STATISTICAL INTERPRETATION AS AN ART OF PERSUASION AND/OR LANGUAGE GAMES GRADUATE SEMINAR DEPARTMENT OF STATISTICS

Transcription

1 STATISTICAL INTERPRETATION AS AN ART OF PERSUASION AND/OR LANGUAGE GAMES GRADUATE SEMINAR DEPARTMENT OF STATISTICS

2 ABSTRACT Statistics belong to the realm of science. Statistical interpretation, however, can be subjective. "There are three kinds of lies: lies, damned lies, and statistics. So how to interpret statistical data becomes an art of persuasion and ethical judgement. The seminar will go over some of the language devices used in statistical interpretation with reference to the consulting report. They include words of probability, modal verbs, subjunctive mood, and conditional statements, to help us avoid unintentional logical blunders and ethical mistakes.

3 PURPOSE, ASSUMPTIONS AND LIMITATIONS PURPOSE: To share a non-statistician s view from the vantage point of rhetoric; To engage in a cross-disciplinary discussion. Assumptions: The audience know more about statistics than the presenter. Statistical interpretation is fundamentally built upon data analysis. The discussion does not intend to provide the right approach to statistical interpretation. Limitations: The examples are not selected to match each topic one by one. The examples are taken out of context it focusing on wording or language games.

4 THE BAD REPUTATION OF STATISTICS Statistics is often perceived to be intentionally misused to favor the data presenters. "There are three kinds of lies: lies, damned lies, and statistics." (Mark twain or/and Benjamin Disraeli) -- Why?

5 THE RHETORIC OF STATISTICS--MAGIC Statistics is viewed as science dealing with data about the condition of a state or community. In presenting numerical data, some subjectivity is unavoidable (Abelson, 1995, p.2). A gap is left by the mathematical model for the exercise of an intuitive process of personal judgement (Pearson, 1962, p.395). As principled argument, statistical claims should meet the criteria of magic magnitude, articulation, generality, interestingness, and credibility (Abelson, 1995). Magic relates statistics to the art of persuasion, or rhetoric. Communicating statistical results to non-statisticians requires translation, explanation, and interpretation, which all belong to the art of rhetoric and strategies of communication.

6 KEYWORDS IN STATISTICS Every culture and society has it own keywords through which they perceive, represent, and understand the world. Likewise, every field has its own cluster of key words or concepts that epitomize the discipline. Probability: Sampling, population, p-value, plausibility, chance, odds, contingency Hypothesis: CI, assumption, deviation, inference, proposition, conjecture, supposition, rationale

7 KEYWORDS IN RHETORIC OR PERSUASION Argument: debate, quarrel, disagreement, clash, conflict, controversy, demand, allegation, assertion, plea, postulation, reclamation Persuasion: rhetorical appeals, audience, purpose, situation, invention, arrangement, style, delivery, evidence Interpretation: words, meaning, intention, position, point of view, objectivity, subjectivity

8 STATISTICS AS PRINCIPLED ARGUMENT, OR PERSUASION There is a boundary in data interpretation beyond which formulas and quantitative decision procedures do not go, where judgment and style enters (Abelson, p. 15). -- Our talk today will focus on the latter.

9 STYLES OF PRESENTING STATISTICAL ARGUMENTS Two extremes in the style of presenting a statistical argument: Assertive and incautious, with reckless and excessive claims Timid and rigid, with unwillingness to make any claim other than the most obvious (Abelson, p. 15)

10 LIBERAL VS. CONSERVATIVE STYLES IN INTERPRETATION Two styles polarize in data interpretation: The liberal style showing readiness to explore data and discover possibly systematic effects The conservative style showing a confirmatory attitude towards claims about marginal or unexpected findings in order to be confident about the remaining claims (Abelson, p. 15)

11 PROBABILITY Probability: the chance that something will happen (almost certainly) Words associated with probability: P-value, possibility, likeliness, plausibility, chance, odds, contingency, supposition, presumption, speculation

12 Modal Verbs Modal verbs, or aauxiliary verbs that express necessity or possibility: Can May Must Shall Will Could Might had to Should Would

13 THREE MOODS Mood: Verbs indicating a state of being or reality Three moods exist in the English language: Indicative -- a verb stating an apparent fact or asking a question Imperative --a verb stating a command or request Subjunctive --a verb expressing a doubt, desire, supposition, or condition contrary to fact

14 SUBJUNCTIVE MOOD Expresses various states of unreality such as wish, emotion, possibility, judgment, opinion, necessity, or action that has not yet occurred: Indicating a hypothetical state or a state contrary to reality, such as a wish, a desire, or an imaginary situation Emphasizing the tentative, contingent, suppositional, or unreal nature of a wish, hope, or suggestion (I wish that, I hope that, I desire that, or I suggest that )

15 SUBJUNCTIVE MOOD, CONT D It is used after if clauses that state or describe a hypothetical situation. It is used after phrases or clauses including "might" and "may." The word "let" can be used to indicate the desire for some hypothetical situation (called a "jussive subjunctive -- a grammatical mood of verbs for issuing orders, commanding, or exhorting within a subjunctive framework. Not marked in English.

