Class_20 - Multiple Contingency-Table Analysis A...

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Multiple Contingency-Table Analysis
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A. Philosophical Introduction We are now in position to begin dealing with cause and effect, that is, causality. Let's take a look at what we are saying and what we are NOT saying when we describe something as the cause (X) of some effect (Y): X → Y There is nothing mystical, metaphysical, or superhuman about this. We are simply playing a game, one with rules created by human beings.
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To label one variable the cause of another variable is nothing more than to have gathered the evidence required by these rules in order to impress other human beings that the labels "cause" and "effect" are being properly used. All we have done is satisfied the rules of the game sufficiently to be granted by others the right to use these labels. What are the rules? There are three of them.
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B. Criteria for Evaluating Causality The three criteria (rules) that you must demonstrate to be allowed to label some X the cause of some Y are: Covariation That is, the independent variable (X) and the dependent variable (Y) must covary (i.e., must NOT be statistically independent).
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Remember statistical independence? It can look like this, . . . ========================================== Years of Formal Annual Salary Education (in $1,000) ( X ) ( Y ) ------------------------------------------------------------------------- 10 35 16 35 21 35 -------------------------------------------------------------------------
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. . . or it can look like this. (“A constant cannot explain a variable.”) ========================================== Years of Formal Annual Salary Education (in $1,000) ( X ) ( Y ) ------------------------------------------------------------------------- 16 25 16 85 16 45 -------------------------------------------------------------------------
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Temporal priority The proposed cause (X) MUST precede in time the proposed effect (Y). X → Y t 1 t 2 Nonspuriousness NO variables OTHER THAN the proposed cause (X) could have produced the proposed effect (Y).
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Before going any further, two qualifiers must be noted: Monocausal —sounds like a search for THE ONE cause Deterministic —seems to say that the presence of the cause GUARANTEES the production of the effect
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Control Group Test Group t 1 t 2 R R Y ij Y ij
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The principal weapon that the controlled experiment possesses is physical control: covariation : established with a t-test or analysis of variance at the end of the experiment; time order : no problem; physically manipulate the treatment (X), so we know the temporal sequence; nonspuriousness : control all potentially spurious variables through both random selection (R 1 ) and random assignment (R 2 ) to groups (test and control) and through control of the physical environment during the experiment; at the end of the experiment, change could ONLY have been caused by the ONE THING that varied, the treatment— present in the test group, absent in the control group.
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Statistical control is the next best thing in non- experimental settings: covariation : use a statistical measure of association (like λ ) AND a significance test ( χ 2 ); time order : can be a problem; research design, measurement, and logic (especially in the case of demographic variables) are ways of establishing; nonspuriousness : this is the real issue; usually have no physical control over subjects in field research strategy: homogenize samples with respect to categories of control variables; need to both know and be able to measure potentially spurious variables in order to do this.
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