Unsolved problems in Statistics.

BrettNortje · Dec 9, 2016

This is quite exciting, as, it mixes maths with economics and philosophy, things i find a liking for, of course. basically, it is about unknown factors coming together for a scientific analysis or study and explanation.

So, let's get started with the first on on the wikipedia list; "how to detect and correct for systematic errors?"

If we were to want to detect errors, we first need to define "an error." an error might be where the facts are false, or the figures are false. to check facts, in something as broad as english, we need to observe some things are obvious and make sense, and others do not. if i was to tell you that investing a million into a blue chip stock would only bring you seven percent yields over a year, and instead investing five hundred thousand in smaller businesses would bring you more, you would laugh, yes? let me explain...

Buying 1,000,000 worth of microsoft would get you say 50,000 shares at 200 a share. selling them would bring in more or less the same as you bought them for, so, as it is better to invest in companies this big rather than simply banking it, it would yield 7% profit for you over a year or so, coming to 70,0000 yes? if you were to invest 500,000 into a company that sells it's shares for 20, you would get 25,000 shares. the rate of growth for the smaller business is about 10%, so, you will have gained 500,000 in profits. as we can see now, it matters more how many slices of cake you have than the icing, yes?

So, it was an error to invest in microsoft, yes? this error is reflected by 'comparisons.' to detect an error, it is good to do some book keeping, to check the facts of all investments, and, find the best one, considering in out ratio or gross capital, depending which is more. this is relevant for investing and banking, of course, errors. this is economics mixed with math and philosophy if you were to ask me, holding true to my own definition, of course.

Now, detecting errors would become easier with 'research.' then, there is comparing known effects, and comparing old data. an error is where you have taken more and given less, so, giving more to the pessimism and less to the optimism is correct. if you were to round up for your income and down for your expenses, that is an error. this way, making errors will have no effect other than present surprises.

11Bravo · Dec 9, 2016

BrettNortje said:
This is quite exciting, as, it mixes maths with economics and philosophy, things i find a liking for, of course. basically, it is about unknown factors coming together for a scientific analysis or study and explanation.

So, let's get started with the first on on the wikipedia list; "how to detect and correct for systematic errors?"

If we were to want to detect errors, we first need to define "an error." an error might be where the facts are false, or the figures are false. to check facts, in something as broad as english, we need to observe some things are obvious and make sense, and others do not. if i was to tell you that investing a million into a blue chip stock would only bring you seven percent yields over a year, and instead investing five hundred thousand in smaller businesses would bring you more, you would laugh, yes? let me explain...

Buying 1,000,000 worth of microsoft would get you say 50,000 shares at 200 a share. selling them would bring in more or less the same as you bought them for, so, as it is better to invest in companies this big rather than simply banking it, it would yield 7% profit for you over a year or so, coming to 70,0000 yes? if you were to invest 500,000 into a company that sells it's shares for 20, you would get 25,000 shares. the rate of growth for the smaller business is about 10%, so, you will have gained 500,000 in profits. as we can see now, it matters more how many slices of cake you have than the icing, yes?

So, it was an error to invest in microsoft, yes? this error is reflected by 'comparisons.' to detect an error, it is good to do some book keeping, to check the facts of all investments, and, find the best one, considering in out ratio or gross capital, depending which is more. this is relevant for investing and banking, of course, errors. this is economics mixed with math and philosophy if you were to ask me, holding true to my own definition, of course.

Now, detecting errors would become easier with 'research.' then, there is comparing known effects, and comparing old data. an error is where you have taken more and given less, so, giving more to the pessimism and less to the optimism is correct. if you were to round up for your income and down for your expenses, that is an error. this way, making errors will have no effect other than present surprises.

the theory of statistics has yet to be approved by the vatican. until this is approved, its just as questionable as global warming or evolution

BrettNortje · Dec 9, 2016

Meta-analysis: Though independent p-values can be combined using Fisher's method, techniques are still being developed to handle the case of dependent p-values.

The p-value is defined as the probability of obtaining a result equal to or "more extreme" than what was actually observed, when the null hypothesis is true.[5][6]

This is where we need to find that the p value gives a better estimate for us than the null hypothesis. this means the value would be exaggerated and lead to faulty planning for whatever field it is used in, of course. if we were to run multiple observed values into one, then take averages from them, and compare that to the p-value, we could find 'a better estimate.'

Maybe if we were to add enough values together, then divide by the amount of values, we would find a good estimate, but, can we find an exact estimate? this would just be an estimate though, so we need something concrete!

