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Statistical Reasoning for everyday life Intro to Probability and Statistics Mr. Spering – Room 113 7.4 The Search for Causality Scatter Plots…Scatter Plot is a graph in which each point corresponds to the values of two variables…{ not necessarily independent and dependent} The best-fit line (or regression line) on a scatter plot is a line that lies closer to the data points than any other possible line (according to the standard statistical measure of closeness). A correlation may suggest causality, but by itself a correlation never establishes causality. Much more evidence is required to establish that one factor causes another. Recall correlation between two variables result in either coincidence, a common underlying cause, or one variable having a direct influence on the other (independent →dependent). 7.4 The Search for Causality • Correlation does not imply causality. • GUIDELINE FOR ESTABLISHING CAUSALITY 1. Look for situations in which the effect is correlated with the suspected cause even while other factors vary. 2. Among groups that differ only in the presence or absence of the suspected cause, check that the effect is similarly present or absent. 3. Look for evidence that larger amounts of the suspected cause produce larger amounts of the effect. 4. If the effect might be produced by other potential causes, make sure that the effect still remains after accounting for the other potential causes. 5. If possible, test the suspected cause with an experiment. If the experiment cannot be performed with humans for ethical reasons, consider doing the experiment with animals, cell cultures, or computer models. 6. Try to determine the physical mechanism by which the suspected cause produces the effect.. 7.4 The Search for Causality Hidden Causality… Sometimes correlations---or lack of a correlation---can hide an underlying causality. Hidden causality often occurs because of confounding variables. ?????? Always question! Be humble! 7.4 The Search for Causality CONFIDENCE IN CAUSALITY….(Be lawyers!) Possible Cause…Correlation is discovered, but cannot yet determine whether the correlation implies causality. In the legal system, possible cause (such as thinking that a particular suspect possibly caused a particular crime) is often the reason for starting an investigation. Probable Cause…We have good reason to suspect that the correlation involves cause, perhaps because some of the guidelines for establishing causality are satisfied. In the legal system, probable cause is the general standard for getting a judge to grant a warrant for a search or wiretap. Cause beyond reasonable doubt… 7.4 The Search for Causality CONFIDENCE IN CAUSALITY…. Cause beyond reasonable doubt…We have found a physical model that is so successful in explaining how one thing causes another that it seems unreasonable to doubt the causality. In the legal system, cause beyond reasonable doubt is the usual standard for convictions and generally demands that the prosecution have shown how and why (essentially the physical model) the suspect committed the crime. Note that beyond reasonable doubt dot not mean beyond all doubt. 7.4 The Search for Causality Classwork : Be a lawyer… try some and discuss your thoughts! pg 319 # 1-12 all, #15, 18