Causation: Can We Say What Caused the Effect?

Sections 4.1 and 4.2

Big Idea of Chapter 4 Previously research questions focused on one proportion

What proportion of the time did Buzz guess the right button?

What proportion of the time did Marine guess the right bag?

We will now start to focus on research questions comparing two groups. Are smokers more likely than nonsmokers to have

lung cancer? Are children who used night light as infants more likely

to need glasses than those that don’t use night lights?

Types of Variables When two variables are involved in a

study, they are often classified as explanatory and response

Explanatory variable (Independent, Predictor) The variable we think is “explaining” the

change in the response variable. Response variable (Dependent)

The variable we think is being impacted or changed by the explanatory variable.

Roles of VariablesChoose the explanatory and response

variable: Smoking and lung cancer Heart disease and Diet Hair color and eye color

Sometimes there is a clear distinction between explanatory and response variables and sometimes there isn’t.

November 7, 2008 12:55 p.m.To the Hope College Campus Community:Within the past few minutes the College Administrators have met with county health officials who issued the letter below with an emergency order. This order is mandatory under Michigan law.Because of the growing number of reported illnesses today, health officials have changed their earlier advice to follow good hygiene practices to a cancellation of all campus activities effectively immediately.

It is strongly recommended by health officials that students refrain from travel and meeting in large groups. President James E. Bultman

Two-Way Table Let’s look to see if there is a difference in the

incidents of contracting the norovirus in males versus females.

Note that we are now comparing one variables against another instead of comparing one variable against some standard.

Which is the explanatory variable?Number of students with norovirus by sex

SexFemale Male

Contracted Norovirus

Yes 212 124No 1049 479Total 1261 603

Explanatory and Response

Explanatory (columns)Response (rows)

SexFemale Male

Contracted Norovirus

Yes 212 124No 1049 479Total 1261 603

Counts versus Proportions We can’t use counts to compare the prevalence of

norovirus among the two genders, we need to use conditional proportions or percentages. When the explanatory variable creates the columns, look at column percentages.

By looking at the percentages from our sample, who was more likely to get the norovirus?

SexFemale Male

Contracted Norovirus

Yes 16.8%212/1261

20.6%124/603

No 83.2%1049/1261

79.4%479/603

Total 1261 603

Observational Studies The norovirus study is an example of an

observational study. In observational studies researchers

observe individuals and measure variables of interest

Examples: A significantly higher proportion of

individuals with lung cancer smoked compared to same-age individuals who don’t have lung cancer

College students who spend more time on Facebook tend to have lower GPAs

Observational StudiesDo these studies prove that smoking causes lung cancer or Facebook causes lower GPAs?

Many people who see these types of studies think so…

It depends on the study design

Nightlights and Near-Sightedness Near-sightedness often develops in childhood Recent studies looked to see if there is an

association between near-sightedness and nightlight use with infants

Researchers interviewed parents of 479 children who were outpatients in a pediatric ophthalmology clinic

Asked whether the child slept with the room light on, with a night light on, or in darkness before age 2

Children were also separated into two groups: near-sighted or not near-sighted based on the child’s recent eye examination

Night-lights and near-sightedness  Darkness Night

LightRoom Light

Total

Near-sighted 18 78 41 137Not near-sighted

154 154 34 342

Total 172 232 75 479The largest group of near-sighted kids slept in rooms with night lights? What is a better way to look at the data?

Conditional proportions 18/172 ≈ 0.105 78/232 ≈ 0.336 41/75 ≈ 0.547

Night-lights and near-sightedness  Darkness Night

LightRoom Light

Total

Near-sighted 10.5% 18/172

33.6%78/232

54.7%41/75

137

Not near-sighted

154 154 34 342

Total 172 232 75 479Notice that as the light level increases, the percentage of near-sighted children also increases.

Nightlights and near-sightedness There is an association between near-

sightedness and nightlights Can we claim that nightlights and room

lights caused the increase in near-sightedness?

Might there be other reasons for this association?

Night-lights and near-sightedness Could parent’s eyesight be another

explanation? Maybe parents with poor eyesight tend

to use more light to make it easier to navigate the room at night and parents with poor eyesight also tend to have children with poor eyesight.

Now we have a third variable of parents’ eyesight

Parents’ eyesight is considered a confounding variable.

Confounding Variables Confounding variables are related to both the

explanatory and response variable Because of this, we can’t draw cause and effect

conclusions when confounding variables are present.

Since confounding variables can be present in observational studies, we can’t conclude causation from these kinds of studies.

This doesn’t mean the explanatory variable isn’t influencing the response variable. Association may not imply causation, but can be a pretty big hint.

