When you learn statistics, there is new terminology to know. Now many of these
words are words that you already know, but I'm going to be using them in a
specific way, and you as a critical thinker, want to know what I mean when I
use certain words. So I'm going to tell you. We've already learned that
statistics can provide a way for us to evaluate claims of truth, like
mind-reading, or knowing what card you picked. I may claim that I know what card
you picked, and tell you to trust me, but you know better (and by the way, never
trust somebody who says trust me). Trustworthy people never tell you to
trust them. They just do the things that trustworthy people do, and other people
trust them because their behavior is consistently trustworthy. The ones who
have to tell you to trust them are the ones you should keep a very close eye on.
So along the way I'm going to be telling you lots of things about statistics, and
I promise that I'm going to do my very best to get it right, but if at any time
you have questions about what I tell you or you need more explanation, or you
think that I may have gotten something wrong, you are free to ask me for
evidence or an explanation, because that's how we do science. If I really do
know what I'm talking about, then I should be able to explain myself and
answer your questions. So since I think I know what I'm talking about, and I like
showing it, you should never be afraid to ask questions. And if I don't know, or if
I have it wrong, then your questions are going to help me get it right, and then
we'll all be smarter. So feel free to ask questions. To begin, let us learn some new
words. This thing that we do in science is called research. Research refers to
procedures for organizing data to better understand the world and to evaluate
claims of truth. We collect data about the world. Data are the scores obtained
in research. The word is actually the plural of a word data, so we say the data
are rather than the data is. We take what we learn from the data and use it to
better understand the world. We tell stories with data. The data are facts, so
data cannot be copyrighted, on the other hand presentations of data, such as that
journal article that you wrote, can be copyrighted. We analyze our data to tell
our stories to better understand the world using statistics. Doing statistical
research involves collecting, organizing, analyzing, and interpreting numerical
data. Collecting: measuring, or quantifying the world. Organizing: structuring data to
understand what they mean. Analyzing: interrogating the data to find out what
they reveal about the world. Interpreting: telling the story that we learned from
the data. Statistics are the point at which common sense meets logic, where
numbers are used to convey ideas. That means that someone else could use your
data, reanalyze it, and write their own article confirming or critiquing what
you wrote. Does your narrative hold up? In science we should be making our data
available to other researchers, because we want more people to look at our
numbers, and so to advance the field. The word statistics may refer to three
things. Number one: the practice of doing statistics, the field or discipline of
using math plus logic to make sense of data. So you are taking a statistics
class where you will learn about this field. I am a statistics teacher. You are
a statistics student. We are studying the application
of statistics. Two: statistics may refer to the mathematical procedures
that we use to organize, summarize and make sense of our data. We will learn how
to do t-tests and correlations, we will learn how to do statistics. Three:
statistics may refer to the numbers obtained from the statistical procedures,
such as means, standard deviations, or correlation coefficients. We might ask,
what are the statistics on gun violence in America? And we want to know how many
people are killed by guns every year in the US? Then we could compare those
statistics to other countries, and ask if the same pattern holds true in other
countries, and if not, why not? What are they doing differently? And let me be
even more specific about the term statistics those means, standard
deviations, and other numbers are properly called statistics when they
characterize data from a sample. You see, we almost never study the whole
population of all possible people, who might be included. Instead, we study a
smaller subset of those people. That subset is called a sample, and the
numbers that we calculate about our sample are called statistics. If we were
to measure the entire population, calculate their mean and standard
deviation, then we would call those numbers parameters. Parameters are
numbers that characterize data from a population. In order to be clear, whether
we are talking about statistics or parameters, we use different letters to
describe them. Statistics tend to use English letters - m and SD for mean and
standard deviation. Parameters tend to use Greek letters, like Sigma, mu, Si, or
lambda. So the mean of the sample would be M, but the mean of the population would
be mu. When we are using a sample that has been drawn from a population, we call
those techniques parametric statistics, because they use population values. We
will learn about other test, like the chi-square that do not rely on
population values, and we will call those techniques non-parametric statistics.
Another way to describe statistics is to separate them based on what they do. We
call them descriptive or inferential statistics. Descriptive statistics are
procedures that organize and summarize a large amount of data, like the mean or
the standard deviation. Descriptive statistics are used to interpret and
describe the important characteristics of the data. They can simplify millions
of numbers into a single number that can be used for comparisons. Examples of
descriptive statistics would be mean, median, mode, average, standard deviation,
or graphs. Inferential statistics on the other hand are procedures that are used
to draw conclusions about data, and to make inferences, or educated guesses, or
predictions about values that are unknown. So if I draw a sample of people
from a population of people who eat a lot of bacon, and then I draw another
sample of people who are vegetarians, and maybe a third sample of people who eat
bacon, but very rarely, each of those samples will have an average blood
cholesterol. If I follow them long-term, each sample will have a certain number
of people who die from heart disease or cancer. I can use inferential statistics
to infer whether bacon consumption is related to cholesterol, heart disease, or
cancer, and inference is a conclusion reached on
the basis of evidence and reasoning. I might ask you to look at the data and
say whether you infer that any differences in health outcomes were due
to random chance or due to the effect of bacon consumption. Infer is different
than imply. If you suggest that a difference in health outcomes might
exist, then you imply there is a difference. If I pick up on your
suggestion, and say "Well based on what you've shown me, I'm going to make some
changes in how I eat." Then I infer what you implied. When we are doing
inferential statistics, we look at the data and infer from the data something
about the population.