Shopping on line can be easy, simple and save you lots of money. It can also take a lot of your time, frustrate you, and result in unwanted purchases. Now the same can be said for regular high street shopping, but with the vast opportunity presented by the Internet it will pay you to spend a few minutes reading this and understanding how to better optimize your Uncertainty shopping experience:
1. Compare - without doubt the biggest advantage that the Uncertainty offers shoppers today is the ability to compare thousands of Uncertainty at a time. This is a great thing, but not necessarily all the time! Too much can be daunting at times so take advantage of the great comparison sites and where possible let them do the hard work for you.
2. Research - if it has been said it will be on the internet. Ignorance is no longer a justifiable reason for buying the wrong thing. Take the time to research in detail everything that you could possible want to know about
3. Testimonials - don't know anybody that has bought a Uncertainty? Wrong! If the Uncertainty is good the internet will let you know. Use the Internet as a friend and get testimonials before you buy.
4. Questions - Got a question about Uncertainty then search the Forums, FAQ's, Blogs etc. Don't be afraid to ask .....
5. Reputation - Never heard of the company selling Uncertainty? Don't worry, no reason why you should know every company in the world, but you know someone that does! Use the internet to find out what people are saying about Uncertainty and build up a picture of their reputation for sales, returns, customer service, delivery etc.
6. Returns - still worried that even after all of the above your Uncertainty wont be what you want? Check out the returns policy. There is so much competition now that someone, somewhere is bound to offer the terms that you are comfortable with.
7. Feedback - happy with your Uncertainty then let people know, after all you are depending on others people input in your buying decision, so why not give a little back.
8. Security - check for the yellow padlock on the Uncertainty site before you buy, and the s after http:/ /i.e. https:// = a secure site
9. Contact - got a question about Uncertainty, or want to leave a comment then check out the sites contact page. Reputable companies have them and respond.
10. Payment - ready to pay for your Uncertainty, then use your credit card or PayPal! Be aware of companies that don't accept them, there may be genuine reasons but given the huge amount of choice you have when buying online there is no reason at all not to buy via credit card or PayPal.
Uncertainty is a term used in subtly different ways in a number of fields, including
philosophy, statistics, economics, finance, insurance,
psychology, engineering and
science. It applies to predictions of future events, to physical measurements already made, or to the unknown unknown.
Relation between uncertainty, probability, vagueness and risk
In his seminal work
Risk, Uncertainty, and Profit Knight, F.H. (1921) Risk, Uncertainty, and Profit. Boston, MA: Hart, Schaffner & Marx; Houghton Mifflin Company University of Chicago economist Frank Knight (1921) established the important distinction between
risk and uncertainty:
"Uncertainty must be taken in a sense radically distinct from the familiar notion of Risk, from which it has never been properly separated.... The essential fact is that 'risk' means in some cases a quantity susceptible of measurement, while at other times it is something distinctly not of this character; and there are far-reaching and crucial differences in the bearings of the phenomena depending on which of the two is really present and operating.... It will appear that a measurable uncertainty, or 'risk' proper, as we shall use the term, is so far different from an unmeasurable one that it is not in effect an uncertainty at all."
Although the terms are used in various ways among the general public, many specialists in decision theory, statistics and other quantitative fields have defined uncertainty and risk more specifically. Doug Hubbard defines uncertainty and risk as:Douglas Hubbard "How to Measure Anything: Finding the Value of Intangibles in Business", John Wiley & Sons, 2007
#
Uncertainty: The lack of certainty, A state of having limited knowledge where it is impossible to exactly describe existing state or future outcome, more than one possible outcome.
#
Measurement of Uncertainty:A set of possible states or outcomes where probabilities are assigned to each possible state or outcome - this also includes the application of a probability density function to continuous variables
#
Risk:A state of uncertainty where some possible outcomes have an undesired effect or significant loss.
#
Measurement of Risk:A set of measured uncertainties where some possible outcomes are losses, and the magnitudes of those losses - this also includes loss functions over continuous variables.
There are other different taxonomy of uncertainties and decisions that include a more broad sense of uncertainty and how it should be approached from an ethics perspective :
For example, if you do not know whether it will rain tomorrow, then you have a state of uncertainty. If you apply probabilities to the possible outcomes using weather forecasts or even just a
calibrated probability assessment, you have quantified the uncertainty. Suppose you quantify your uncertainty as a 90% chance of sunshine. If you are planning a major, costly, outdoor event for tomorrow then you have risk since there is a 10% chance of rain and rain would be undesirable. Furthermore, if this is a business event and you would lose $100,000 if it rains, then you have quantified the risk (a 10% chance of losing $100,000). These situation can be made even more realistic by quantifying light rain vs. heavy rain, the cost of delays vs. outright cancellation, etc.
