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From Means to Methods: A Beginner's Guide to Statistical Analysis · Professor Peterson’s Psychology Classroom

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Welcome to Professor Peterson's Psychology Classroom,
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connecting the science of human behavior to everyday life.
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Here's Dr. Curtis Peterson. Last 2 weeks
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we have learned about mean, median, mode, measures of central
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tendency, and then last week we learned about standard
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deviation, which is the most common technique
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to look at variation within a population.
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So together, when we have a mean, we have a central
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tendency of 50% on one side, 50% on the other
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on some measurable variable. And then we have a standard
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deviation, which tells us kind of the average distance between
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individual scores. So it gives us a good idea about the
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variation within a given sample,
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and it lets us know where the average for individuals
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is. Now there's a lot more to this
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that provides us more information as we move along, and we'll
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get to that here in a few minutes. Now where we're heading into
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is actually analyzing data,
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and we're going to use— now I want to make this clear. This, this,
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we're going to go through kind of the scientific process to
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use statistics, but this, these methods can be used when analyzing
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market data, business data, and the
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like. So this, this isn't limited to just what I'm about to talk to here
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for the next few minutes regarding the scientific method.
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It really goes well beyond that. So keep
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that in mind for our business students and students who are not necessarily
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going into the social or life sciences. Okay,
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but we're going to start with the basic process of
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developing a— not only a research program
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or a research process, but a statistical
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process to analyze that data that we're about to collect through our
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research. So we will start with,
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again, just the most basic high
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school scientific
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method. You've probably all seen this before, where we
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start with what's called a research question, and that's a general question that
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we may want to ask. And then we go and
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we look at other research and see what is known about
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this certain topic or the certain question.
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And from that, we find hypotheses.
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Okay, and this is going to be the important thing for statistics is
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we develop a hypothesis, which is in its most basic
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terminology is an educated measurable
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guess about what's going to happen if
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you implement this research process. And then of course
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we go in and we test this hypothesis and
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then we analyze, right? This is where the magic
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of statistics is going to occur is right here when we're developing our
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results. And then in the scientific world,
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we share those results and then that develops new
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questions and the process starts all over again.
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So we're going to look at these different components really
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starting with this idea of hypothesis and hypothesis testing.
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And that's really the strength of statistical
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probabilities and statistical methods is it allows
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us to really determine, you know,
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whether we have evidence for or against a given topic.
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And I know I'm talking in the abstract at the
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moment, but it'll make more sense as we go along.
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So let's talk about
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again, so in any type of
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problem-solving situation in research,
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we always want to have a method of analysis.
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Okay, that method of analysis comes from a couple sources.
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One, Back to our research question,
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what we know, and then what is driving
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our hypotheses or what's testing that.
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These— the combination of these 3 things will determine
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our method. All right, so I want to kind of
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give an example. So real quickly, we have qualitative,
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quantitative, or we have a mix of both.
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And to kind of elaborate on this issue,
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a quantitative method is when we
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want to know the objective situation.
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We want to know what the average individuals—
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we want to know what the average differences in groups are, or the average
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similarities within a group.
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Qualitative methods are when we want to know the subjective
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reality of the people
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of interest in our research or the subject matter.
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So qualitative, subjective, quantitative,
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objective. A mixed method is when you want to know
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both. Okay, so for example, when I
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used to do organizational consultation, I used
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to use a mixed method. Basically what I— what would happen is when
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I did consultation, I had organizations that were struggling with over— with high
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overturn rates with employees, or they weren't accomplishing
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programmatic goals for some reason that
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are non-financial. It's due to the performance or,
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or the organizational structure. And in
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that situation, what I would start with is a quantitative
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method where I would go in and I would measure with
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surveys and the like,
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different aspects of the organization. So I'd give a measure on,
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say, organizational commitment, burnout, job satisfaction,
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performance. Based on that, I would
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then develop some ideas about what's going on in that
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organization. So maybe in this case we have high burnout and low
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job satisfaction. Well, that objective reality
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only gets me so far. It only tells me what's objectively
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going on in that organization. What I don't
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know is what is the subjective lived
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reality of the employees who are experiencing that high
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rate of turnover and that low rate of job satisfaction.
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So the second thing is I
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would go in and I would do interviews and I would interview samples
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of the organization. Organization to really get to why they
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individually, they're experiencing these 2
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issues. That combination is what we call a mixed
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method, where you're using both quantitative and qualitative measures
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to really get at what's
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going on. For us,
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this is the one that we are concerned about
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when it comes to statistics is the quantitative aspects.
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You really don't use statistical
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methods when looking at quantitative data.
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Okay, it's a— there's qualitative methodology.
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And so for the sake of this class, we're not going to worry about this.
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If you'd like to know information, you're more than welcome to set
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up some time in my office hours or to give me an email and we
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can talk more about the qualitative method. But what we're going to focus on here
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is the quantitative method.
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So we have already talked about some of the descriptive
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methods, right? We've talked about summarizing data. We've talked
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about presenting what the average is or the mean is.
