"Name me one proposition in all of the social sciences
which is both true and non-trivial." -Mathematician Stanislaw Ulam to Paul Samuelson
Monday, November 27, 2017
Sunday, October 11, 2015
5 Sigma What's That? By Evelyn Lamb | July 17, 2012 | 10
Chances are, you heard this month about thediscovery of a tiny fundamental physics particle that may be the long-sought Higgs boson. The phrase five-sigma was tossed about by scientists to describe the strength of the discovery. So, what does five-sigma mean?
In short, five-sigma corresponds to a p-value, or probability, of 3x10-7, or about 1 in 3.5 million. This is not the probability that the Higgs boson does or doesn't exist; rather, it is the probability that if the particle does not exist, the data that CERN scientists collected in Geneva, Switzerland, would be at least as extreme as what they observed. "The reason that it's so annoying is that people want to hear declarative statements, like 'The probability that there's a Higgs is 99.9 percent,' but the real statement has an 'if' in there. There's a conditional. There's no way to remove the conditional," says Kyle Cranmer, a physicist at New York University and member of the ATLAS team, one of the two groups that announced the new particle results in Geneva on July 4.
Scientists use p-values to test the likelihood of hypotheses. In an experiment comparing some phenomenon A to phenomenon B, researchers construct two hypotheses: that "A and B are not correlated," which is known as the null hypothesis, and that “A and B are correlated,” which is known as the research hypothesis.
The researchers then assume the null hypothesis (because it's the most conservative supposition, intellectually) and calculate the probability of obtaining data as extreme or more extreme than what they observed, given that there is no relationship between A and B. This calculation, which yields the p-value, can be based on any of several different statistical tests. If the p-value is low, for example 0.01, this means that there is only a small chance (one percent for p=0.01) that the data would have been observed by chance without the correlation. Usually there is a pre-established threshold in a field of study for rejecting the null hypothesis and claiming that A and B are correlated. Values of p=0.05 and p=0.01 are very common in many scientific disciplines.
High-energy physics requires even lower p-values to announce evidence or discoveries. The threshold for "evidence of a particle," corresponds to p=0.003, and the standard for "discovery" is p=0.0000003.
The reason for such stringent standards is that several three-sigma events have later turned out to be statistical anomalies, and physicists are loath to declare discovery and later find out that the result was just a blip. One factor is the "look elsewhere effect:" when analyzing very wide energy intervals, it is likely that you will see a statistically improbable event at some particular energy level. As a concrete example, there is just under a one percent chance of flipping an ordinary coin 100 times and getting at least 66 heads. But if a thousand people flip identical coins 100 times each, it becomes likely that a few people will get at least 66 heads each; one of those events on its own should not be interpreted as evidence that the coins were somehow rigged.
So where do the sigmas come in? The Greek letter sigma is used to represent standard deviation. Standard deviation measures the distribution of data points around a mean, or average, and can be thought of as how "wide" the distribution of points or values is. A sample with a high standard deviation is more spread out—it has more variability, and a sample with a low standard deviation clusters more tightly around the mean. For example, a plot of dogs' heights would probably have a larger standard deviation than a plot of heights of dogs from a particular breed, even if that breed had the same average height as dogs in general.
For particle physics, the sigma used is the standard deviation arising from a normal distribution of data, familiar to us as a bell curve. In a perfect bell curve, 68% of the data is within one standard deviation of the mean, 95% is within two, and so on.
Wednesday, November 20, 2013
Retrieval Practice Produces More Learning than Elaborative Studying with Concept Mapping
Educators rely heavily on learning activities that encourage elaborative studying, whereas activities that require students to practice retrieving and reconstructing knowledge are used less frequently. Here, we show that practicing retrieval produces greater gains in meaningful learning than elaborative studying with concept mapping. The advantage of retrieval practice generalized across texts identical to those commonly found in science education. The advantage of retrieval practice was observed with test questions that assessed comprehension and required students to make inferences. The advantage of retrieval practice occurred even when the criterial test involved creating concept maps. Our findings support the theory that retrieval practice enhances learning by retrieval-specific mechanisms rather than by elaborative study processes. Retrieval practice is an effective tool to promote conceptual learning about science.
