A mistake in reasoning McGraw-Hill Higher Education. All rights reserved.

Transcription

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2 A mistake in reasoning 2

3 What s the first criticism that comes to your mind about this reasoning? 3

4 For one thing, what is the Feature? What is it to not believe in family values????? 4

5 What s another problem? The sample is very small, plus it may be atypical. 5

6 Everything else being equal SMALL SAMPLE decreases confidence level or expands error margin. An ATYPICAL SAMPLE also decreases confidence level or expands error margin. 6

7 No hard and fast answer The point to remember: We want it large enough so we can tell if it is atypical (biased). 7

8 Even a small sample won t be atypical if the population is undiversified! E.g. These three samples of gold all melted at º F; therefore all samples of gold have that Feature. 8

9 Unclear Generalizing 9

10 College kids party too much, judging from what goes on here at Choo-Choo State. Sample? Target? Feature? Choo-Choo State students this speaker knows about All college kids Party too much But what exactly is that feature??? Unclear Generalizing! 10

11 I know from my own experience. You have to put yourself forward if you want to succeed! Sample: Me Target: All people Feature: Being successful requires putting yourself forward. Putting oneself forward?? Success?? Unclear Generalizing. 11

12 The conservatives I ve met say they re going to support John McCain, so I imagine that s true of conservatives everywhere. Sample? Target? Conservatives I ve met. Conservatives everywhere. Great. But what is a CONSERVATIVE??? The population (target) is unclear! (And so is the Feature: going to support ) 12

13 Sample is too small for the implied confidence level/error margin Called Hasty Generalizing or Over-generalizing 13

14 1. Like, EVERYONE in New York is friendly! Everybody I met was as nice as can be! 2. This beer is terrible. I can tell that from one sip. 14

15 Man! Old folks around here are terrible drivers! Did you see that old coot passing me on the right??!! Jogging isn t for me. Tried it three, four times; I can t stand it. I d rather pick up after my dog. 15

16 What is an anecdote? 16

17 One time I saw this airplane parked right in the middle of the tarmac in everyone s way. I asked who it belonged to. Someone told me it was John Travolta s. Folks, that s the trouble with these Hollywood liberals. They only care about themselves. Rush Limbaugh, paraphrased 17

18 ARGUING FROM ANECDOTE is just a form of Hasty Generalizing. Now you know why statisticians say Anecdotes don t prove anything. 18

19 This global warming stuff what a crock. We had the coldest January on record right here in Columbus last year. Anecdotes are often use to refute a body of contrary evidence. 19

20 It won t work!!! ARGUING FROM ANECDOTE is nothing more than generalizing from a single case or two. It yields a very low confidence level. 20

21 What is a stereotype? 21

22 A small sample CAN adequately support a sweeping general statement about an UNDIVERSIFIED population. But a sweeping general statement about a LARGE AND DIVERSE population requires a large sample, unless it is very cautious. 22

23 If you hear someone utter a sweeping generality like: These people all think The media would have us believe Republicans can t stand Illegal immigrants are all Muslims say 23

24 Small samples demand very weak confidence-level indicators! 24

25 BIASED GENERALIZING 25

26 It s generalizing from a sample that would probably be ATYPICAL no matter how large it might be. George W. Bush is really popular in South America. Look at how many people came out to cheer when he went down there. The sample (South Americans outside cheering) UNDER-REPRESENTS South Americans who don t feel like going out. It is atypical. 26

27 George W. Bush is really popular in South America. Look at how many people came out to cheer when he went down there. Notice that the sample is plenty large. So the problem isn t SIZE! It s that there are IMPORTANT DIFFERENCES between the sample and the population of all South Americans. 27

28 George W. Bush is really popular in South America. Look at how many people came out to cheer when he went down there. A modest confidence level indicator is required: George W. Bush may be really popular in South America. Look at how many people came out to cheer when he went down there. 28

29 Americans hate the president. His approval rating in the latest Field Poll is around 25%. The Field Poll only samples Californians. So, given the target, this is a biased generalization, even though the Field Poll is not a biased poll if the target is Californians. Notice, the problem isn t size of the sample, but fact that it is not representative of Americans. 29

30 People in Hastings don t want a new parking garage. Everyone in last Saturday s Person on the Street poll said they were opposed. What s the problem here??? The sample is tiny; plus it is atypical, excluding people who don t go downtown and people who don t care to be interrogated by a reporter. So this is both Biased Generalizing and Hasty Generalization! 30

31 Generalizing from a small sample often is both Hasty Generalizing and Biased Generalizing. If enlarging the sample would solve the problem, then it s just a case of Hasty generalization. 31

32 A random sample of 10 Choo-Choo State students shows that 50% of all Choo-Choo State students take their dogs to parties. If this random sample were large enough (and the error margin made larger), then it would be an okay generalization. So, it s really just Hasty Generalizing, rather than both Hasty and Biased Generalizing. 32

33 1. Unclear what Sample, Target or Feature is? Unclear generalizing. 2. Sample too small for confidence level/ error margin? Hasty generalizing. 3. Sample atypical (biased) even if were made larger? Biased generalizing. 33

34 4. Using a story to prove a general statement? Arguing from Anecdote (a form of Hasty Generalizing). 5. Using a story to DISPROVE a general statement? Also Arguing from Anecdote (Hasty Generalizing). 6. STEREOTYPING is issuing a sweeping generality (usually about a group of people) supported by small or biased sample. 34

35 35

36 Do any need clarifying? Is the implied confidence level or error margin inappropriate for the conclusion? 36

37 Sample? Tar pop? Feature? Any of these unclear? Yes! Unclear Feature! What is ultra-liberal? 37

38 Any other fallacies? Yes! Hasty Generalizing and Biased Generalizing! 38

39 MRS. BRUDER: Bruder! Bruder! Guess what! The music department is selling two of their grand pianos! MR. BRUDER: Well, let s check it out, but remember the last pianos they sold were way overpriced. Might be the same this time. Sample? Tar pop? Feature? All sufficiently clear? Any fallacies? 39

40 Only a 35 percent approval rating? Forget it: Them polls is rigged by the liberal media! People I know say he s the best president we ve ever had. Sample? Tar pop? Feature? All sufficiently clear? Any fallacies? Small sample, includes only people he knows. Confidence level too high. Hasty/Biased Generalizing. 40

41 Sample? Tar pop? Feature? All sufficiently clear? Any fallacies? N=1; hasty/biased generalizing. Unclear feature. 41

42 The parties at the university always get out of control. Why, just last week the police had to go out and break up a huge party at Fifth and Ivy. Sample? Tar pop? Feature? All sufficiently clear? Any fallacies? N=1; hasty/biased generalizing. Feature is somewhat unclear, but the main problem is sample size/bias. 42

43 Men just can t tolerate stress. My husband even freaks when the newspaper is late. Sample? Tar pop? Feature? All sufficiently clear? Any fallacies? N=1; hasty/biased generalizing. Feature ( can t tolerate stress ) is unclear. 43

44 Sample? Tar pop? All sufficiently clear? Feature? Any fallacies? Unclear: sample size, target ( technical people?), and feature ( difficult to communicate with ). 44

45 Sample? Tar pop? Feature? All sufficiently clear? Any fallacies? Sample of 1. Feature unclear: too graphic. 45