Given a choice, a no-win situation is to be avoided unless the alternatives are even worse. In gambling, craps is a slow-lose proposition, and someone who knows such about the game does not play it. There are better ways to use a bankroll than to fritter it away. Slots and poker allow one to lose more slowly, but with the prospect of huge wins. But on the whole both are losing propositions.

OK. I don't gamble. If I got a cheap flight to Vegas I would rent a car to go to the Grand Canyon, where I would get some memories of the majesty of nature, taking back memories. If one enjoys how one spends one's money, what is wrong?

Originally Posted by Mikebert

Supporting proof is provided by the result of the experiment or study.

Statistical significance testing is used to show indication that something is different. That is, is the result different from what would happen without the treatment?

But, for the millionth time now, your four sigma storm is possible without the treatment and therefor, in isolation, can not be evidence that the treatment did anything.

Suppose one comes up a process modification shown that increases yield in the laboratory. It is tried in a 15 lot production campaign and the average yield was 83.2% with standard deviation 2.3%. The average of the previous 600 lots run with the SOP process yielded 85.1% with standard deviation 2.4%. At the end of 15 lot test the process engineer concluded that the new process did not increase yield and goes back to the SOP. Is there any need for statistical analysis? That is, will it change the conclusion that the change did not increase yield?

Suppose the yield had been 84.7%. Does this change the conclusion that the change did not increase yield?

You did do a statistical analysis. Your one-tailed test has failed to reject the null.

Know what Vandal?

I think you just like to argue.

Originally Posted by TnT

Know what Vandal?

I think you just like to argue.

He is on the internet, and he's an academic. QED.

Originally Posted by Vandal-72

But, for the millionth time now, your four sigma storm is possible without the treatment and therefor, in isolation, can not be evidence that the treatment did anything.

And getting a statistically significant result using methods of which you approve is also possible without the treatment.

You did do a statistical analysis. Your one-tailed test has failed to reject the null.

Huh? What analysis? The question asked (which you dodged) was is statistical analysis needed?

Originally Posted by Mikebert

And getting a statistically significant result using methods of which you approve is also possible without the treatment.

Yeah, so? That's how all statistical analysis goes. Choosing an appropriate alpha reduces your chances of a type I error.

Now, are you going to tell us which statistical analysis you are using in order to conclude that your single storm is significant evidence of warming or not?

Huh? What analysis? The question asked (which you dodged) was is statistical analysis needed?

Your example was so simple that you can do the analysis in your head. Noting that your sample mean was less than the original mean will always give you a fail to reject in a one-tailed t test. Just because you can see the result without having to do the calculation does not mean that an analysis wasn't done.

Your example is also one more reason that your four sigma storm criteria is useless. What do you conclude if you get a single four sigma storm but all the rest of the storms are very, very light making the seasonal average lower than before? Your four sigma test will give you a false positive and more importantly you have no idea how likely a false positive will be!

Proper statistical analysis allows one to calculate levels of confidence in their conclusions, yours doesn't.

Originally Posted by Bad Dog

He is on the internet, and he's an academic. QED.

Academic? Hardly.

Originally Posted by Vandal-72

Academic? Hardly.

Are you in adjunct professor purgatory? If so, my condolences.

Originally Posted by The Wonkette

Are you in adjunct professor purgatory? If so, my condolences.

No. I teach at the secondary level (high school).

Global warming causes severe weather, including cold spells. The news anchor said this winter spell is "unheard of." Contrary to the dogmatic religionists who deny global warming, and the dogmatic science believers like vandal who parse words and argue over trivia and irrelevance, the wise folks know that each severe weather event adds to the testimony that we need to change our sources of energy-- like yesterday-- and that all excuses for not doing so are just condemning us and other species to needless death and deprivation.

Brrrrrrr!

Originally Posted by Eric the Green

Global warming causes severe weather, including cold spells. The news anchor said this winter spell is "unheard of." Contrary to the dogmatic religionists who deny global warming, and the dogantic science believers like vandal who parse words and argue over trivia and irrelevance,

Translation: topics that Eric doesn't really understand but likes to pretend that he does.

the wise folks know that each severe weather event adds to the testimony that we need to change our sources of energy-- like yesterday-- and that all excuses for not doing so are just condemning us and other species to needless death and deprivation.