Sunday, January 1, 2012
entangled diamonds
OTTAWA -- An Ottawa physicist's team has "entangled" two diamonds, bringing the mysterious world of quantum physics to objects big enough to see.
Entanglement is a process in quantum mechanics by which two objects act like a single object even though they're not physically connected.
It usually involves very small objects -- atoms or molecules, for example.
Now Ben Sussman of the National Research Council has entangled objects far bigger than molecules -- pieces of diamond about half a millimetre thick. It's a step toward extremely fast quantum computing.
Sussman and his group write that "our intuition about the natural world" says quantum physics rules the tiny scale of atoms, while "classical" laws of motion cover objects big enough to see, such as cars or golf balls.
Quantum physics has been stretched to larger objects already, but there are usually special circumstances. For instance, scientists have used ultracold superconductors isolated from their surroundings.
These diamonds are large and operate at room temperature, some 15 centimetres apart. Sussman said they could, in principle, be even more distant. (He used synthetic diamonds to avoid impurities, but natural stones would work too.)
Entanglement contradicts what our senses tell us. It means two distinct objects have a relationship where a change in one means a simultaneous change in the other.
Physicists sometimes use the analogy of a teeter-totter: When one end goes up, the other has to go down at the same time.
But entangled objects aren't physically joined like the teeter-totter's two ends.
Einstein didn't like the concept; he called it "spooky action at a distance." Still, experiments show it's real.
The quantum world has captured popular imagination for decades with its puzzles. There's Edwin Schrodinger's cat, where the principle of uncertainty says the cat may be alive and dead at the same time.
There are possibilities of teleportation and time-travel -- staples of science fiction that always want to bend reality. The concept of entanglement leads to dreamy notions that everything is connected to everything else.
Now the reality of quantum mechanics is leading toward a more matter-of-fact goal: computers faster and more secure than anything made today.
Sussman's group used diamonds because they react to laser light by showing some characteristics of the quantum world, and their extreme hardness helps preserve that quantum character.
"This (entangled diamonds) is a state that simply can't be described with classical physics," Sussman said.
"There's great interest in understanding the transition between this microscopic world of quantum mechanics and our macroscopic world, which we live in every day."
What the diamonds shared "is a bit ethereal," Sussman said. "They shared a deep connection. They shared a vibration. They shared the same state. In a sense, these two objects shared each other. They became one... It's a bit romantic, but could be suitable, given that they're diamonds.
"They're both about steps toward quantum computing and are really fascinating because we've been able to make all this microscopic quantum stuff exist at large sizes (millimetres) and at room temperature," he said.
"I've been using the idea of building on our 'quantum workbench' -- something quantum that you can really get your hands on."
Entanglement is a process in quantum mechanics by which two objects act like a single object even though they're not physically connected.
It usually involves very small objects -- atoms or molecules, for example.
Now Ben Sussman of the National Research Council has entangled objects far bigger than molecules -- pieces of diamond about half a millimetre thick. It's a step toward extremely fast quantum computing.
Sussman and his group write that "our intuition about the natural world" says quantum physics rules the tiny scale of atoms, while "classical" laws of motion cover objects big enough to see, such as cars or golf balls.
Quantum physics has been stretched to larger objects already, but there are usually special circumstances. For instance, scientists have used ultracold superconductors isolated from their surroundings.
These diamonds are large and operate at room temperature, some 15 centimetres apart. Sussman said they could, in principle, be even more distant. (He used synthetic diamonds to avoid impurities, but natural stones would work too.)
Entanglement contradicts what our senses tell us. It means two distinct objects have a relationship where a change in one means a simultaneous change in the other.
Physicists sometimes use the analogy of a teeter-totter: When one end goes up, the other has to go down at the same time.
But entangled objects aren't physically joined like the teeter-totter's two ends.
Einstein didn't like the concept; he called it "spooky action at a distance." Still, experiments show it's real.
The quantum world has captured popular imagination for decades with its puzzles. There's Edwin Schrodinger's cat, where the principle of uncertainty says the cat may be alive and dead at the same time.
