What? What?

And giving it history.

And show me the normal curve superimposed on top of that histogram so you can see if it was perfectly normal, what it would look like.

Yeah. What did you mean? And then what?

on the frequency statistics. Frequency statistics, I picked mean, and then I also picked standard deviations that tell you how normal or deviated

your distribution is.

I'll talk about those in detail in a week or two or three, but right this second, just show me.

This thing here

meets our needs. You look at it, you're like, "Well, this black line is a perfectly normal distribution, and gosh, this is too peaky.

It doesn't all fit exactly over there." Yeah, yeah, yeah.

But But for it to be too far from normal,

you need,

numbers, see this unit and this cryptosis, as long as both of those, and we don't even write that yet, we're gonna talk about this later,

but for right now I'm just telling you, if skewness and kurtosis have an absolute value within two, you're fine, and these are both closer to zero.

In other words, in the grand mathematical scheme of things, this is an extremely normally distributed set of responses.

You got as few previous as, as, as can be.

So I am absolutely comfortable treating that as a scale level variable, so much so that I presume In this data set,

two under left, right.

Look how I,

look at that! I called it scale. I set it to, you know, the flag right there is scale because that's scale enough.

This matters because we're going to be doing a bunch of tests that require scale up, and I really- I really haven't been keeping up with political things, and so now I'm so delighted that I have this basic measure

of political orientation left right that I can put into regression, t-tests, ANOVA, yay!

All right,

that's all the stuff that I hoped to get through by, on Tuesday.

And so now, we're starting Thursday. if you will

log in, Kevin, and go to assignments,

you will see, yours probably doesn't even show because it's not yet published, you probably just see one assignment, the assignment one, and it's published today at, at eleven,

and look, look at this,

read these carefully, right? If you're familiar with Canvas, it puts the wrong thing first.

Once in a while, students who are new to Texas State or Canvas, they're like, "Oh, come on, I saw September 2nd, 10:30, I added in before that, but no, no, no, look, due

September 1st,

available for half a day through the next day, so read carefully." And we're done.

Here we go. Assignment one. Here's your instruction.

Do that.

and what we'll do each week is,

you know, I'll let you get started and go along, and then depending on how complex it is or how much,

help seems appropriate for me, I'll come along after you go, all right?

Here's me generating the output. Does yours look like this?

Then you'll be able to look and go, "Yeah, actually, I'm matchy-matchy, good, sweet, great.

" Anything else? You can do like that.

What, what we'll try to do most weeks is have it be the case that you can get your output generated while we're sitting here together, and then routinely, that then, that'll,

then you, you got five days to do the rest, right?

'Cause generating output often will only take just a few minutes.

Today that'll be the case. We'll, we'll have our output here in ten minutes.

and then, some weeks you might be able to get much of the assignment done while we're still sitting here together and able to ask each other questions, right?

I mean, we're, we're, an engaged and sophisticated student can say, "Oh, you know what?

Your fourth question there, do you mean this or that

Ask a good question, do we mean this or that?

We can kinda talk about stuff together. But sometimes the assignments will be extensive enough where we'll get the output generated,

and then you will save it in some form you can get off of this machine, right?

You'll either put it in your Dropbox or your OneNote or your flash drive if you're brave enough.

We use a pretty clean machine.

And then you've got until Tuesday to write up your now that's, that's,

that's what you get an A for. you're gonna have the output together, we're gonna do that rather mechanically, you'd have to goof not that you're output, but then you've gotta say smart things about the output and why it

is.

So,

start.

And then in a minute I'll say, "Alright, here's what I was doing at the start, we'll see." And if you're completely overwhelmed, you're like, "Man, I can't remember how to start," don't worry, in five minutes I'll come along

and see how far you can get.

Bowie,

Emily.

Hey, it's Liam calling. What's your name? You're Liam.