Some may represent the risk in this example as the "expected opportunity loss" (EOL) or the chance of the loss multiplied by the amount of the loss (10% x $100,000 = $10,000). That is useful if the organizer of the event is "risk neutral" which most people are not. Most would be willing to pay a premium to avoid the loss. An insurance company, for example, would compute an EOL as a minimum for any insurance coverage, then add on to that other operating costs and profit. Since many people are willing buy insurance for many reasons, then clearly the EOL alone is not the perceived value of avoiding the risk.
Quantitative uses of the terms uncertainty and risk are fairly consistent from fields such as probability theory, actuarial science, and
information theory. Some also create new terms without substantially changing the definitions of uncertainty or risk. For example, surprisal is a variation on uncertainty sometimes uses in information theory. But outside of the more mathematical uses of the term, usage may vary widely. In
cognitive psychology, uncertainty can be real, or just a matter of perception, such as
expectations, threats, etc.
Vagueness or ambiguity are sometimes described as "second order uncertainty", where there is uncertainty even about the definitions of uncertain states or outcomes. The difference here is that this uncertainty is about the human definitions and concepts not an objective fact of nature. It has been argued that ambiguity, however, is always avoidable while uncertainty (of the "first order" kind) is not necessarily avoidable.Douglas Hubbard "How to Measure Anything: Finding the Value of Intangibles in Business", John Wiley & Sons, 2007:
Uncertainty may be purely a consequence of a lack of knowledge of obtainable facts. That is, you may be uncertain about whether a new rocket design will work, but this uncertainty can be removed with further analysis and experimentation. At the subatomic level, however, uncertainty may be a fundamental and unavoidable property of the universe. In
quantum mechanics, the Heisenberg Uncertainty Principle puts limits on how much an observer can ever know about the position and velocity of a particle. This may not just be ignorance of potentially obtainable facts but that there is no fact to be found. There is some controversy in physics as to whether such uncertainty is an irreducible property of nature or if there are "hidden variables" that would describe the state of a particle even more exactly that Heisenberg's uncertainty principle allows.
Relation between uncertainty, accuracy, precision, standard deviation, standard error, and confidence interval
The uncertainty of a measurement is stated by giving a range of values which are likely to enclose the true value. This may be denoted by error bars on a graph, or as value ± uncertainty, or as decimal fraction(uncertainty). The latter "concise notation" is used for example by IUPAC in stating the List of elements by atomic mass of
Chemical element. There, 1.00794(7) stands for 1.00794 ± 0.00007.
Often, the uncertainty of a measurement is found by repeating the measurement enough times to get a good estimate of the
standard deviation of the values. Then, any single value has an uncertainty equal to the standard deviation. However, if the values are averaged and the mean is reported, then the averaged measurement has uncertainty equal to the
standard error (statistics) which is the standard deviation divided by the square root of the number of measurements.
When the uncertainty represents the standard error of the measurement, then about 68.2% of the time, the true value of the measured quantity falls within the stated uncertainty range. For example, it is likely that for 31.8% of the atomic mass values given on the
list of elements by atomic mass, the true value lies outside of the stated range. If the width of the interval is doubled, then probably only 4.6% of the true values lie outside the doubled interval, and if the width is tripled, probably only 0.3% lie outside. These values follow from the properties of the
normal distribution, and they apply only if the measurement process produces normally distributed errors. In that case, the quoted standard error (statistics)s are easily converted to 68.2% ("one sigma"), 95.4% ("two sigma"), or 99.7% ("three sigma") confidence intervals.
Fields of activities or knowledge where uncertainty is important
- Investing in financial markets such as the stock market.
- Uncertainty is used in engineering notation when talking about significant figures. Or the possible error involved in measuring things such as distance.
- Uncertainty is designed into games, most notably in gambling, where chance is central to play.
- In scientific modelling, in which the prediction of future events should be understood to have a range of expected values.
- In physics in certain situations, uncertainty has been elevated into a principle, the uncertainty principle.
- In meteorology it is now commonplace to include data on the degree of uncertainty in a weather forecast.
- Uncertainty is often an important factor in economics. According to economist Frank Knight, it is different from risk, where there is a specific probability assigned to each outcome (as when flipping a fair coin). Uncertainty involves a situation that has unknown probabilities, while the estimated probabilities of possible outcomes need not add to unity.
