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Causal Reasoning Inductive because it is limited by our inability to know (1) all of the relevant causes, and (2) the ways in which these causes interact Inductive because it is limited by our inability to know (1) all of the relevant causes, and (2) the ways in which these causes interact We can address uncertainty by speaking not of CAUSES, but of CAUSAL FACTORS We can address uncertainty by speaking not of CAUSES, but of CAUSAL FACTORS Main danger to avoid is the Post Hoc fallacy: inferring that X caused Y because it happened prior to Y. This creates a False Cause. Main danger to avoid is the Post Hoc fallacy: inferring that X caused Y because it happened prior to Y. This creates a False Cause.

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Mill’s Methods for Analyzing Causes Method of Agreement: look for common factor in all cases where the effect is present Method of Agreement: look for common factor in all cases where the effect is present Method of Difference: look for factor that is present when the effect occurs, and absent when the effect does not occur Method of Difference: look for factor that is present when the effect occurs, and absent when the effect does not occur Joint Method: combination of Agreement and Difference Joint Method: combination of Agreement and Difference Method of Concomitant Variation: used when effect comes in degrees; look for a factor that varies along with effect (correlation) Method of Concomitant Variation: used when effect comes in degrees; look for a factor that varies along with effect (correlation)

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Correlation A correlation is a (statistical) measurement of the association of two variables. A correlation is a (statistical) measurement of the association of two variables. Positive Correlation: As one variable increases, the other increases. (Examples: cigarette smoking and lung cancer; education and income; unemployment and homelessness) Positive Correlation: As one variable increases, the other increases. (Examples: cigarette smoking and lung cancer; education and income; unemployment and homelessness) Negative Correlation: As one variable increases, the other decreases. (Examples: caffeine intake and sleep; age and working memory capacity; stress and life expectancy) Negative Correlation: As one variable increases, the other decreases. (Examples: caffeine intake and sleep; age and working memory capacity; stress and life expectancy)

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Identifying and Assessing Correlations Correlations are identified by: r=. Correlations are identified by: r=. Correlations range between -1 and 1; positive numbers identify positive correlation, negative numbers identify negative correlation. r=0 is no correlation. Correlations range between -1 and 1; positive numbers identify positive correlation, negative numbers identify negative correlation. r=0 is no correlation. The further away from 0 the correlation is, the more strongly the variables are related. Correlations above.5 or below -.5 are strong correlations; correlations between.2 and.5 (or -.2 and -.5) are moderate correlations. The further away from 0 the correlation is, the more strongly the variables are related. Correlations above.5 or below -.5 are strong correlations; correlations between.2 and.5 (or -.2 and -.5) are moderate correlations. r 2 will give us the percentage of difference in one variable that is due to difference in the other. (Example: if the correlation between smoking and lung cancer is.7, 49% of differences in lung cancer rates are due to differences in smoking levels.) r 2 will give us the percentage of difference in one variable that is due to difference in the other. (Example: if the correlation between smoking and lung cancer is.7, 49% of differences in lung cancer rates are due to differences in smoking levels.)

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2 Basic Forms of Statistical Reasoning Statistical Syllogism: x% of A is B; p is an A; therefore p is a B (to x% likelihood). (Example: 86% of college students are broke. Fred is a college student, so it’s pretty likely that he’s broke.) Statistical Syllogism: x% of A is B; p is an A; therefore p is a B (to x% likelihood). (Example: 86% of college students are broke. Fred is a college student, so it’s pretty likely that he’s broke.) Inductive Generalization: x% of known As are Bs; therefore x% of As are Bs. (Example: Almost all of the students in this logic class hated the Deductive Reasoning assignment. Thus, I should expect that almost all students in any logic class would hate that assignment.) Inductive Generalization: x% of known As are Bs; therefore x% of As are Bs. (Example: Almost all of the students in this logic class hated the Deductive Reasoning assignment. Thus, I should expect that almost all students in any logic class would hate that assignment.)

