- 22 Apr '16 12:38Does any mathematical concept or measurement exist for the idea of being improbable? For example, the idea of flipping a coin and getting heads three times in a row isn't considered improbable; but flipping a coin 1,000 times and getting heads for each flip is.

Does a mathematical concept exist where we can identify the point at which the odds of something happening are too low to be considered plausible? Or do possible vs. plausible odds exist only in human perception? - 22 Apr '16 12:49 / 1 edit

It is entirely human perception.*Originally posted by vivify***Or do possible vs. plausible odds exist only in human perception?**

Context also matters, as something that is implausible becomes plausible when there are enough repetitions. The odds of winning a lottery are so low that it is implausible to think you will win it. But take part in a million lotteries and things change. (or from a different perspective, have a million people play the lottery) - 22 Apr '16 12:51

When playing Monopoly the laws of chance always favour my opponents.*Originally posted by vivify***Does any mathematical concept or measurement exist for the idea of being improbable? For example, the idea of flipping a coin and getting heads three times in a row isn't considered improbable; but flipping a coin 1,000 times and getting heads for each flip is.**

Does a mathematical concept exist where we can identify the point at which the odds of someth ...[text shortened]... w to be considered plausible? Or do possible vs. plausible odds exist only in human perception? - 22 Apr '16 13:30

How about the random formation of a living cell?*Originally posted by vivify***Does any mathematical concept or measurement exist for the idea of being improbable? For example, the idea of flipping a coin and getting heads three times in a row isn't considered improbable; but flipping a coin 1,000 times and getting heads for each flip is.**

Does a mathematical concept exist where we can identify the point at which the odds of someth ...[text shortened]... w to be considered plausible? Or do possible vs. plausible odds exist only in human perception? - 22 Apr '16 13:45

The question betrays your ignorance. What do you even mean by 'random formation of a living cell'? How would a living cell form randomly? Describe the process, the initial conditions etc or we can't even begin to talk about probability.*Originally posted by whodey***How about the random formation of a living cell?** - 22 Apr '16 16:17

How long's a piece of string? Typically in medical research they require 95% confidence. In particle physics experiments the requirement is much higher, a probability that the outcome can come about by chance of one in 500 million. What is used as a threshold for provability depends on something called power, which is the number of times the trial has to be repeated to get a result given the expected size of the effect. For medical research trials typically are on a few hundred patients. In physics experiments they can just leave the accelerator running more or less indefinitely. So what the threshold for "proof" is tends to depend on practical considerations rather than any objective standard.*Originally posted by vivify***Does any mathematical concept or measurement exist for the idea of being improbable? For example, the idea of flipping a coin and getting heads three times in a row isn't considered improbable; but flipping a coin 1,000 times and getting heads for each flip is.**

Does a mathematical concept exist where we can identify the point at which the odds of someth ...[text shortened]... w to be considered plausible? Or do possible vs. plausible odds exist only in human perception? - 22 Apr '16 17:56 / 13 edits

Given the vast number of galaxies and the vast number of Earth-like planets with all the right condition for it being widespread over much of the planet, it is highly plausible that there may be a very high probability that it will happen somewhere within our universe over a period of billions of years on at least one Earth-like planet.*Originally posted by whodey***How about the random formation of a living cell?**

Then, after that happens at least once somewhere in the universe, the question (just in case someone here would imply it; don't*think*anyone here would be silly enough to but, just in case: ) of how likely it is that it happened exactly where and when it did, as in exactly on which planet and exactly where on the planet to the nearest millimeter coordinates and in exactly which second of which day of which year, became an idiotically irrelevant one; like asking the question of how likely it is that a particular person will win the lottery at exactly a particular place and time, with the motive of the question being to argue that a person winning the lottery is a miracle; and yet some people do win the lottery and it is no miracle because there is an extremely high probability that a person (no particular person) somewhere (no particular place) at a time (no particular time) will win a lottery and that is all that counts for the lottery to be won by somebody. - 22 Apr '16 19:09

It varies, but they typically have much larger trials if the results of the first ones are promising, and then continue to monitor even after that. It takes a lot before a drug is really considered proven to be effective. The smaller trials are usually to check for safety rather than effectiveness.*Originally posted by DeepThought***For medical research trials typically are on a few hundred patients.** - 22 Apr '16 19:32

I did some editing for the BMJ once, there are phase I, II and III trials, there are also what are sometimes called phase 0 trials. The phase 0 trials are laboratory trials which are in test tubes or on animal models. Phase I trials are the safety trials where the drug is given to healthy volunteers. Phase II trials are in actual patients and typically involve about 100 people - 50 per arm, the drug is compared either with placebo or with standard treatment (i.e. the old drug). If the drug is still looking good they do a phase III trial which is much larger and will have a few hundred to a few thousand per arm. The monitoring after that can't be considered as a trial because there isn't a comparison group.*Originally posted by twhitehead***It varies, but they typically have much larger trials if the results of the first ones are promising, and then continue to monitor even after that. It takes a lot before a drug is really considered proven to be effective. The smaller trials are usually to check for safety rather than effectiveness.** - 22 Apr '16 20:08

I don't know all the details, but there are often meta studies where they look at all the different trials and studies and make a determination as to whether or not a drug has any effect. To do it right you have to look at the procedures used in the trials etc. Certainly one trial with a few hundred people is rarely enough to be considered conclusive unless there is a dramatic effect. I guess if a drug appeared to work on all the people it was used on and the placebo did nothing in all the control subjects, it would be taken as quite conclusive even for a small sample size, but most drugs are less clear.*Originally posted by DeepThought***The monitoring after that can't be considered as a trial because there isn't a comparison group.** - 23 Apr '16 00:11

Yes, with a meta-analysis you'll often have several trials looking at a drug, or class of drugs, typically they'll give a relative risk with a 95% confidence interval (relative risk is the probability of the outcome for the treatment group divided by the probability of the outcome for the control group) and the group size. There's software that lets you put in the confidence intervals and group sizes and produces a new relative risk as if it were one big study.*Originally posted by twhitehead***I don't know all the details, but there are often meta studies where they look at all the different trials and studies and make a determination as to whether or not a drug has any effect. To do it right you have to look at the procedures used in the trials etc. Certainly one trial with a few hundred people is rarely enough to be considered conclusive unle ...[text shortened]... would be taken as quite conclusive even for a small sample size, but most drugs are less clear.**

If the effect is large then it's a lot easier to get a statistically significant result. But typically the relative risk is around 2. So quite often you may as well take a placebo as the harms won't be that much.