- In metrology, measurement uncertainty is a central concept quantifying the dispersion one may reasonably attribute to a measurement result. Such an uncertainty can also be referred to as a measurement error. In daily life, measurement uncertainty is often implicit ("He is 6 feet tall" give or take a few inches), while for any serious use an explicit statement of the measurement uncertainty is necessary. The expected measurement uncertainty of many measuring instruments (scales, oscilloscopes, force gages, rulers, thermometers, etc) is often stated in the manufacturers specification.
The most commonly used procedure for calculating measurement uncertainty is described in the Guide to the Expression of Uncertainty in Measurement (often referred to as "the GUM") published by ISO. A derived work is for example the National Institute for Standards and Technology (
NIST) publication NIST Technical Note 1297 "Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results" and the Eurachem/Citac publication "Uncertatinty in measurements" (available at the Eurachem homepage). The uncertainty of the result of a measurement generally consists of several components. The components are regarded as random variables, and may be grouped into two categories according to the method used to estimate their numerical values:
*Type A, those which are evaluated by statistical methods,
*Type B, those which are evaluated by other means, e.g. by assigning a probability distribution.
By propagating the
variances of the components through a function relating the components to the measurement result, the combined measurement uncertainty is given as the square root of the resulting variance. The simplest form is the
standard deviation of a repeated observation.
Uncertainty as an artistic theme
Uncertainty has been a common theme in art, both as a thematic device (see, for example, the indecision of
Hamlet), and as a quandary for the artist (such as
Martin Creed's difficulty with deciding what artworks to make).
See also
References
External links
- Measurement Uncertainties in Science and Technology, Springer 2005
- Proposal for a New Error Calculus
- Estimation of Measurement Uncertainties — an Alternative to the ISO Guide
- Bibliography of Papers Regarding Measurement Uncertainty
- Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results
- Strategic Engineering: Designing Systems and Products under Uncertainty (MIT Research Group)
- Research results regarding uncertainty models, uncertainty quantification, and uncertainty processing
- Decision tree to choose an uncertainty method for hydrological and hydraulic modelling, Choosing an uncertainty analysis for flood modelling.
- Decision Analysis in Health Care George Mason University online course offering lectures and tools for modeling and mitigating uncertainty in health care scenarios.
- Uri Weiss, The Regressive Effect of Legal Uncertainty
Uncertainty is a term used in subtly different ways in a number of fields, including
philosophy, statistics, economics,
finance,
insurance, psychology, engineering and science. It applies to predictions of future events, to physical
measurements already made, or to the
unknown unknown.
Relation between uncertainty, probability, vagueness and risk
In his seminal work
Risk, Uncertainty, and Profit Knight, F.H. (1921) Risk, Uncertainty, and Profit. Boston, MA: Hart, Schaffner & Marx; Houghton Mifflin Company
University of Chicago economist
Frank Knight (1921) established the important distinction between
risk and uncertainty:
"Uncertainty must be taken in a sense radically distinct from the familiar notion of Risk, from which it has never been properly separated.... The essential fact is that 'risk' means in some cases a quantity susceptible of measurement, while at other times it is something distinctly not of this character; and there are far-reaching and crucial differences in the bearings of the phenomena depending on which of the two is really present and operating.... It will appear that a measurable uncertainty, or 'risk' proper, as we shall use the term, is so far different from an unmeasurable one that it is not in effect an uncertainty at all."
Although the terms are used in various ways among the general public, many specialists in
decision theory, statistics and other quantitative fields have defined uncertainty and risk more specifically. Doug Hubbard defines uncertainty and risk as:Douglas Hubbard "How to Measure Anything: Finding the Value of Intangibles in Business", John Wiley & Sons, 2007
#
Uncertainty: The lack of certainty, A state of having limited knowledge where it is impossible to exactly describe existing state or future outcome, more than one possible outcome.
#
Measurement of Uncertainty:A set of possible states or outcomes where probabilities are assigned to each possible state or outcome - this also includes the application of a probability density function to continuous variables
#
Risk:A state of uncertainty where some possible outcomes have an undesired effect or significant loss.
#
Measurement of Risk:A set of measured uncertainties where some possible outcomes are losses, and the magnitudes of those losses - this also includes loss functions over continuous variables.
