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YOU are better than YOU think. Show
yourself how:
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Logic
chapters 1 to 5 re- appear not in sequence, as is or longer,
in Volume 1A, Pattern Based
Reason, Bon Appetite.
Logic
Mastery
Amazing, Amusing, Amorous, Delicious, Delightful, Edifying,
Strengthening Elixir.
It eases work & learning difficulties Makes the hard easier. Opens eyes.
Leads to greater precision.
in reading and
writing
Logic
mastery makes the hard, easier. Logic
mastery leads to better, stronger and richer comprehension. Logic
mastery improves reading and writing. Logic
mastery ease learning difficulties. Logic
mastery gives a headstart. In sum, logic
mastery will develops critical thinking, improve reading and writing,
and give a firmer base for work and studies at many levels. Good luck.
After logic,
(a) continue reading Three
Skills for Algebra, chapters 8 to 14 and do so alongside site area on solving
liinear Equations ; or (b) see this calculus
starter lesson and Volume 3, Why
Slopes & More Math, chapters 2 to 6;
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Caution: Site advice is approximately
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What may be learnt and when depends on how skills
and concepts are developed. Making the hard easier and clearer will allow
earlier & richer development of skills and concepts.
Try the Twiddla
Whiteboard. In principle, it allows
to people to draw and chat together online on a copy of this webpage or a clean
sheet. The chat may be via text or audio. Visit www.twiddla.com
to set up whiteboards to work with the webpage of your choice.
For online automated help in senior high school maths & calculus,
visit quickmath.com For Automatic
Calculus and Algebra Help with derivatives, integrals, graphs, linear equations,
matrix algebra, visit calc101.com
With overlap, each site quickmath
& calc101offers a different range of
services, some free, some not, all based on webmathematica. Good luck.
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Statistical Inference
Chapter 16
Previous: Chaos, or Unpredictable, Uncertain
Situations
A statistic is a number or function which depends on
the data collected or observed. It provides one window, a narrow one perhaps,
on the data.
In controllable situations where we can repeat processes and procedures,
patterns can be observed and tested. In the study of situations not fully
controlled, counts and measurements may be made and collected. Then statistical
computations are done to find patterns and characteristics which may be
reliable. Here chance and probabilistic estimates are used to recognize or judge
whether observed or imagined patterns of behavior hold. All this belongs to the
art of statistical inference.
There is a true art to statistical pattern identification. Unfortunately,
many people apply its methods without fully understanding them. If you engage in
statistical inference, please use only the concepts which you fully understand,
and when in doubt, don't. The further description of statistical inference is
left to other books.
Scandal and Hype
In colleges and universities, I have seen students with insufficient
mathematical background (a) run and rerun statistical programs in order to
compute fashionable but ill-understood numbers; and (b) from these estimate the
significance or reliability of a pattern. The uncertainty here, coupled with an
incomplete understanding of how the numbers and measurement were handled or
interpreted, invites skeptism. Statistical inference has its limitations. The
blind application of this art in any discipline is a scandal. It leads to error.
Beyond this, politicians and bureaucrats sometimes use the many ways in which
numbers and measurements can be described and reported to select those
perspectives most favorable to their cause — hype, hype, hype, hooray with
numbers. There is a classic 1954 book How to Lie With Statistics by D.
Durf which describes these matters further. It is published by Norton and
Company (ISBN -0-393-31072-8). A more recent work with a similar theme is Use
and Abuse of Statistics by W. J. Reichmann, 1961, Pelican Books (ISBN 0-14-
02-0707-4). Both books were mentioned in the chapter Deception.
Chapter Sections: [ 16 Private Agreements ] [ 16 Public Laws ] [ 16 Physical Laws ] [ 16 Accidental Patterns ] [ 16 Reliable(?) Patterns ] [ 16 Scientific Method ] [ 16 Reaction to Failed Tests ] [ 16 Chaos ] [ 16 Statistical Inference ] [ 16 End Notes ]
Next: End Notes and Review or
Recapitulation
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www.whyslopes.com
Volume 1A, Pattern Based Reason
Chapters 1 to 24
FOREWORD
Three Remarks
1 Introduction
2 Communication
3. Elements of Reason
4 Implication Rules
5. Deception
6 Chains of Reason
7 Longer Chains
For & From Consistency
8. Language Change
9 Next Chapters
10 Responsibility
11 Accidental Patterns
12 Knowledge Islands
13 Euclidean Logic
14 Deductive
& Empirical Views of Mathematics
15 Objectivity
16 Origin of Rules
and Patterns
17 Objective Ways
18. Waking up
19. Symbols & Logic
20. Pronouns or Symbols
21. Truth Tables I.
22. Truth Tables II
22. Biconditional
22. Contrapositive
23. IF-THEN table
24. Indirect Reason Again
To reason often means to persuade someone of
the need for an idea or action. That someone could be yourself. So be
careful.
Vol 1A Postscripts
- online only
+Proof by
Absurdity alias proof by contradiction
+How the demand
for consistency supports the law of the excluded middle
There is a difference between
knowing how to spend money,
and having money to spend.
There is likewise a difference
between mastering a skill
and having meeting a situation in which it applies.
.
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