Brrrrrrr!

Originally Posted by The Wonkette

Are you in adjunct professor purgatory? If so, my condolences.

I was...

Originally Posted by Vandal-72

No. I teach at the secondary level (high school).

Condolences. If you don't consider yourself an academic, console yourself that everyone will remember you the way I remember my TI from Basic Training (chortle).

Originally Posted by Eric the Green

Global warming causes severe weather, including cold spells. The news anchor said this winter spell is "unheard of." Contrary to the dogmatic religionists who deny global warming, and the dogmatic science believers like vandal who parse words and argue over trivia and irrelevance, the wise folks know that each severe weather event adds to the testimony that we need to change our sources of energy-- like yesterday-- and that all excuses for not doing so are just condemning us and other species to needless death and deprivation.

Brrrrrrr!

This time it is a weak polar vortex that allows an extreme lobal flow of air warm air masses to go unusually far poleward and cold air masses to go unusually far equator-ward. When the polar vortex strengthens, the westerlies dominate and temperatures even out more.

If you are wondering how you can escape the cold -- go south. Way south. http://www.huffingtonpost.com/2014/0...tml?1389132458

http://www.smh.com.au/environment/we...106-30dx5.html

45 sounds nice, right, if you have been shoveling snow? Not if it is 45 Celsius, as used in Australia -- which has record heat in much of the country. 45C is 113F. That is the record high temperature for Dallas, Texas, a place infamous for infernal summers. You can always dress for the cold. You can't dress for heat -- you can only take shelter. Some places could reach 122F -- the record for Phoenix... but it's a dry heat.

Originally Posted by pbrower2a

If you are wondering how you can escape the cold -- go south. Way south. http://www.huffingtonpost.com/2014/0...tml?1389132458

http://www.smh.com.au/environment/we...106-30dx5.html

45 sounds nice, right, if you have been shoveling snow? Not if it is 45 Celsius, as used in Australia -- which has record heat in much of the country. 45C is 113F. That is the record high temperature for Dallas, Texas, a place infamous for infernal summers. You can always dress for the cold. You can't dress for heat -- you can only take shelter. Some places could reach 122F -- the record for Phoenix... but it's a dry heat.

But, there is no global warming!

Originally Posted by Bad Dog

I was...

Yeah, me too. It's a test of ones virtue to do the job under the Rules of the Game^TM, to say nothing of the crappy pay.

Originally Posted by Bad Dog

But, there is no global warming!

According to some, there is no globe.

Originally Posted by Marx & Lennon

According to some, there is no globe.

lol I guess the same people subscribe to both views!

Cheap Battery Can Store Energy for a Rainy Day http://bit.ly/1gmx8ZQ
Scientific American ‏@sciam

http://www.scientificamerican.com/article.cfm?id=cheap-battery-can-store-energy-for-a-rainy-day…"“Now we have a good chance of solving that problem,” says Michael Aziz, a materials scientist at Harvard University in Cambridge, Massachusetts. His solution is a flow battery that packs a high energy density with no need for the expensive metals found in other models.”...

Proper statistical analysis allows one to calculate levels of confidence in their conclusions, yours doesn't.

Probability analysis is what is used to obtain levels of confidence. I already showed the probability analysis. Statistical significance testing is a probability analysis like that for the coin problems. It uses the experimental and control data to construct a model that is used in place of the population probability distribution (which is unknown) in a probability calculation. When you do a t-test you are calculating the probability of obtaining a single value from a control population. If the probability is low, like the probability go getting a tails from a >95% head coin, then you assign a 95% confidence to the result.
To see this it is useful to consider a limiting case: a t test done when the number of controls is very large.
Let Ns be the number of experiments that got the treatment and Np be the number of control experiments. The null hypothesis in this case is that the treatment had no effect. That is, the treatment sample is hypothesized to be equivalent to a random sample of Ns lots drawn from the control population. One might proceed by doing a t test with assumed equal variance.
In this case you calculate t as follows:

1. t = (SA – CA)/Se

Here SA is sample average, CA is control average and Se is the standard error of the mean.