16 CONDITIONAL STATEMENTS Also known as if-then statements: When the statement following if is true, the statement following then is a logical consequence. SOURCE:

17 LOGICAL FALLACIES Formal (deductive) fallacies: (1) all men are mortal. (2) Socrates is a man. Therefore: (3) Socrates is mortal. Both (1) and (2) have to be true for (3) to be true or the argument to be deductively valid. Informal fallacies most inductive arguments are technically invalid. A good argument with true premises only establishes that its conclusion is probably true. Source:

18 WORDING CI for the sample mean are calculated. -- Hypotheses and confidence intervals are always about population parameters. -- Never say something like CI for the sample mean (or any other statistic).

19 WORDING The coefficient on education was statistically significant at the 0.05 level. --Substantively ambiguous and filled with methodological jargon

20 QUALIFIER? Other things being equal, an additional year of education would increase your annual in-come by $1,500 on average. --The sentence does not convey the key quantity of interest: how much higher the starting salary would be if the student attended college for an extra year. -- Qualifier needed ( plus or minus about $500 )

21 ACCEPTABLE TO THE CLIENT? Cis provide a range of plausible values for the population parameter. -- Acceptable or not in a consulting report for the client? Why?

22 ACCEPT/REJECT? Based on the results of the statistical test, the hypothesis is accepted (or rejected). -- Not a suitable conclusion form a statistical test. -- Rather, summarize the strength of the evidence in the data and its implications. -- State your conclusions in plain descriptive words (no, weak, strong, very strong evidence of an effect) -- never treat 0.05 (or any other cut-off) as a sharp boundary: p=0.051 is really no different from p=0.049!

23 TRUE? Since we have failed to reject h 0, we conclude that h 0 is true. -- True? The absence of evidence (in the data to reject h 0 ) suggest the evidence of absence (of an effect/difference/etc.). -- The same?

24 INFERENCE Based on the observational data, it is inferred that. -- To what population does the inference apply? -- In the situation of the consulting report, the inference is entirely model-based. There is no randomization or sampling basis for carrying out the inference.

25 RANDOM OR REPRESENTATIVE? You must randomly select your samples. -- Samples don t have to be randomly selected, but they must be representative. The only approach guaranteed to produce representative samples is random sampling but the client does not have to select the samples randomly. -- The client wishes to rely on the random sampling-based approaches to make statistical inferences from non-randomly selected samples, so they have to be willing to assume that those samples are representative (behave as if they are random samples).

26 AS THE SAMPLES INCREASES --NONSENSE As the sample increases in asymptotic approximations -- Better to say for large samples as former is relevant for stating theorems but your client doesn t want a statement of the theorem; he needs to know when he can use the result. Further, your client either has a fixed sample size (if the study is already completed) or has one in mind (if in the planning stages), so as the sample size increases sounds like nonsense to clients.

27 SUGGESTION OR ORDER? To obtain the mean, you must/need to/should. -- avoid wording that sounds like an order or makes it sound as if an approach you are suggesting is the only possibility.

28 ABILITY OR POSSIBILITY? You can/may always use the software to help you -- Is there a difference between can and may?

29 CLEAR TO THE CLIENT? Large samples justify a normal approximation. -- Not a meaningful statement unless you clearly state what is being approximated. -- If you don t state this clearly, your client might think you are talking about the distribution of the data.

30 VERIFYING ASSUMPTIONS? The Q-Q plot looks reasonable, so the normality assumption is verified. -- Aassumptions can t be verified. -- What you presumably mean is that the normal appears to be reasonable as an approximation to the distribution of the data that is very different from the distribution of the data being exactly normal (as the original phrase claims)! -- Explicitly describe the feature(s) of the q-q plot that lead you to say it looks reasonable.

31 REFERENCES ABELSON, R. P. (1995). STATISTICS AS PRINCIPLED ARGUMENT. NEW YORK, NY: PSYCHOLOGY PRESS/TALOR & FRANCIS GROUP. HAND, D.J. & EVERITT, B. S. (EDS.) (1987). THE STATISTICAL CONSULTANT IN ACTION. CAMBRIDGE: CAMBRIDGE UNIVERSITY PRESS. PEARSON, E. S. (1962). SOME THOUGHTS ON STATISTICAL INFERENCE. ANNALS OF MATHEMATICAL STATISTICS, 33,

32 ACKNOWLEDGMENT SINCERE THANKS TO: Professor John who has given me the permission to use his notes freely; Eric, David and Seong for making the arrangement to accommodate my schedule; All of you who have taught me statistics and found time to attend the discussion.