There are possibilities of teleportation and time-travel -- staples of science fiction that always want to bend reality. The concept of entanglement leads to dreamy notions that everything is connected to everything else.
Now the reality of quantum mechanics is leading toward a more matter-of-fact goal: computers faster and more secure than anything made today.
Sussman's group used diamonds because they react to laser light by showing some characteristics of the quantum world, and their extreme hardness helps preserve that quantum character.
"This (entangled diamonds) is a state that simply can't be described with classical physics," Sussman said.
"There's great interest in understanding the transition between this microscopic world of quantum mechanics and our macroscopic world, which we live in every day."
What the diamonds shared "is a bit ethereal," Sussman said. "They shared a deep connection. They shared a vibration. They shared the same state. In a sense, these two objects shared each other. They became one... It's a bit romantic, but could be suitable, given that they're diamonds.
"They're both about steps toward quantum computing and are really fascinating because we've been able to make all this microscopic quantum stuff exist at large sizes (millimetres) and at room temperature," he said.
"I've been using the idea of building on our 'quantum workbench' -- something quantum that you can really get your hands on."
Wednesday, November 17, 2010
Pain Prevalence Increases at the End of Life
The prevalence of pain increases rapidly in the last few months of life, regardless of the cause of death, a study in the Annals of Internal Medicine reports.
Researchers used data from the national Health and Retirement Study to examine levels of pain in some 4700 people over age 50 who died within 24 months of being interviewed about their pain levels. The participants were placed within 24 groups, according to the time span between their interviews and death.
Clinically significant pain — defined as pain of moderate or severe intensity most of the time — was present in about one quarter of the patients over the first 20 months. However, starting about 4 months before death, the prevalence of clinically significant pain began rising steadily, reaching a prevalence of about 50% in the final month of life. (The rate reached 60% among those with arthritis.)
An editorialist advises clinicians to routinely ask about clinically significant pain and be prepared to treat it.
Researchers used data from the national Health and Retirement Study to examine levels of pain in some 4700 people over age 50 who died within 24 months of being interviewed about their pain levels. The participants were placed within 24 groups, according to the time span between their interviews and death.
Clinically significant pain — defined as pain of moderate or severe intensity most of the time — was present in about one quarter of the patients over the first 20 months. However, starting about 4 months before death, the prevalence of clinically significant pain began rising steadily, reaching a prevalence of about 50% in the final month of life. (The rate reached 60% among those with arthritis.)
An editorialist advises clinicians to routinely ask about clinically significant pain and be prepared to treat it.
Saturday, August 28, 2010
MP3 Players Associated with Short-Term Hearing Loss
Listening to an MP3 player for just an hour can lead to temporary hearing loss, according to a small study in the Archives of Otolaryngology—Head & Neck Surgery.
Researchers in Belgium had 21 young adults with normal hearing listen to pop rock on an MP3 player at comfortable volumes for an hour, on six different occasions at least 2 days apart. The researchers found that, after listening, subjects experienced significant deterioration in hearing at high and low frequencies. Analyses revealed that hearing loss was temporary — participants recovered their normal hearing in between listening sessions.
The authors call for more research but say their findings "indicate the potential harmful effects" of listening to MP3 players.
Researchers in Belgium had 21 young adults with normal hearing listen to pop rock on an MP3 player at comfortable volumes for an hour, on six different occasions at least 2 days apart. The researchers found that, after listening, subjects experienced significant deterioration in hearing at high and low frequencies. Analyses revealed that hearing loss was temporary — participants recovered their normal hearing in between listening sessions.
The authors call for more research but say their findings "indicate the potential harmful effects" of listening to MP3 players.
