>> In this tutorial we are going to overview the entire class,
Social Statistics, Sociology 3123.
The first question we're going
to address is: what is statistics?
Statistics is nothing more than a set of procedures,
a set of procedures used to organize,
arrange and communicate data.
That leads to the question, what are data?
Data are nothing more
than information that's represented by numbers.
This is the basic focus of our course, and we're going to delve
into this a little more closely.
One way to think about statistics,
it absolutely is a set of procedures used to organize,
arrange and communicate about data, but a simple way to think
about statistics is the role that it plays.
Statistics is a part of the larger scientific
or research process, and that research process starts
with a simple research question.
It's the starting point for the scientific process
or the research process.
We start with a research question
that basically asks a question about the world we live in.
From there we devise a plan, a study, to collect data.
We go out and collect those data,
and then we have all this information.
The next step is to analyze the data.
This is the stuff of statistics.
Statistics is the analysis of data.
Once we analyze those data,
which in fact provides the answer to our research question,
and once we have that answer it leads to more questions.
So the research process is this circular pattern
that never ends.
Answering one question just leads to another,
and statistics, the analysis of data,
is the final step in that process.
This research question that we start
with are generally one of two types.
Our research questions are either descriptive in nature
or explanatory and sometimes called predictive.
These are the two basic types of questions we might have.
So what is a descriptive question?
This is a question that might ask, how many?
What does a group look like?
What does the subject we're interested in look like?
How many of them are there?
So, for example, we might be interested
in a simple question like:
what is the average income in the United States?
That's a descriptive question in nature.
It just asks how much money do people have on average,
how much money do they make annually on average.
An explanatory or predictive question examines the
relationship between two things.
So we may know the average income in the United States,
but then we may move on to another question.
What helps us explain that income?
Perhaps one's education level might help us explain income.
That is an explanatory or predictive.
Does knowing education help us predict or explain income?
So those are the two basic types
of research questions that we'll have.
Now, these questions can be answered
under two circumstances.
Okay, under two circumstances.
When we have population data and/or if we have sample data,
and as we'll learn later in this course,
a sample is just a relatively small subset
from the entire population, and when we have sample data we have
to do an additional step.
We have to infer how well our sample represents our
population, and that's the third component of the course.
So we're going to focus on descriptive statistics,
explanatory or predictive statistics
and inferential statistics, and to be sure,
we can calculate descriptive statistics using sample data
or predictive or explanatory statistics with sample data.
The defining feature
of inferential statistics is whether we have sample data.
The key to this course is understanding data
and the variables that represent those data.
So we know that data is information represented
by numbers.
These numbers represent variables.
What is a variable?
A variable is simply a characteristic of interest to us
that varies from one observation to another,
from one person to another.
These variables are key
to understanding statistical analysis.
So suppose we have two people, and this person,
person A we'll call them, is a white male,
age 21 with a 3.1 GPA.
We have another person, person B here, that is a black female,
age 23 with a 3.7 GPA.
Notice all of these descriptors: white, male, 21,
3.1 and so forth, these are variables or characteristics
that vary from one observation to the other,
and we're interested in either describing these variables
or predicting these variables.
What helps us predict GPA, for example?
How many females or black females are there
in the group we're interested in?
These are the types of questions we're going
to be addressing throughout this course.
So variables are absolutely key.
So we're going to also talk just a moment
about how we think about variables.
Variables are distinguished along the lines of what's known
as level of measurement.
This concept is absolutely key to understanding the material
in this course and what we'll be doing from this point forward.
Level of a measurement simply means that variables differ,
and they differ along this level of measurement,
which means more specifically,
how much information each variable type can provide to us,
and we have several different levels of measurement.
For this course we're going to categorize all variables
into one of three levels of measurement: nominal,
ordinal or interval-ratio.
So we're going to distinguish a variable
that is considered nominal, ordinal or interval-ratio.
Nominal variables are those variables that only allow us
to distinguish between two observations.
So a variable such as race -- an individual can be white, black,
Asian and so forth, and we can distinguish those individuals
along this variable race,
but that's all we can do is distinguish them.
We can't rank them, and we can't do anything else.
We can't say that a black person has more race
than a white person or an Asian person has more race
than a black person.
All we can do is distinguish
into nominal or named categories.
Ordinal variables, on the other hand, as the name implies,
allow us to order the categories of the variable.
We can say that one category represents more
of that variable than another.
A simple example of an orbital variable is social class.
We can say that someone might identify as from lower class,
middle class, upper class; and we can certainly say
that someone that is
in the upper class has more socioeconomic status
or social class than someone in the lower class.
What we can't say is precisely how much more social class
they have.
We can only say that one is more than the other, which leads us
to our final level of measurement, interval-ratio.
Again, it allows us to categorize just
like a nominal variable.
It allows us to rank order like an ordinal variable,
but it adds an additional piece of information
such that we know the precise amount of difference
between the categories.
So age is a good example of an interval ratio.
If someone is 21 and another person is 28,
we can say that 28 is different than 21.
We can say 28 is more than 21,
and we can say precisely how much more 28 is than 21.
That means we know the interval between the categories.
Understanding this concept, level of measurement,
is absolutely critical, and here's why.
We're going to talk about lots
of different statistical procedures.
All of them fall into the categories
that I already outlined here, descriptive or predictive
and inferential if the data are sample data.
We're going to talk about several descriptive statistics.
We're going to talk about several predictive statistics.
Which descriptive statistic do we use?
Which predictive statistic do we use?
It depends on level of measurement of the variables.
What descriptive statistic we use depends on the level
of measurement of that variable we're trying to describe.
What predictive statistic we use depends on the level
of measurement of the independent
and dependent variable that we'll describe
in more detail later in this course.
But absolutely, positively key here: level of measurement.