STATISTICAL INTERPRETATION AS AN ART OF PERSUASION

AND/OR LANGUAGE GAMESGRADUATE SEMINAR

DEPARTMENT OF STATISTICS

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.

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.

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?

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 anintuitive 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.

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…

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

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.

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)

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)

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…

Modal Verbs

Modal verbs, or aauxiliary verbs that express necessity or possibility:

Can Could

May Might

Must had to

Shall Should

Will Would

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

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…)

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.

CONDITIONAL STATEMENTS

Also known as “if-then” statements:

When the statement following “if” is true, the statement following “then” is a logical consequence.

SOURCE: HTTP://STATISTICS.ABOUT.COM/OD/MATHSTAT/A/WHAT-ARE-CONDITIONAL-STATEMENTS.HTM

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: http://www.logicalfallacies.info/

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).

WORDING

“The coefficient on education was statistically significant at the 0.05

level.”

--Substantively ambiguous and filled with methodological jargon

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”)

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?

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!

TRUE?

“Since we have failed to reject h0, we conclude that h0 is true.”

-- True?

“The absence of evidence (in the data to reject h0) suggest the

evidence of absence (of an effect/difference/etc.).”

-- The same?

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.

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).

“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.

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.

ABILITY OR POSSIBILITY?

“You can/may always use the software to help you …”

-- Is there a difference between “can” and “may”?

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.

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.

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, 394-403.

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.