Chapter 9 Lecture 1

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Chapter 9 Lecture 1

• The limits of correlational research and the
  logic of experimentation.

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Concepts

• The limits of correlation
• The experimental method
• Comparing Mean Squares between groups to Mean
  Squares within groups

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The limits of correlational research

• Correlational research tells us that variables
  are related.
• It does not tell us what causes that
  relationship.
• The relationship could be caused by some other,
  unstudied variable.

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The 3rd variable problem.

• In correlational research we started with
  participants who were different from each other
  in at least 2 ways.
• Participants who differ in 2 ways will differ in
  3 ways, in 3000 ways, in an almost infinite
  number of ways and combinations of ways.
• Any of these other ways in which participants
  differ from each other may be responsible for the
  relationship between X and Y you find in a
  correlational study

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So

• There are an infinite number of such unstudied
  3rd variables and combinations of variables
• So even though you can predict one thing from
  another, you dont know what causes either or
  what to change to get either X or Y to change

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An example of 3rd variable causation

• Randomly select participants. Find out how many
  friends each has and how many days each was ill
  and stayed home from work last year.
• Results more friends are significantly
  correlated with less sick days.
• Using the regression equation, you can predict
  how many days a person will be ill if you know
  how many friends they have.
• Can you conclude social support protects against
  stress and illness? NO!
• What else might cause the relationship you found?

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Alternative Explanations

• Perhaps people with generally better immune
  systems get ill less often.
• If such people are generally healthier, they may
  have time and energy to be outgoing and to spend
  with friends.
• So better immune function may cause both fewer
  sick days and more friendships.
• Or something else (e.g., gregariousness and
  robust health are genetically linked)
• Or a combination of factors control the
  relationship between days ill and number of
  friends.

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Another Example

• You can predict who will commit suicide by simply
  finding the time that people wake up in the
  morning.
• The earlier you wake up, the more likely you are
  to commit suicide.
• To make prediction more accurate take into
  account (control for) other factors (e.g. age,
  gender, shift work).
• But you can really predict suicide from the time
  people wake up the two are correlated in the
  population as a whole.

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WHY????

• Is it that waking up when it is dark is
  depressing?
• Is it that suicidal people are so worried they
  cant sleep?
• NO!!
• The same biochemical lesion that makes people
  vulnerable to clinical depression also affects
  circadian rhythms. The biological clock of people
  with depression is set earlier. They get tired
  earlier and wake up earlier.
• A classic symptom of depression is early morning
  awakening.
• So, depression causes both heightened levels of
  suicide and waking up early

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You can write prescriptions for change only if
you know causes

• If waking up early directly causes suicide, you
  should give people sleeping pills.
• Give depressed people sleeping pills and you get
  more suicide, not less.
• Instead you must treat the cause, depression,
  with psychotherapy and/or antidepressant
  medication

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If you want to change things, you need experiments

• The lesson is that correlational research can
  never tell you how to cause a change in Y.
• Experimental research can isolate causal factors.
• Then, you can change things by altering what
  causes them.
• Like curing depression gets rid of both the
  desire to commit suicide and waking early.

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Remember, there is no way to know what causes
what on the basis of correlational studies. Only
experimentation can provide causal information.
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SO WE NEED EXPERIMENTAL RESEARCH IF WE ARE TO
HELP PEOPLE KNOW HOW TO CHANGE THINGS
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How and why experiments can find causal
relationships
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The Key Start with groups that are the same, not
different

• In an experiment, you start off with a random
  sample of participants drawn from the population
  of interest.
• Then you randomly assign participants to
  experimental groups.
• Each experimental group is therefore a random
  sample of the population.

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Since each group is a random sample of the same
population

• The typical score in each group, the group mean,
  will be similar to the population mean.
• The spread of scores around the group mean will
  be similar to the spread of scores around the
  population mean.
• So, the mean and variance of each group is
  similar to that of the population.
• Things that are similar to a third thing (mu and
  sigma) are similar to each other.
• That is, the average score and spread of scores
  will be similar in all the groups.

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ON WHAT MEASURE(S) ARE THE GROUPS THE SAME?? ON
EVERY POSSIBLE MEASURE!!!

• Hairs on heads, size of great aunts backyard,
  your self-confidence multiplied by your
  grandmothers self confidence, the size of your
  mothers left thumb, how nice your third grade
  teacher was
• ETCETERA, ETCETERA, ETCETERA.

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If the groups are similar in every way, no
pre-existing differences can account for
differences after the experimental treatments.

• That is the groups all start off the same in
  every way.
• The ways the groups are the same include all the
  preexisting differences (and combination of
  differences) that underlie the 3rd variable
  explanation in correlational research.

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Since the groups all start off the same, the only
thing about them that will systematically differ
is how we treat themIf, after we treat them
differently, they respond differently, it will be
because of the different ways they were treated.
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During an experiment

• Groups start off the same
• Groups are TREATED DIFFERENTLY
• Responses thought to be effected by the different
  treatments are measured
• If the average response in the groups is now
  different from each other, the differences may
  well have been caused by the different ways the
  groups were treated.