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Components of a Statistical Study Target Population: This is the group about which you want to make an overall judgment. It could be all people, voters, college students, etc. Target Population: This is the group about which you want to make an overall judgment. It could be all people, voters, college students, etc. Sample (or Experimental) Group: This is the group studied or experimented upon to get information used to infer claims about the Target Population. Sample (or Experimental) Group: This is the group studied or experimented upon to get information used to infer claims about the Target Population. Control Group: Needed whenever one is looking for differences between groups; this group serves as an “anchor” against which to evaluate the Experimental Group. The Control Group helps to weed out spurious results. (Example: If you want to see if viewing pornography alters perceptions about women, you need a Control Group that takes the same questionnaire but does not view pornography beforehand.) Control Group: Needed whenever one is looking for differences between groups; this group serves as an “anchor” against which to evaluate the Experimental Group. The Control Group helps to weed out spurious results. (Example: If you want to see if viewing pornography alters perceptions about women, you need a Control Group that takes the same questionnaire but does not view pornography beforehand.)

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Sample Size Indicated by: N=. (Also sometimes ss=.) Indicated by: N=. (Also sometimes ss=.) Good statistical studies should tell you both (1) how many subjects one has overall, and (2) how many subjects are in each group. Good statistical studies should tell you both (1) how many subjects one has overall, and (2) how many subjects are in each group. Sample size gives us information about how well results can be generalized from the Sample Group to the Target Group. The larger, the better. Sample size gives us information about how well results can be generalized from the Sample Group to the Target Group. The larger, the better. This is because in large samples, extreme and otherwise unrepresentative cases are more likely to be balanced off. This is because in large samples, extreme and otherwise unrepresentative cases are more likely to be balanced off.

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Hasty Generalization Small or atypical sample sizes lead to the fallacy of Hasty Generalization. Small or atypical sample sizes lead to the fallacy of Hasty Generalization. The Hasty Generalization involves inferring claims about the Target Group from the Sample Group that lack sufficient support. The Hasty Generalization involves inferring claims about the Target Group from the Sample Group that lack sufficient support.

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Sample Diversity Sample Diversity is important because it (1) helps to balance off extreme or unrepresentative cases, and (2) reduces the likelihood that the study reflects the researcher’s biases. Sample Diversity is important because it (1) helps to balance off extreme or unrepresentative cases, and (2) reduces the likelihood that the study reflects the researcher’s biases. Representative Sample: sampling picked to match, as closely as possible, the actual distribution of traits in the Target Population. Representative Sample: sampling picked to match, as closely as possible, the actual distribution of traits in the Target Population. Random Sample: sampling based on some arbitrary and irrelevant criterion. Random Sample: sampling based on some arbitrary and irrelevant criterion.

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Statistical Significance Indicated by: p= ( ); this is a measurement of how likely it is that the results of the experiment are due to chance factors. Indicated by: p= ( ); this is a measurement of how likely it is that the results of the experiment are due to chance factors. This is NOT ‘significant’ in the sense of ‘large’, NOR in the sense of ‘important’. This is NOT ‘significant’ in the sense of ‘large’, NOR in the sense of ‘important’. Researchers usually declare a finding statistically significant if p <.05. Researchers usually declare a finding statistically significant if p <.05.

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Statistical Significance Continued Failing to attain a statistically significant result should not necessarily be viewed as a failure. The finding that two groups do NOT differ in a reliable way (affirming the Null Hypothesis) can be a highly important finding. Failing to attain a statistically significant result should not necessarily be viewed as a failure. The finding that two groups do NOT differ in a reliable way (affirming the Null Hypothesis) can be a highly important finding. Statistical Significance is linked to the importance of replication in scientific experimentation. A study with p=.05 is still 5% likely to have its results due to chance. Think of Significance as a claim on the likelihood that repetition will produce the same results, and replication as a test of this contention. Statistical Significance is linked to the importance of replication in scientific experimentation. A study with p=.05 is still 5% likely to have its results due to chance. Think of Significance as a claim on the likelihood that repetition will produce the same results, and replication as a test of this contention.

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Margin of Error Margin of Error: this is a measurement of variability in the sample. A standard margin of error for well-conducted surveys and polls is +/- 2 to 3%. This will give us the range of the study. (Example: if a study shows that 51% of IVCC students prefer Coke to Pepsi, with a margin of error of 3%, this means that between 48- 54% of IVCC students prefer Coke to Pepsi.) Margin of Error: this is a measurement of variability in the sample. A standard margin of error for well-conducted surveys and polls is +/- 2 to 3%. This will give us the range of the study. (Example: if a study shows that 51% of IVCC students prefer Coke to Pepsi, with a margin of error of 3%, this means that between 48- 54% of IVCC students prefer Coke to Pepsi.)