There are other different taxonomy of uncertainties and decisions that include a more broad sense of uncertainty and how it should be approached from an ethics perspective :
For example, if you do not know whether it will rain tomorrow, then you have a state of uncertainty. If you apply probabilities to the possible outcomes using weather forecasts or even just a
calibrated probability assessment, you have quantified the uncertainty. Suppose you quantify your uncertainty as a 90% chance of sunshine. If you are planning a major, costly, outdoor event for tomorrow then you have risk since there is a 10% chance of rain and rain would be undesirable. Furthermore, if this is a business event and you would lose $100,000 if it rains, then you have quantified the risk (a 10% chance of losing $100,000). These situation can be made even more realistic by quantifying light rain vs. heavy rain, the cost of delays vs. outright cancellation, etc.
Some may represent the risk in this example as the "expected opportunity loss" (EOL) or the chance of the loss multiplied by the amount of the loss (10% x $100,000 = $10,000). That is useful if the organizer of the event is "risk neutral" which most people are not. Most would be willing to pay a premium to avoid the loss. An insurance company, for example, would compute an EOL as a minimum for any insurance coverage, then add on to that other operating costs and profit. Since many people are willing buy insurance for many reasons, then clearly the EOL alone is not the perceived value of avoiding the risk.
Quantitative uses of the terms uncertainty and risk are fairly consistent from fields such as probability theory,
actuarial science, and
information theory. Some also create new terms without substantially changing the definitions of uncertainty or risk. For example, surprisal is a variation on uncertainty sometimes uses in information theory. But outside of the more mathematical uses of the term, usage may vary widely. In cognitive psychology, uncertainty can be real, or just a matter of perception, such as expectations, threats, etc.
Vagueness or ambiguity are sometimes described as "second order uncertainty", where there is uncertainty even about the definitions of uncertain states or outcomes. The difference here is that this uncertainty is about the human definitions and concepts not an objective fact of nature. It has been argued that ambiguity, however, is always avoidable while uncertainty (of the "first order" kind) is not necessarily avoidable.Douglas Hubbard "How to Measure Anything: Finding the Value of Intangibles in Business", John Wiley & Sons, 2007:
Uncertainty may be purely a consequence of a lack of knowledge of obtainable facts. That is, you may be uncertain about whether a new rocket design will work, but this uncertainty can be removed with further analysis and experimentation. At the subatomic level, however, uncertainty may be a fundamental and unavoidable property of the universe. In
quantum mechanics, the
Heisenberg Uncertainty Principle puts limits on how much an observer can ever know about the position and velocity of a particle. This may not just be ignorance of potentially obtainable facts but that there is no fact to be found. There is some controversy in physics as to whether such uncertainty is an irreducible property of nature or if there are "hidden variables" that would describe the state of a particle even more exactly that Heisenberg's uncertainty principle allows.
Relation between uncertainty, accuracy, precision, standard deviation, standard error, and confidence interval
The uncertainty of a measurement is stated by giving a range of values which are likely to enclose the true value. This may be denoted by
error bars on a graph, or as value ± uncertainty, or as decimal fraction(uncertainty). The latter "concise notation" is used for example by IUPAC in stating the List of elements by atomic mass of
Chemical element. There, 1.00794(7) stands for 1.00794 ± 0.00007.
Often, the uncertainty of a measurement is found by repeating the measurement enough times to get a good estimate of the
standard deviation of the values. Then, any single value has an uncertainty equal to the standard deviation. However, if the values are averaged and the mean is reported, then the averaged measurement has uncertainty equal to the
standard error (statistics) which is the standard deviation divided by the square root of the number of measurements.
When the uncertainty represents the standard error of the measurement, then about 68.2% of the time, the true value of the measured quantity falls within the stated uncertainty range. For example, it is likely that for 31.8% of the atomic mass values given on the list of elements by atomic mass, the true value lies outside of the stated range. If the width of the interval is doubled, then probably only 4.6% of the true values lie outside the doubled interval, and if the width is tripled, probably only 0.3% lie outside. These values follow from the properties of the normal distribution, and they apply only if the measurement process produces normally distributed errors. In that case, the quoted
standard error (statistics)s are easily converted to 68.2% ("one sigma"), 95.4% ("two sigma"), or 99.7% ("three sigma")
confidence intervals.
Fields of activities or knowledge where uncertainty is important
- Investing in financial markets such as the stock market.
- Uncertainty is used in engineering notation when talking about significant figures. Or the possible error involved in measuring things such as distance.
- Uncertainty is designed into games, most notably in gambling, where chance is central to play.
- In scientific modelling, in which the prediction of future events should be understood to have a range of expected values.
- In physics in certain situations, uncertainty has been elevated into a principle, the uncertainty principle.