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We talked about variation with the standard deviation.
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But there's also within the descriptive— beyond describing
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the data in the descriptive methods, we want to know whether
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variables are associated with each other or if variables predict
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each other. And this is where we use what's called correlational
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or regression methods. Now for the sake of basic statistics
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class, we're not going to worry about factorial analysis.
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That goes beyond the scope of this course. But what we are going to look
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at is correlation and regression.
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Correlation tells us whether or not 2 variables are
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associated with each other, meaning as As scores on one goes up,
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scores on the other goes up. As scores go down on one, the scores
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go down on the other. So correlation
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tells us that 2 variables are related with
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each other. Regression tells
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us if one variable predicts another variable,
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meaning, you know, does A predict be in
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some context. Now, the important
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thing is, and why this is put under descriptive methods,
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is this can tell us nothing about cause
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and effect. It can only tell us whether or not 2
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variables are associated with each other and/or predict
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each other. It doesn't tell us whether one causes the other.
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In order to do that, in order to find cause and effect
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using statistical methods, we have to use the experimental method.
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In the experimental method, instead of just having
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2 variables and we're looking to whether and describe their association
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and describe what they are, what we're looking for is to see
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if one variable represented with the i causes
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a change in another variable,
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okay, which is represented here by D.
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Now I is going to be known as our independent
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variable, where D is going to be
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known as our dependent variable.
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So if I were to, uh,
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So to kind of explain this, so independent variable is a variable
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that does not depend on anything else, where a dependent
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variable depends on changes in the independent variable.
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That's why they're named the way they are.
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Now statistically, to test whether
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an independent variable causes changes in the dependent variable
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when we're doing statistics, the 2 most used
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methods are what's called a t-test and
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an ANOVA. A t-test
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is when you have one independent variable and one
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dependent variable. And you're just trying
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to determine if that one variable causes changes in
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the other. An ANOVA
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can work 2 ways. One, you can have
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several independent variables in this
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situation and one dependent variable,
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and you're trying to see which of these
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3 independent variables causes a change in your dependent variable.
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The other way this can work out is you have an
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independent variable and you have several dependent
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variables. And you're trying to determine which of
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these dependent variables are affected by the independent
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variable. This is what we call multivariate statistics.
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ANOVA stands for analysis of variance, meaning what
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it takes into account is not just whether groups
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are different based on their mean, Okay, because that really doesn't
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tell us much, and I'll explain that in a minute. What the ANOVA tells us
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is whether the variance is so much different between
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the 2 groups that statistically and probabilistically
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those 2 groups are different, which is much more meaningful than just looking
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at means. Okay, so the
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analyses that we're going to focus on
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for the remainder of this course are the 2 basic
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association variables
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and the 2 tests for difference variables.
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And we'll end the class with something called nonparametric
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methods. Now, one of the things that
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we need to look at when we look at these
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variables, kind of like when we were talking about the graphs
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and whatnot, is these tests,
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these 4 tests that I just mentioned, require the variables
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to be continuous.
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Meaning that the dependent variable for the t-test and both
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variables for the correlation and regression have
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to have some type of variation, meaning that they have
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to have a— people
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can score differently on it, not just based on groups. So for
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example, age is a continuous variable because it can
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go from 0 to, you know, the last person on
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Earth, and people vary continuously on that depending upon
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how long they've lived here. Another example of continuous
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variables is when you do a survey
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and it asks you, you know, do you agree,
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strongly agree, neutral,
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disagree, strongly disagree? That wasn't
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exactly in the correct order, but you start one with 0 and
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the other ends in 5, and you make that a continuous measure,
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that continuous measurement. That's what we call a
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Likert scale, and that's a very important term because
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when you go on into statistics and
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you talk about the Likert scale, one of the things we have to recognize is
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it's not a true continuous variable,
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meaning that it's actually categorical. If you think about selecting strongly
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agree versus disagree, what is the actual continuum?
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So there's no exact distance between disagree
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versus agree, meaning unlike age
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where there's an exact difference between the age of 23
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and the age of 24, it's 12 months, it doesn't vary, but we
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can't tell, you know,
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what is the true numbers between strongly
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agree and agree. Is it 1 unit,
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2 units, 5 units? When we do a Likert scale,
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we assume— it's an assumption that there's
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a difference. But again, that's where you also can add
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a subjective measure in.
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Nonparametric methods are meant
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to analyze what we call categorical data.
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So categorical data, you know, we can look at traditionally things
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like gender, nationality,
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Whether you're a coal miner or
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a sanitation
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worker. Okay, you fit them in categories and
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then you want to see if, you know, is there more?
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For example, if we go to the example of miners
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versus sanitation workers, maybe what we want to do is we want to know
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within a region, Is there statistically more sanitation
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workers than there are miners? Well, what we can do
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is a nonparametric method where we go in and we sample
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and see how many individuals are sanitation
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workers versus miners. And then using nonparametric methods,
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it can give us a probability of whether there's
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more miners or whether there's more sanitation
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workers in the larger population, and that's nonparametric