Se is given by:

1. Se = Spool (1/Ns + 1/Np)^0.5

Here Spool is the pooled standard deviation of the controls (Sp) and treatments (Ss):

1. Spool = {((Ns-1) *Ss^2 + (Np-1)*Sp^2)/(Ns + Np -2)}^0.5

For Np >> Ns, ((Ns-1) *Ss^2 << (Np-1)*Sp^2 and the first term can be neglected. Equation 3 can be approximated as

1. Spool = { (Np-1)*Sp^2)/(Ns + Np -2)}^0.5

Similarly, for very large Np, (Np – 1) and (and Ns + Np -2) can be approximated as Np; equation 4 can be written as

1. Spool = (Np*Sp^2)/Np)^0.5 = Sp

Substituting 5 into 2 gives

1. Se = Sp (1/Ns + 1/Np)^0.5

For very large Np. 1/Np is negligible compared to 1/Ns and 6 can be written as:

1. Se = Sp / Np^0.5

What this says is for very large Np, you can obtain a very good estimate for sigma the standard deviation of the population of all lots from the very large collection of historical lots. The degrees of freedom (dof) are so large that the t-distribution is no longer sensitive to dof, and there is no need to use the extra 14 dof from the experimental sample to improve the estimate of the population standard deviation (sigma). In this case a test of a sample of Ns lots would involve comparing the sample average to the control average using the control standard error in the calculation of the t statistic. A t-value of 1.5 means the two averages are 1.5 standard errors apart. With this information the statistical analysis is finished. To obtain a value of p, you must do a probability calculation like you did for coins, except you use the t-distribution instead of the binomial distribution.

Another way of looking at this would be to recast the controls can as Np/Ns successive averages of Ns lots. The distribution of averages data will show the same mean as the original sample and a standard deviation equal to the standard error of the average. In this case you are calculating the probability that a single value (the experiment average) came from the control population of averages. If the sample average is 3 standard deviations out, the probability that it belongs in the control population is small. It is not zero, you could have gotten lucky--there is a p chance of that happening. Hence one concludes that the null hypothesis (the sample average belongs in the population of averaged controls) is rejected with confidence 1-p.

Statistical significance testing is NOT the analysis of patterns. It is a straightforward probability calculation that makes use of a model for the population probability distribution that is generated from the experimental data themselves. This model is used to calculate probabilities. The goodness of the model depends in the number of values use to “fit” the model.

Recall from algebra that N data points can define up to N parameters. A typical probability model uses two parameters, an average and standard deviation. To calculate the second you need a value for the first. You do this by taking an average of the data, but doing this “uses up” one of your N degrees of freedom leaving N-1 independent values (deviations from the average) that can be used to calculate the standard deviation. This is why N-1 shows up frequently for dof.

Originally Posted by pbrower2a

If you are wondering how you can escape the cold -- go south. Way south. http://www.huffingtonpost.com/2014/0...tml?1389132458

http://www.smh.com.au/environment/we...106-30dx5.html

45 sounds nice, right, if you have been shoveling snow? Not if it is 45 Celsius, as used in Australia -- which has record heat in much of the country. 45C is 113F. That is the record high temperature for Dallas, Texas, a place infamous for infernal summers. You can always dress for the cold. You can't dress for heat -- you can only take shelter. Some places could reach 122F -- the record for Phoenix... but it's a dry heat.

Of course this is due to the fact that the Earth is at perihelion during the Southern Hemisphere summer.