- In meteorology it is now commonplace to include data on the degree of uncertainty in a weather forecast.
- Uncertainty is often an important factor in economics. According to economist Frank Knight, it is different from risk, where there is a specific probability assigned to each outcome (as when flipping a fair coin). Uncertainty involves a situation that has unknown probabilities, while the estimated probabilities of possible outcomes need not add to unity.
- In metrology, measurement uncertainty is a central concept quantifying the dispersion one may reasonably attribute to a measurement result. Such an uncertainty can also be referred to as a measurement error. In daily life, measurement uncertainty is often implicit ("He is 6 feet tall" give or take a few inches), while for any serious use an explicit statement of the measurement uncertainty is necessary. The expected measurement uncertainty of many measuring instruments (scales, oscilloscopes, force gages, rulers, thermometers, etc) is often stated in the manufacturers specification.
The most commonly used procedure for calculating measurement uncertainty is described in the Guide to the Expression of Uncertainty in Measurement (often referred to as "the GUM") published by ISO. A derived work is for example the National Institute for Standards and Technology (
NIST) publication NIST Technical Note 1297 "Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results" and the Eurachem/Citac publication "Uncertatinty in measurements" (available at the Eurachem homepage). The uncertainty of the result of a measurement generally consists of several components. The components are regarded as random variables, and may be grouped into two categories according to the method used to estimate their numerical values:
*Type A, those which are evaluated by
statistical methods,
*Type B, those which are evaluated by other means, e.g. by assigning a probability distribution.
By propagating the
variances of the components through a function relating the components to the measurement result, the combined measurement uncertainty is given as the square root of the resulting variance. The simplest form is the standard deviation of a repeated observation.
Uncertainty as an artistic theme
Uncertainty has been a common theme in art, both as a thematic device (see, for example, the indecision of Hamlet), and as a quandary for the artist (such as
Martin Creed's difficulty with deciding what artworks to make).
See also
References
External links
- Measurement Uncertainties in Science and Technology, Springer 2005
- Proposal for a New Error Calculus
- Estimation of Measurement Uncertainties — an Alternative to the ISO Guide
- Bibliography of Papers Regarding Measurement Uncertainty
- Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results
- Strategic Engineering: Designing Systems and Products under Uncertainty (MIT Research Group)
- Research results regarding uncertainty models, uncertainty quantification, and uncertainty processing
- Decision tree to choose an uncertainty method for hydrological and hydraulic modelling, Choosing an uncertainty analysis for flood modelling.
- Decision Analysis in Health Care George Mason University online course offering lectures and tools for modeling and mitigating uncertainty in health care scenarios.
- Uri Weiss, The Regressive Effect of Legal Uncertainty
Uncertainty - Wikipedia, the free encyclopedia
Uncertainty is a term used in subtly different ways in a number of fields, including philosophy, statistics, economics, finance, insurance, psychology, sociology, engineering, and ...
Uncertainty principle - Wikipedia, the free encyclopedia
In quantum physics, the Heisenberg uncertainty principle is the statement that locating a particle in a small region of space makes the velocity of the particle uncertain; and ...
The Uncertainty Division
Making up an entire play spontaneously is tricky ... they achieve this remarkable feat with panache - TCS
The Uncertainty Division - Gallery
Violence, poetry and recreational drugs ... definitely worth catching - Varsity
Science Media Centre - communicating uncertainty in a soundbite
Communicating Uncertainty, in a Soundbite is a guide for scientists preparing for a news interview about expressing the concept of risk in relation to scientific research.
Uncertainty of Measurement Results from NIST
From NIST website: Guidelines and perspectives (U.S. and international) on how to express uncertainties.
Heriot-Watt University Edinburgh. Institute of Petroleum Engineering ...
The page description goes here ... Introduction. Uncertainty and Upscaling is a Joint Industry Project which started in March 2002.
BBC NEWS | Business | Northern Rock shares fall again
Shares at troubled bank Northern Rock fall by up to 25% as uncertainty about a buyout continues. ... Shares in Northern Rock fell by more than 25% on Tuesday, before recovering to ...
Uncertainty Workshop Introduction
A workshop organized by the International Working Group on Uncertainty Analysis in Hydrologic Modeling as part of the Prediction in Ungauged Basins (PUB) initiative.
Amazon.co.uk: Embracing Uncertainty: Susan Jeffers: Books
Amazon.co.uk: Embracing Uncertainty: Susan Jeffers: Books ... RRP: £8.99 : Price: £6.69 & eligible for Free UK delivery on orders over £15 with Super Saver Delivery. See details ...