Thursday, August 19, 2010
experimental data
Intention to Treat Analysis
P-value
Confidence Interval
Absolute Risk Reduction or Relative Risk Reduction
Number Need to Treat an Number Need to Harm
Odds Ratio
When looking at the results it is important to understand if an intention to treat analysis was applied. An intention to treat analysis is a statistical analysis of all the patients that started the trial, regardless of whether they were in the treatment or placebo group, or completed the trial. For instance, consideration should be given when there are 150 patients in the treatment group and 150 patients in the placebo group, but 50 patients in the treatment group drop-out half-way through the trial because of side effects. In this situation, it would be biased to look at just the 100 patients in the treatment group left at the end of trial and then artificially report a favourable benefit/risk profile for the treatment. However, when equal numbers of patients drop out in both groups, for known and unknown reasons, then the results are likely to be more valid. An intention to treat analysis, therefore maintains the integrity of the randomization process, reveals the similarities/differences between groups and attempts to provide a likely scenario of what would happen if this intervention was implemented in clinical practice.86
A p-value of ≤ 0.05 (or 1 divided by 20) means that if the trial was repeated 20 times that the results of 1 of those trials would probably be due to chance. A p-value of ≤ 0.05 is often acceptable and gives credence to the strength of the results but not the magnitude of treatment effect.
To understand the true treatment effect the confidence interval (CI) should be reported. The CI is expressed as a percentage of the likelihood that the treatment effect lays within a specified range. For instance, if 50% of the patients were likely to benefit from the treatment, and a 95% CI (40% to 60%) was reported, this means you can be confident 95% of the time that the treatment effect would lie within this range. A reporting of 50% is therefore a point estimate where it could be as low as 40% or as high 60% reasonable to expect a treatment effect of 50%. It is generally satisfactory to have a 95% CI with a tight range. However, any time a zero is reported in the interval range, you cannot assume the treatment effect to be true.85
The treatment effect can be reported as an absolute risk reduction (ARR) or relative risk reduction (RRR). For example, in a scenario where stroke occurred in 2% of patients (2 out of 100) given active treatment to lower blood pressure versus 4% of patients (4 out of 100) given placebo over a 5 year-period: a relative risk reduction of 50% (2% divided by 4%) or absolute risk reduction of 2% (4%-2%) could be reported. The magnitude of the RRR obviously looks much more significant than the ARR. However, what you want to know in this case is the number need to treat (NNT), which is 1 divided by the ARR. In this case you would get a NNT of 50 (1/.02) , which means you would have to give the blood pressure treatment to 50 patients for 5 years before you prevented 1 patient from having a stroke. The number need to harm (NNH) is calculated in the same way and tells you what the harm would be and how many patients you would have to give the treatment to before you saw 1 patient being harmed in that specific way. Obviously, you could then compare the NNT to NNH to understand the benefits versus the risks but the key is to have confidence in the results or a 95% CI or higher.86
It should be noted that in some instances the results are reported as an odds ratio (OR), which is comparable but not identical to the relative risk reduction. The OR is typically used in case control studies to assess risk of an adverse event or in cohort studies to assess disease outcome. The OR is calculated by dividing the number of occurrences in the intervention/treatment group by the number of occurrences in the control group. For instance, if an adverse effect of a drug is reported as an OR of 1.0 this means that the number of events in treatment group where equal to number of events in the placebo group. Similarly, if an adverse effect of drug is reported as an OR of 1.0, this means that the number of events in the treatment group were equal to number of events in the placebo group. Similarly, if an adverse effect of a drug is reported as an OR of greater than 1, this means that more individuals experienced an event in the treatment group compared to the placebo group. Therefore, an OR of less than 1 in this case means that the number of individuals in the treatment group that experienced an adverse effect was less than the placebo group.86
Taking this one step further, let’s say a particular treatment effect on reducing colds was reported as an OR of 0.42 with 95% CI of 0.25-0.71 and p<0.001. It is therefore accurate to say that the intervention group experienced a 58% (calculated as 1-0.42 X 100) reduction in catching a cold compared to the placebo group. However, regardless of whether the OR or RRR is used the CI and p-value should be reported in order for the trial outcome to be viewed as reliable. The NNT and NNH is not as easily calculated for OR because it requires a much more involved mathematical formula or can be estimated using tables.