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In the simplest experiments

• The groups are exposed to treatments that vary on
  a single dimension.
• The dimension that differs is called the
  independent variable (because, given that who
  gets which treatment is random, differences in
  treatment during the experiment are unrelated to
  or independent of pre-existing differences).
• Relevant responses (called dependent variables)
  are then measured to see whether the independent
  variable caused differences among the treatment
  conditions beyond those expected given ordinary
  sampling fluctuation.

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Analysing data from an experiment

• Of course the groups will always differ somewhat
  from each other on anything you measure due to
  sampling fluctuation.
• These are just random difference, you can afford
  those
• In 3 groups, one will score highest, one lowest
  and one in the middle just by chance.
• So the simple fact that the groups differ
  somewhat is not enough to determine that the
  independent variable, the different ways the
  groups were treated, caused the differences.
• We have to determine whether the groups are more
  different than they should be if only sampling
  fluctuation is at work.

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Example ECT, Pills or Psychotherapy?

• We know that for severe, psychotic depression,
  electroconvulsive therapy (ECT) is the most
  effective treatment.
• A managed care company wants everyone
  hospitalized for depression to be given ECT, even
  those with only moderately severe depression.
• They say that antidepressant medication and
  cognitive therapy take longer to work, require
  maintenance treatment and are ultimately more
  expensive, so everyone should get shock.

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What can you do about it?

• Just because they can plausibly say that ECT is
  better, doesnt mean it is so.
• Would you like to be given a choice if the
  treatments are equally effective, though one
  costs your insurance company less than the
  others.
• How about running an experiment meant to show
  that medication and psychotherapy work as well or
  better than ECT with moderately depressed
  patients, that there are no differences in the
  effectiveness of the differing forms of treatment.

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Designing the experiment

• Population from which random sample was gathered
  Moderately depressed inpatients
• Number of research participants and groups 9
  participants divided equally into 3 groups
• Experimental design Single factor, unrelated
  groups design.

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Design - continued

• Independent variable Type of treatment
• Levels of the independent variable
• (1) Electroconvulsive Therapy
• (2) Cognitive Behavioral Therapy
• (3) Antidepressant Medication
• Dependent variable Hamilton Rating Scale
  Depression Scores (HAM-D)
• (Higher scores greater depression.)

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H0 H1 Mutually exclusive and exhaustive
hypotheses. If one is wrong, the other must be
right.

• Either the independent variable would cause
  differences in responses (the dependent variable)
  in the population as a whole or it would not.
• H0 The different conditions embodied by the
  independent variable would have NO EFFECT if
  administered to the whole population
• H1 The different conditions embodied by the
  independent variable would produce different
  responses if administered to the whole
  population. In this case, one or two of the
  treatments will do better than the other(s).

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The Null Hypothesis keeps us from a truly
shocking situation

• The null hypothesis (H0) states that the only
  reason that the treatment means are different is
  sampling fluctuation. It says that the
  independent variable causes no systematic
  differences among the groups.
• A corollary Try the experiment again and a
  different group will score highest, another
  lowest. If that is so, you should not generalize
  from which group in your study scored highest or
  lowest to the population from which the samples
  were drawn.

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The null hypothesis must be retained or rejected

• The way we do statistical tests on experimental
  data is the same way we did it in Ch. 6 and Ch.8
• H0 make a prediction of what our sample statistic
  will be.
• We establish a 95 confidence interval for that
  prediction.
• We see whether the sample statistic falls inside
  or outside the confidence interval.
• Inside retain H0
• Outside reject H0, look around for another
  possible explanation, probably accept H1.

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THE ONLY HYPOTHESIS TESTED STATISTICALLY IS THE
NULL HYPOTHESIS.

• Therefore any statistical statements made can
  only be about the null hypothesis.
• In analyzing the results of an experiment, you
  must either find that your results are
  statistically significant and (because H0 has
  predicted badly) declare the null false and
  reject it.
• Or you can get nonsignificant results, fail to
  reject the null, and be unable to extrapolate
  from the differences among your experimental
  (treatment) groups to the population.

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The Experimental Hypothesis

• The experimental hypothesis (H1) states that
  between group differences on the dependent
  variable are caused by the independent variable
  as well as by sampling fluctuation.
• Unlike the null, H1 is different in each
  experiment.
• The experimental hypothesis tells us the way(s)
  we must treat the groups differently and what to
  measure.
• Therefore the experimental hypothesis tells us
  (in broad terms) how to design the experiment.

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YOU NEVER TEST THE EXPERIMENTAL HYPOTHESIS
STATISTICALLY.

• You can only examine the data in light of the
  experimental hypothesis after rejecting the null.
• Good research design makes the experimental
  hypothesis the only reasonable alternative to the
  null.
• Accepting the experimental hypothesis is based on
  good research design and logic, not statistical
  tests.

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Remember

• If the groups start off the same, then the
  subsequent differences in measured responses may
  be due to the differing treatments the groups
  receive as well as to sampling fluctuation.
• The independent variable (IV) consists of the
  treatment conditions. Note that since
  participants are randomly assigned to groups, who
  gets a treatment is unrelated to (independent of)
  pre-existing differences
• The dependent variable consists of relevant
  responses that are observed.