Originally Posted by Mikebert

Probability analysis is what is used to obtain levels of confidence. I already showed the probability analysis. Statistical significance testing is a probability analysis like that for the coin problems. It uses the experimental and control data to construct a model that is used in place of the population probability distribution (which is unknown) in a probability calculation. When you do a t-test you are calculating the probability of obtaining a single value from a control population. If the probability is low, like the probability go getting a tails from a >95% head coin, then you assign a 95% confidence to the result.
To see this it is useful to consider a limiting case: a t test done when the number of controls is very large.
Let Ns be the number of experiments that got the treatment and Np be the number of control experiments. The null hypothesis in this case is that the treatment had no effect. That is, the treatment sample is hypothesized to be equivalent to a random sample of Ns lots drawn from the control population. One might proceed by doing a t test with assumed equal variance.
In this case you calculate t as follows:

1. t = (SA – CA)/Se

Here SA is sample average, CA is control average and Se is the standard error of the mean.

Se is given by:

1. Se = Spool (1/Ns + 1/Np)^0.5

Here Spool is the pooled standard deviation of the controls (Sp) and treatments (Ss):

1. Spool = {((Ns-1) *Ss^2 + (Np-1)*Sp^2)/(Ns + Np -2)}^0.5

For Np >> Ns, ((Ns-1) *Ss^2 << (Np-1)*Sp^2 and the first term can be neglected. Equation 3 can be approximated as

1. Spool = { (Np-1)*Sp^2)/(Ns + Np -2)}^0.5

Similarly, for very large Np, (Np – 1) and (and Ns + Np -2) can be approximated as Np; equation 4 can be written as

1. Spool = (Np*Sp^2)/Np)^0.5 = Sp

Substituting 5 into 2 gives

1. Se = Sp (1/Ns + 1/Np)^0.5

For very large Np. 1/Np is negligible compared to 1/Ns and 6 can be written as:

1. Se = Sp / Np^0.5

What this says is for very large Np, you can obtain a very good estimate for sigma the standard deviation of the population of all lots from the very large collection of historical lots. The degrees of freedom (dof) are so large that the t-distribution is no longer sensitive to dof, and there is no need to use the extra 14 dof from the experimental sample to improve the estimate of the population standard deviation (sigma). In this case a test of a sample of Ns lots would involve comparing the sample average to the control average using the control standard error in the calculation of the t statistic. A t-value of 1.5 means the two averages are 1.5 standard errors apart. With this information the statistical analysis is finished. To obtain a value of p, you must do a probability calculation like you did for coins, except you use the t-distribution instead of the binomial distribution.

Another way of looking at this would be to recast the controls can as Np/Ns successive averages of Ns lots. The distribution of averages data will show the same mean as the original sample and a standard deviation equal to the standard error of the average. In this case you are calculating the probability that a single value (the experiment average) came from the control population of averages. If the sample average is 3 standard deviations out, the probability that it belongs in the control population is small. It is not zero, you could have gotten lucky--there is a p chance of that happening. Hence one concludes that the null hypothesis (the sample average belongs in the population of averaged controls) is rejected with confidence 1-p.

Statistical significance testing is NOT the analysis of patterns. It is a straightforward probability calculation that makes use of a model for the population probability distribution that is generated from the experimental data themselves. This model is used to calculate probabilities. The goodness of the model depends in the number of values use to “fit” the model.

Recall from algebra that N data points can define up to N parameters. A typical probability model uses two parameters, an average and standard deviation. To calculate the second you need a value for the first. You do this by taking an average of the data, but doing this “uses up” one of your N degrees of freedom leaving N-1 independent values (deviations from the average) that can be used to calculate the standard deviation. This is why N-1 shows up frequently for dof.

A single storm is not an average of anything. Your t-test comparison is irrelevant. Besides, you butchered the t-test as they are actually done. Every one of them requires knowledge of the variance of your sample set. What is the variance of a single storm? You are also faced with the fact that your data sets are likely
not normally distributed. There are much better statistical tools for analysis of data like that (rank sum and Mann-Whitney).

All you can do with your single storm is state the probability of the storm happening based on the pre-warming data. You wish to conclude that the storm is evidence of warming's effect but you can't tell me the likelihood of your conclusion being a type I error can you?

ax+by+c=0

Originally Posted by Bad Dog

ax+by+c=0

Can I disprove that if I find one axe by the sea?