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Base-Rate Data Base-Rate Data is information that tells you how prevalent some trait is within the general population, or how likely the occurrence of some event is independently of what we do. Base-Rate Data is information that tells you how prevalent some trait is within the general population, or how likely the occurrence of some event is independently of what we do. This is crucial when you are checking for causal factors for ruling out spurious causes. This is crucial when you are checking for causal factors for ruling out spurious causes. Example #1: Freud’s “It Works!” Argument Example #1: Freud’s “It Works!” Argument Example #2: John Hinckley’s brain Example #2: John Hinckley’s brain Example #3: Post-9/11 airport security Example #3: Post-9/11 airport security

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Other Guidelines for Evaluating Statistical and Demographic Data Date of Study: While older studies can still have cogent results, in many cases new research (and new methodologies) may have invalidated the previous results. Date of Study: While older studies can still have cogent results, in many cases new research (and new methodologies) may have invalidated the previous results. Author and Sponsor of Study: Is the study being produced by (or funded by) someone with a stake in how the results turn out? This can increase the likelihood that biased research methods were used. Author and Sponsor of Study: Is the study being produced by (or funded by) someone with a stake in how the results turn out? This can increase the likelihood that biased research methods were used. Publication Conditions: Studies published in peer reviewed journals have their findings analyzed by other experts in the field, some of whom disagree with the author. Beware of studies that are neither peer reviewed or reviewed only within an organization. Publication Conditions: Studies published in peer reviewed journals have their findings analyzed by other experts in the field, some of whom disagree with the author. Beware of studies that are neither peer reviewed or reviewed only within an organization.

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Analogies Analogies are prevalent in literature, philosophy, religion and law Analogies are prevalent in literature, philosophy, religion and law In literature and religion, they are often present as comparisons, metaphors and parables. In literature and religion, they are often present as comparisons, metaphors and parables. In law, they are typically present as precedents and hypothetical cases In law, they are typically present as precedents and hypothetical cases In philosophy, they are typically present as thought experiments (“intuition pumps”) In philosophy, they are typically present as thought experiments (“intuition pumps”) Analogies are even present in science—esp. in scientific discovery and in science education Analogies are even present in science—esp. in scientific discovery and in science education

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Steps for Analyzing an Analogy (Simplified) Clarify the terms of comparison Clarify the terms of comparison Identify the principle or characteristic that is being applied Identify the principle or characteristic that is being applied Identify relevant similarities (False analogies rely on trivial similarities.) Identify relevant similarities (False analogies rely on trivial similarities.) Identify relevant differences Identify relevant differences Weigh up relative strength of similarities and differences to reach a final assessment of strength Weigh up relative strength of similarities and differences to reach a final assessment of strength

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Example Iraq is the new Vietnam. In both cases, our enemy is some nebulous, indefinable entity (communism, terrorism). In both cases we lost many American lives from insurgency for which we were unprepared. Both wars seem like futile endeavors with no hope for success. In each case, we lacked support for the war, both at home and abroad. Presidents Johnson and Nixon both escalated the war in Vietnam in response to popular dissent; President Bush has responded to popular dissent by sending more troops. Mission creep in Vietnam led us to invade Cambodia; the Bush administration has been talking about expanding the Iraq war into Iran or Jordan. History’s verdict on the Vietnam War is clear: it was an unjustifiable act of aggression. Shouldn’t we view the Iraq war in the same way? Iraq is the new Vietnam. In both cases, our enemy is some nebulous, indefinable entity (communism, terrorism). In both cases we lost many American lives from insurgency for which we were unprepared. Both wars seem like futile endeavors with no hope for success. In each case, we lacked support for the war, both at home and abroad. Presidents Johnson and Nixon both escalated the war in Vietnam in response to popular dissent; President Bush has responded to popular dissent by sending more troops. Mission creep in Vietnam led us to invade Cambodia; the Bush administration has been talking about expanding the Iraq war into Iran or Jordan. History’s verdict on the Vietnam War is clear: it was an unjustifiable act of aggression. Shouldn’t we view the Iraq war in the same way?

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Understanding Statistics

Understanding Statistics

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