By measuring air temperature and humidity for things like biology, we will find our 'exact outcome' with enough factors being pressed in. in the case of biology, for example, the other determining factors would be lineage more importantly, as then there would be something of a d.n.a. map. this map is more accurate than other factors, as, this is the blue print for what the mature thing will resemble, of course.

Back to economics and other uses for p-values. have you ever noticed how those boards at the stock exchange always nearly stay the same, with the majority of everything staying so much the same they need to take it to fractions of percentages? this means there is little change with the stock exchange, unless new d.n.a. or investment comes in, and, if 'recessive genes' leave, yes?

Calculating this can be down to finding out how many policies are maturing, as, it is only with that information that you will find new money being freed up, or, how much the diet is changing of the creature or cell.

BrettNortje · Dec 9, 2016

Behrens–Fisher problem: Yuri Linnik showed in 1966 that there is no uniformly most powerful test for the difference of two means when the variances are unknown and possibly unequal. That is, there is no exact test (meaning that, if the means are in fact equal, one that rejects the null hypothesis with probability exactly α) that is also the most powerful for all values of the variances (which are thus nuisance parameters). Though there are many approximate solutions (such as Welch's t-test), the problem continues to attract attention[4] as one of the classic problems in statistics.

So, we need to find the most powerful test, or die trying! yes!

If we were to test via 'heat exchanges,' that would be where we measure the heat generated by all living creatures on a hill, we could discard all 'masses' that are 'too small' to be 'sheep.' this will leave us with subtracting all identifiable 'heat compositions' that we identify as not being sheep, or, we could measure the heat of the wool on the hill by using thermal imaging to see the wool on their backs. this would let us measure it in weight as if it were 'biomass giving off less heat than the actual sheep' and we could 'count it' perfectly, up to the second of taking the 'thermal image,' yes?

Now, in a marketplace, we could detect how many people are hungry on their way in, and adjust prices like the markets do, yes? this could be done by listening for their stomachs groaning, or, measuring how much the cells have in them compared to cells in the stomach and in the blood stream, finding the difference would show how hungry they are, more or less.

If we were to take this to the boardroom, we could count the number of people in the city and get the average income. to find how much business you will do, merely phoning everyone and asking them to place a deposit will result in you making those gains that day, week or month. this can come with a secure deal, over the phone, simply and easily. to get enough people to phone around like that, you merely need a s.m.s. program to count the 'pledges.'

BrettNortje · Dec 9, 2016

Multiple comparisons are where there are a large amount of stats to compare. if you were to ignore some, how do you know they won't all lead to the same answer while the ninety percent of them swing the other way? this is hard to tell...

So, if you were to observe that seasons can change markets 'purchasing,' then you will find that everything should be compared due to different dates, as this will show the real comparisons.

Let's say you are selling 'tampons?' this would mean you would sell a set amount each month, with more coming in each month that a girl 'reaches maturity.' so, if you were to take the ratio women die at, compared the the influx of women, and add that to the stats for 'sales' so far, you would find it easier to predict, nearly exactly, the amount of 'tampons' to produce.

~ The only problem is that there might be a 'woman' buying for two months. even if women 'share packets,' they will still have to buy another one to 'adjust' for the 'double consumption.'

pinqy · Dec 9, 2016

BrettNortje said:
This is quite exciting, as, it mixes maths with economics and philosophy, things i find a liking for, of course. basically, it is about unknown factors coming together for a scientific analysis or study and explanation.

So, let's get started with the first on on the wikipedia list; "how to detect and correct for systematic errors?"

If we were to want to detect errors, we first need to define "an error." an error might be where the facts are false, or the figures are false. to check facts, in something as broad as english, we need to observe some things are obvious and make sense, and others do not.

Error has a more specific meaning in statistics. It means the difference between an observed value and the actual value. Errors occur due to measurement difficulties, the effects of random sampling, definitional difficulties and others.

if i was to tell you that investing a million into a blue chip stock would only bring you seven percent yields over a year, and instead investing five hundred thousand in smaller businesses would bring you more, you would laugh, yes? let me explain...

Buying 1,000,000 worth of microsoft would get you say 50,000 shares at 200 a share. selling them would bring in more or less the same as you bought them for, so, as it is better to invest in companies this big rather than simply banking it, it would yield 7% profit for you over a year or so, coming to 70,0000 yes? if you were to invest 500,000 into a company that sells it's shares for 20, you would get 25,000 shares. the rate of growth for the smaller business is about 10%, so, you will have gained 500,000 in profits. as we can see now, it matters more how many slices of cake you have than the icing, yes?