P-value
Confidence Interval
Absolute Risk Reduction or Relative Risk Reduction
Number Need to Treat an Number Need to Harm
Odds Ratio
When looking at the results it is important to understand if an intention to treat analysis was applied. An intention to treat analysis is a statistical analysis of all the patients that started the trial, regardless of whether they were in the treatment or placebo group, or completed the trial. For instance, consideration should be given when there are 150 patients in the treatment group and 150 patients in the placebo group, but 50 patients in the treatment group drop-out half-way through the trial because of side effects. In this situation, it would be biased to look at just the 100 patients in the treatment group left at the end of trial and then artificially report a favourable benefit/risk profile for the treatment. However, when equal numbers of patients drop out in both groups, for known and unknown reasons, then the results are likely to be more valid. An intention to treat analysis, therefore maintains the integrity of the randomization process, reveals the similarities/differences between groups and attempts to provide a likely scenario of what would happen if this intervention was implemented in clinical practice.86
A p-value of ≤ 0.05 (or 1 divided by 20) means that if the trial was repeated 20 times that the results of 1 of those trials would probably be due to chance. A p-value of ≤ 0.05 is often acceptable and gives credence to the strength of the results but not the magnitude of treatment effect.
To understand the true treatment effect the confidence interval (CI) should be reported. The CI is expressed as a percentage of the likelihood that the treatment effect lays within a specified range. For instance, if 50% of the patients were likely to benefit from the treatment, and a 95% CI (40% to 60%) was reported, this means you can be confident 95% of the time that the treatment effect would lie within this range. A reporting of 50% is therefore a point estimate where it could be as low as 40% or as high 60% reasonable to expect a treatment effect of 50%. It is generally satisfactory to have a 95% CI with a tight range. However, any time a zero is reported in the interval range, you cannot assume the treatment effect to be true.85
The treatment effect can be reported as an absolute risk reduction (ARR) or relative risk reduction (RRR). For example, in a scenario where stroke occurred in 2% of patients (2 out of 100) given active treatment to lower blood pressure versus 4% of patients (4 out of 100) given placebo over a 5 year-period: a relative risk reduction of 50% (2% divided by 4%) or absolute risk reduction of 2% (4%-2%) could be reported. The magnitude of the RRR obviously looks much more significant than the ARR. However, what you want to know in this case is the number need to treat (NNT), which is 1 divided by the ARR. In this case you would get a NNT of 50 (1/.02) , which means you would have to give the blood pressure treatment to 50 patients for 5 years before you prevented 1 patient from having a stroke. The number need to harm (NNH) is calculated in the same way and tells you what the harm would be and how many patients you would have to give the treatment to before you saw 1 patient being harmed in that specific way. Obviously, you could then compare the NNT to NNH to understand the benefits versus the risks but the key is to have confidence in the results or a 95% CI or higher.86
It should be noted that in some instances the results are reported as an odds ratio (OR), which is comparable but not identical to the relative risk reduction. The OR is typically used in case control studies to assess risk of an adverse event or in cohort studies to assess disease outcome. The OR is calculated by dividing the number of occurrences in the intervention/treatment group by the number of occurrences in the control group. For instance, if an adverse effect of a drug is reported as an OR of 1.0 this means that the number of events in treatment group where equal to number of events in the placebo group. Similarly, if an adverse effect of drug is reported as an OR of 1.0, this means that the number of events in the treatment group were equal to number of events in the placebo group. Similarly, if an adverse effect of a drug is reported as an OR of greater than 1, this means that more individuals experienced an event in the treatment group compared to the placebo group. Therefore, an OR of less than 1 in this case means that the number of individuals in the treatment group that experienced an adverse effect was less than the placebo group.86
Taking this one step further, let’s say a particular treatment effect on reducing colds was reported as an OR of 0.42 with 95% CI of 0.25-0.71 and p<0.001. It is therefore accurate to say that the intervention group experienced a 58% (calculated as 1-0.42 X 100) reduction in catching a cold compared to the placebo group. However, regardless of whether the OR or RRR is used the CI and p-value should be reported in order for the trial outcome to be viewed as reliable. The NNT and NNH is not as easily calculated for OR because it requires a much more involved mathematical formula or can be estimated using tables.
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