-: Hello and welcome to the video lecture
on Quantitative Data Analysis.
So this is the first of two parts of how do you analyze data
such as that you would get in a survey
and that's we'll be doing as well with our research project.
So we're gonna look at
how to analyze data one variable at a time, univariate.
Bivariate, which is two at a time.
Multivariate, which is many variables at the same time.
And we're gonna do a review
of the four types of variables that we talked about
just because I wanna make sure that you understand that.
So univariate analysis is looking at a single variable.
Usually we look at frequencies
and if it's a ratio or interval,
we can also look at central tendency and dispersion,
which tells us valuable information about that variable.
So a frequency analysis
is how many respondents gave that answer.
It can be done by the number of answers,
it could be done by the percentages.
And especially for nominal,
this would be really the only way to do it,
since they don't have a unit, they're not numerical.
Usually you report ordinal variables in this way as well.
So if you have a ratio or interval,
you can talk about the Central Tendency.
And the three of those are Mean, Median and Mode.
And you can think about which one
gives the best information about a given variable,
about the data.
Which one can best sort of tell the story
of what's happening.
Mean is when you simply add up all the values
and divide by the number of responses.
The weakness of this is that if there are extreme values,
they will skew it.
So an example here where the mean age of 21,
but that really doesn't do a very good job of describing it.
Median is when you rank them from high to low
and take the one in the middle.
That if it's an odd number, it's the middle one.
If it's an even the number,
you take the two middle ones
and take the mean of those two.
In many cases, things like home prices or income,
things that have some very high, extreme values can...
That you'll often see them expressed as median.
And finally, mode is how many...
Or what was the one response that the greatest number
of individuals gave.
And that can be good if there's sort of
a cluster of responses, it can help to tell that.
So in class we'll think a bit more about when is mean,
median and mode the best,
under which circumstances is each one
sort of the best way to tell what is happening
with our data.
Another thing that you can do with numerical data
like ratio or interval that has a unit
is to measure the dispersion.
How spread out among out are the data.
So you can see here,
there's two bell curves here that have the same mean,
but the one in blue has a much small...
The data are much more sort of huddled around the middle.
That you get like a tall thin peak there,
as is the one in red,
which is much more sort of spread out
even though they have the same mean.
This is a measure of precision
and it tends to be expressed in standard deviation
or in variance.
And basically the standard deviation measures on average,
how far away from the mean is the average response.
And it's the positive square root of the variance.
So as I said,
for a nominal variable you wanna report the frequency.
And we'll talk about why...
We'll talk in class,
why does the mean of the nominal variable not make sense.
Ordinal, some people say use frequencies.
Sometimes you will report the mean.
But note that
because there are no units,
frequency might be best.
Like you could say on a five point scale
that the mean response was 3.8.
The sort of danger there is that your four
and my four aren't the same but many still do that.
For interval and ratio,
we very often report the mean.
You could do a frequency,
but especially if you have a lot of subjects
and a lot of responses,
it's just going to be a really long data table
that may not provide that much valuable information,
that's not in the mean media mode
and standard deviation.
Next, we'll jump to bivariate analysis.
The relationship between two variables.
And this is very often done as a cross tab.
So you can see here the rows are where folks live
and the columns are what's their favorite baseball team.
And you can see it has it reported both
in numbers and in percentages.
This allows for subgroup comparisons.
Very often, it's thought of as you think of the demographic
as the independent and some sort of attitude
or behavior as the dependent.
So you could think about how different age groups,
their views on gay marriage,
student versus faculty use of tobacco group,
where the demographic is age or occupation,
which we just said.
And the dependent is some sort of behavior or
belief, attitude, things like that.
Multivariate is where we have several independence.
So you might wanna think about,
like your class year and your major
and its a fact on some sort of dependent level,
like income or again like where you work,
or your support for some view and things like that.
The last example of multivariate
that I wanted to talk to you about is Regression.
And here, you have one dependent,
and a whole lot of independent.
Here is a case where we only have one dependent
and you can think about
if Y is how much was spent on local food in a month,
and X is income.
This B1, this beta one measures how...
What is the predicted change in expenditure on local food
for a unit change in income.
That on average, if you put one more dollar
into somebody's pocket,
how much of it are they going to spend on local food?
And then the error term is the part of the model
that's not explained by the Xs.
And we're gonna talk a lot more about regression.
And here's a video about it if you wanna watch that.
So here's an example,
where there's two regressors, two Xs,
two independence and it might be something like,
age and income.
And again, you look at each of these Bs
is the effect of the change in Y for a given change in X.
And you can think of it as the slope of that line,
so if you have Y your dependent on your Y axis,
and one of your independent on Xs,
and you see what is the slope of that line,
of that best fit line?
And that is the average change in Y
for a given amount index.
We can add a whole lot of regressors,
some number K,
many models might have 10 or more.
And well what this does is holding all else equal.
So holding say age and household size constant,
it looks just at the effective income.
And again, the goal of it is to find
the marginal effect, these betas, or these Bs
of how much does it change in X1 holding all else equal.
Well, what is the expected or predicted,
or average change in Y?
So just a quick reminder of the four types of data.
Nominal is where it has no rank, no high or low,
it's just name for things like what state were you born.
Ordinal tends to be a scale, a rating, or a ranking.
How likely are you to do something interview?
I mean interval is has no true zero,
like what year we're born.
And ratio can be expressed as you know,
a response can be twice as big as another
and this has a true zero.
And that can be something like number
of people in your household.
Also, dollars or height, or miles away, or things like that.
And these also have units, both interval and ratio,
variables have units.
Years,
pounds, dollars,
whereas nominal and ordinal have none.
So see if you can get this quiz right.
What kind of variables are these?
And if you want to pause it and then go to the next one
and well, when I'm done speaking and change the slide.
It will tell you which is which.
So pause now and see if you can get it right.
And here you are.
So the first one,
expenditure is a ratio you can spend zero.
If you spend 20 and I spend 10, you spend twice as much.
The sort of a scale here is ordinal.
Degrees Fahrenheit are interval.
And then what's your major is nominal.
So this is what we did.
We talked about univariate, bivariate,
multivariate and regression.
And we talk more about variable types.
And this is what you should know.
Thank you.