- 00:11
ROBERT BRUHL: Hello, I'm Professor Robert Bruhl.I teach Political Science at the Universityof Illinois in Chicago.My specialties are statistics and research methodology.In this tutorial, I'll be addressingways in which we use statistical inferencein observational studies to assesspossible relationships between traits of phenomenonin which we are interested.

- 00:31
ROBERT BRUHL [continued]: To begin our discussion, a common question and researchis this.Are these two traits related?For example, is a student who drinks coffee more likelyto score higher grades than a student who doesn't?Is a smoker more likely to prefer cola B over Cola Athan a non-smoker?To test such propositions using behavioral observations,we employ the methods of statistical inference.

- 00:55
ROBERT BRUHL [continued]: In turn, statistical inference employs probability theory,and we'll discuss two important concepts in that regard.Number one is defining relationshipbetween traits, and two, assessing the generalizabilityof an observed relationship.

- 01:17
ROBERT BRUHL [continued]: First, we're going to start with definingrelationship between traits.And that topic is stochastic independence.Depending upon the types of traits involved,there are different ways of assessing the existenceor nonexistence of a relationship between the twotraits.However, there are three levels of relationshipthat can be identified.One is, are the traits absolutely relatedor said to be deterministic?

- 01:41
ROBERT BRUHL [continued]: Or two, are the traits probably related or saidto be stochastic or are the traits probably not related,also stochastic?In the social and behavioral sciences,it's unlikely that any two behavioral traitswill be absolutely related.Consequently, we're left with assessingif two traits are probably related or probablynot related.

- 02:03
ROBERT BRUHL [continued]: Unfortunately we can only precisely definewhat we mean by probably not related.So we use that as a basis for assessing whether or nottwo traits are actually related.Then if our observations don't fit the criteria of traits thatare probably not related, we infer that the traitsare indeed probably related.This is said to be a proof by contradiction.

- 02:24
ROBERT BRUHL [continued]: So what do we mean when we say two traits are probablynot related?Mathematically, the explanation is long and complicated.However, a simple example can easily illustrate the concept.Suppose we're market researchers and for advertising purposeswe'd like to know if men and women aredifferent in their preferences for cola A versus cola B.

- 02:45
ROBERT BRUHL [continued]: To test this proposition, we collecta set of 100 men and 100 women to perform a taste test.As a point of reference, our sample taste testersincludes 35 men and 65 women.After the testing, we find that 40 individualsor 40% of our sample preferred cola A and 60 individualsor 60% of our sample preferred cola B. Nowif gender, which is a trait, does notmake a difference in one's cola preference, whichis another trait, we would expect to find in our sample40% of the men preferred cola A, 40% of the women preferred colaA, 60% of the men preferred cola B, and 60% of the womenpreferred cola B.

- 03:29
ROBERT BRUHL [continued]: If these conditions are met, we wouldsay the traits are probably not related.More formally, we would say the two traitsare stochastically independent.On the other hand, if the conditions are not met,we would say that the traits mightbe related for our specific set of observations.However, if we wish to generalize our results,we need to establish the statistical significanceof those results.

- 03:58
ROBERT BRUHL [continued]: In research, we often use a small set of observationsto represent a larger population.This is said to be sampling.If the sample is obtained in an unbiased manner, whichis said to be random selection, wecan be confident that the sample islikely to be a good representationof the population.We know this because of what is said to be the central limittheorem of probability theory.

- 04:20
ROBERT BRUHL [continued]: However, when we say a sample is a good representation,we do not mean perfect.That is, each sample is really a snapshot of a populationand these snapshots will not all be exactly the same.Most of the snapshots will be perfect representations.Some of the snapshots will be near perfect representations.And a few of the snapshots will be poor representations.

- 04:42
ROBERT BRUHL [continued]: Fortunately, the central limit theoremcan help us in guessing, but unfortunately,the central limit theorem can onlyhelp us determine if a snapshot is a poor representation.Returning then to the case in which wehave a set of observations that suggest a possible relationshipbetween two traits, to establish the statistical significanceof the suspected relationship, we have the following.

- 05:09
ROBERT BRUHL [continued]: We can only define the criteria of no relationship.And we can only determine if our sample is a poor snapshotof a population.Consequently, we have to use double negative logic.That is, we propose a hypothetical populationfitting the criteria of no relationship between the traitsof interest and we use the central limit theoremto determine if our sample is a poor representationof that hypothetical population.

- 05:35
ROBERT BRUHL [continued]: Then, if our sample is a poor representationof a population with no relationship,we can be confident that our sample is insteada good representation of a population in which the twotraits are related.This is said to be significance testing,and different types of traits willbe assessed using different forms of the central limittheorem.However, all significance testingis reported in terms of a probability.

- 06:04
ROBERT BRUHL [continued]: Snapshot is judged to be a poor representationif it has a probability of occurrence givena specific hypothetical population and, by convention,a low probability is considered to be less than 5%.In other words, an observed relationshipbetween two traits found in a sampleis deemed to be statistically significant if the sample isjudged to have a low probability of beinga snapshot of a population in which the traits are notrelated.

- 06:33
ROBERT BRUHL [continued]: In more formal terms, constructinga hypothetical population is saidto be the forming of a hypothesis.And showing a sample to be a poor representationof that population is said to be the rejectionof that hypothesis.If a hypothetical population is constructedto represent the absence of a relationship between twotraits, it's said to be the null hypothesis.

- 06:54
ROBERT BRUHL [continued]: Consequently, an observed relationshipbetween two traits found in a sampleis deemed to be statistically significantif the appropriate null hypothesis canbe formed and rejected.For further reference to topics of statistical inferenceand probability analysis are covered in substantial detailin my forthcoming book, Understanding StatisticalAnalysis and Modeling, by Sage.

### Video Info

**Publisher:** SAGE Publications Ltd.

**Publication Year:** 2017

**Video Type:**Tutorial

**Methods:** Statistical inference

**Keywords:** behavior (psychology); mathematics; practices, strategies, and tools; traits

### Segment Info

**Segment Num.:** 1

**Persons Discussed:**

**Events Discussed:**

**Keywords:**

## Abstract

Professor Robert Bruhl discusses the use of statistical inference to assess relationships between observed traits. He says relationships can be categorized as absolutely related, probably related, or probably not related.