Non-EmpiricalRational approach to theory making represented by mathematics generated by deduction. Theory laid out through assumptions.

Example of a formal theory: Theory of competition between parties through spatial theory of voting. Politics is fought over the continuum of liberal vs. conservative

lib------------------------------con 

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Empirical: Explaining a theory through research. How the world actually works. Example: Explanation of voting patterns among the young.

Example of pure research: Theory of voting (Michigan model)

                  Who do people vote for when they vote?

1. Generality vs. Specific (How much can you explain within a given class of values. How many independent variables could you actually explain with this theory?)
2. Breadth vs. Narrow (How much about the world could you explain with your conclusion? How many possible dependent variables could you explain?)
3. Accuracy
4. Parsimony

How much or how little the theory explains (tree)

A good general theory would explain something about war, instead of something more specific such as civil wars in South America in the 1800’s. Theories that could explain more about a given phenomena, instead of one given event in a point in time is what a good theory needs to be

(Broad vs Narrow)

the richness of the facets/details explored and explained relative to the theory

Ex. theory on voting

voter, candidate, media, voter laws

In other words, how many conclusions could you reach from your theory? It’s not just about explaining one thing but explaining many things.

1. Parsimony (simplicity)

Conclusion solidly reached with less 'working parts', rather than more is the prefered one when all else is equal in two theories.

Oocam's Razor: simplest solution is usually the correct one. 

is explaining things from the bottom (evidence) going up. In simpler terms,   this is trying to make a general statement about the world from a few pieces of evidence (IE From specific to general)

Inductive reasoning (such as the Michigan model) is extremely accurate, but LACKS parsimony since there are many factors. This helps us understand that parsimony and accuracy are mutually exclusive.

x is a necessary condition if the presence of x is required for y to occur.  Cannot have y occur without x being present, however you can have an x without y. 

Necessary cause: If Y does occur, X will be present

ex. being female is a necessary condition for being preggers, but you could be female and not preg.

taking the college courses is necessary to earn a degree. You can't get a degree if you didnt take classes, however you could take classes and not get a degree

x is a sufficient condition when the presence of x is enough to ensure y will occur. Y may occur without the presence of x, however if x is present y will always occur.

skipping the final is sufficent to fail the course (you could fail the class some other way, but if you skip final, you WILL fail). 

Sufficient cause: If X is present, Y will occur

4 pieces of evidence required to sustain a conclusion about a causal effect of X on Y

4 pieces of evidence required to sustain a conclusion about a causal effect of X on Y

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  1. X and Y must be empirically correlated/associated in the expected direction. (Can’t be proven wrong)
  2. The correlation MUST NOT be a fluke
  3. X must proceed Y in time, or at least not follow Y in time (in research design)
  4. The correlation MUST NOT be spurious

1. Clues that a relationship is a fluke (a chance occurance)

1. Clues that a relationship is a fluke (a chance occurance)

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  1. Not replicable
  1. Non-sensical explanation
  2. Resulted from a data dredging process
  3. Fails a statistical significance test

Common cause spurious scenario (X and Y are correlated, but Z is actually causing both X and Y)

Correlated cause spurious scenario (X and Y are correlated; X and Z are correlated, but Z causes Y)

Modifying/Moderating Variables “P”:

Does X affect Y in all cases, or only in a subset of your sample set? P distinguishes a subset to which there is variation in a given population.

Allows you to see relationships that are present among a subset of a population that wouldn’t be seen if you analyzed the whole population all at once.

Experiment Designs: 

Static Group Comparison (SGC):

                  X  O (symbolic notation)

O

      (O- Observation in research design, or the dependent variable)

      (X column determines who has some amount of X and who doesn’t. If blank, it’s usually the       control group)

      (Different rows are different cases)

      Static refers to data collected at one point in time in a cross-sectional matter

      Group comparison is comparing how much of X there is between two groups 

Example: Hypothesis- A person who exercises will be more likely to have a lower BMI

      X- How exercise a person got last week

      Y- BMI 

Group 1 (A lot)          X2    O

Group 2 (some)         X1   O

Is this a good research design to reach a causal conclusion on X and Y? No. Lowest on Intern. Val. scale

The problem is that a difference between the groups could be pre-existing, so how do we account for that? Could it be spurious? How do you know that the treatment caused  the outcome?

Questions like these go under internal validity.

SGC is a weak design because it provides no assistance to whether cause precedes effect, since data is only gathered at one point in time!

external validity concerns the extent to which you can generalize your findings to cases other than those studied, settings and circumstances other than those studied, and times other than those studied.

Extent to which you can generalize findings to the real world, outside the exper. 

2 reasons expectation of equivalence could fail in RCE

2 reasons expectation of equivalence could fail

1. Number of subjects is small. Deviations from equivalence is more likely
2. Chance happens even with LARGE GROUPS, wacky outcomes happens.

CONTROLLED EXPERIMENT Post-test only (CEpo) 

(J) x  o

(J)    o 

A CEpo is a controlled experiment. The experimenter puts subjects into groups using THEIR own judgment. Not random process.

      The GOAL is to construct equivalent groups using non-random procedures.

Researchers rarely use this IF random assignment is available. 

Matched control group: Making sure that treatment groups are matched on equal proportion of a characteristics

      Problem:1) Equivalence is only there on the variables you are testing on 
 -Increases threat to internal validi -Spuriousness (chance event, maybe it wasn’t X that caused Y) 

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  1. groups that seem equivalent, they might NOT actually be all that equivalent even on those traits you matched them on (like degree of economic degradation (ex. low income 0-30k)

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  Controlled experiment with pre and post test (CEpp)

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  (J) O   X   O

•  

  (J) O        O 

 A factorial treatment design is trying to test more than 1 variable at a time. Example 2x2

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  Adding a factor will assess moderating variables. Factorial designs could also assess two independent variables.