Observational Studies vs. Experiments Observational studies may have

confounding variables present that prevent us from determining a cause and effect.

Well designed experiments can control for confounding variables so we can determine cause and effect.

Experiments: Control for Confounding Variables

Physicians’ Health Study I (study aspirin’s affect on reducing heart attacks.• Started in 1982 with 22,071 male

physicians.• The physicians were randomly assigned

into one of two groups.• Half took a 325mg aspirin every other

day and half took a placebo.

Results Intended to go until 1995, the aspirin study was

stopped in 1988 after finding significant results. 189 (1.7%) heart attacks occurred in the placebo

group and 104 (0.9%) in the aspirin group. (45% reduction in heart attacks for the aspirin group.)

What about confounding variables? Could the aspirin group be different than the placebo group in some other ways? Did they have a better diet? Did they exercise more? Were they genetically less likely to have heart attacks? Were they younger?

The big idea Confounding variables are controlled in

experiments due to the random assignment of subjects to treatment groups.

Randomly assigning people to groups tends to balance out all other variables between the groups.

So variables that could have an effect on the response should be equalized between the two groups and therefore should not be confounding

Thus, cause and effect conclusions are possible in experiments through random assignment. (It must be a well run experiment.)

Random vs. Random With observational studies, random

sampling is often done. This allows us to make inferences from the sample to the population where the sample was drawn.

With experiments, random assignment is done. This allows us to conclude causation.

Blocking and Random Assignment The goal in random assignment is to make two

groups as similar as possible. Sometime there are characteristics (or variables)

of subjects that you can see and you can block on these variables.

For example, if our subjects consist of 60% females and 40% males, we can force our two groups to both consist of 60% female and 40% male.

Let’s look at an applet to see what blocking and random assignment does to help keep both groups as similar as possible.

Exploration 4.1

In Exploration 4.1 we will see if playing in front of a large crowd (at home) is a disadvantage for the Oklahoma Thunder compared to a smaller crowd?

HW: Do exercises 4.1.4, 4.2.1-4, 4.2.6.

Paired DesignsSection 4.3

Variability in quantitative variables impacts the distribution of the sample statistics like .

Reducing variability in data improves inferences: Narrower confidence intervals Smaller p-values when the null hypothesis is false

We can sometimes reduce variability in the response variable by using an alternative study designs called paired design.

Introduction

Can You Study With Music Blaring?

Example 4.3

Many students study while listening to music. Does it hurt their ability to focus? In “Checking It Out: Does music interfere with

studying?” Stanford Prof Clifford Nass claims the human brain listens to song lyrics with the same part that does word processing

Instrumental music is, for the most part, processed on the other side of the brain and Nass claims that reading and listening to instrumental music has virtually no interference.

Studying with Music

Consider the experimental designs: Experiment 1—Random assignment to 2

groups 27 students were randomly assigned to 1 of 2 groups:

One group listens to music with lyrics One group listens to music without lyrics

Students play a memorization game while listening to the music.

Experiment 2—Paired design All students play the memorization game twice:

Once while listening to music with lyrics Once while listening to music without lyrics.

Studying with Music

What if everyone could remember exactly 2 more words when they listened to a song without lyrics.

There could be a lot of overlap between the two sets of scores and it would be difficult to detect a difference as shown here.

 

Studying with Music

Without Lyrics

With Lyrics

Variability in people’s memorization abilities may make it difficult to see differences between the songs in the first experiment.

The paired design focuses on the difference in the number of words memorized, instead of the number of words memorized.

By looking at this difference, the variability in general memorization ability is taken away and we may have reduced variability.

Studying with Music

While there is lots of variability in the number of words memorized between students, there would be no variability in the difference in the number of words memorized in our hypothetical example.

All values would be exactly 2. Hence we would have extremely strong

evidence of a difference in ability to memorize words between the two types of music.

Studying with Music

Pairing often makes it easier to detect statistical significance

Can we still make cause-and-effect conclusions in paired design?

Can we still have random assignment?

Pairing and Random Assignment

Imagine that we ran the following experiment: All students play the game listening to the song with lyrics Then play the game a second time while listening to the

song without lyrics. If we see significant improvement in performance, is

it attributable to the song? What about experience? Could that have made the

difference? What is a better design?

Randomly assign each person to which song they hear first - with lyrics first, or without.

This cancels out an “experience” effect

Pairing and Random Assignment

We can use pairing in observational studies.

If you are interested in which test was more difficult in a course, the first or the second, compare the average difference in scores for each individual.

Use a Pretest and a Postest.

Paring and Observational Studies

Complete questions 1 – 9 on Exploration 4.3: Rounding First Base.

Exploration 4.3

HW: Do exercises 4.3.1, 4.CE.2-4.