So, it was an error to invest in microsoft, yes?

No. It was a mistake. A statistical error is completely different.

if you were to round up for your income and down for your expenses, that is an error. .

Not in the statistical sense it's not.

It's not that hard a concept.
A sample is picked. It will not be perfectly representative of the universe. How far it's off is the error.
The interviewer asks questions of respondents. Not everyone understands the question the same way. The differences between what was meant and was said is the error.
The respondents answer differently to different interviewers based on race/gender/age, etc The bias results in error.
The interviewer acts differently to different races/ages/genders. The bias results in error.
A response is accidentally misclassified. That's an error (and the only example of a mistake).

Even with a full count (a census), there is still error as miscounting and misclassification and misunderstanding still occur.

BrettNortje · Dec 9, 2016

pinqy said:
Error has a more specific meaning in statistics. It means the difference between an observed value and the actual value. Errors occur due to measurement difficulties, the effects of random sampling, definitional difficulties and others.

No. It was a mistake. A statistical error is completely different.

Not in the statistical sense it's not.

It's not that hard a concept.
A sample is picked. It will not be perfectly representative of the universe. How far it's off is the error.
The interviewer asks questions of respondents. Not everyone understands the question the same way. The differences between what was meant and was said is the error.
The respondents answer differently to different interviewers based on race/gender/age, etc The bias results in error.
The interviewer acts differently to different races/ages/genders. The bias results in error.
A response is accidentally misclassified. That's an error (and the only example of a mistake).

Even with a full count (a census), there is still error as miscounting and misclassification and misunderstanding still occur.

A mistake that costs money can be statistically observed.

pinqy · Dec 9, 2016

BrettNortje said:
A mistake that costs money can be statistically observed.

But it is not an error. The words are not synonymous in statistics.

BrettNortje · Dec 9, 2016

pinqy said:
But it is not an error. The words are not synonymous in statistics.

On a roulette table only one number will win. choosing the wrong one is an error?

This means there is no way to error then, if you can invest your money anywhere and even lose it. it is a 'researched gamble.'

pinqy · Dec 9, 2016

BrettNortje said:
On a roulette table only one number will win. choosing the wrong one is an error?

Not a statistical error, no.

This means there is no way to error then, if you can invest your money anywhere and even lose it. it is a 'researched gamble.'

No, it means that you don't understand the terminology. In statistics, error is a problem of MEASUREMENT.

Let's say you are doing research on roulette and asked the casinos for information on winners and losers. Some casinos included spins of 0 and 00 as losses, while others didn't include those spins at all. Your data will be off, error, because you're not receiving the same type of results.

BrettNortje · Dec 9, 2016

pinqy said:
Not a statistical error, no.

No, it means that you don't understand the terminology. In statistics, error is a problem of MEASUREMENT.

Let's say you are doing research on roulette and asked the casinos for information on winners and losers. Some casinos included spins of 0 and 00 as losses, while others didn't include those spins at all. Your data will be off, error, because you're not receiving the same type of results.

You have points, but i think you drifted from the points i made.

pinqy · Dec 9, 2016

BrettNortje said:
You have points, but i think you drifted from the points i made.

Because your points were wrong. a statistical error is not a business mistake.

fredmertzz · Jan 11, 2017

BrettNortje said:
This is quite exciting, as, it mixes maths with economics and philosophy, things i find a liking for, of course. basically, it is about unknown factors coming together for a scientific analysis or study and explanation.

So, let's get started with the first on on the wikipedia list; "how to detect and correct for systematic errors?"

If we were to want to detect errors, we first need to define "an error." an error might be where the facts are false, or the figures are false. to check facts, in something as broad as english, we need to observe some things are obvious and make sense, and others do not. if i was to tell you that investing a million into a blue chip stock would only bring you seven percent yields over a year, and instead investing five hundred thousand in smaller businesses would bring you more, you would laugh, yes? let me explain...

Buying 1,000,000 worth of microsoft would get you say 50,000 shares at 200 a share. selling them would bring in more or less the same as you bought them for, so, as it is better to invest in companies this big rather than simply banking it, it would yield 7% profit for you over a year or so, coming to 70,0000 yes? if you were to invest 500,000 into a company that sells it's shares for 20, you would get 25,000 shares. the rate of growth for the smaller business is about 10%, so, you will have gained 500,000 in profits. as we can see now, it matters more how many slices of cake you have than the icing, yes?

So, it was an error to invest in microsoft, yes? this error is reflected by 'comparisons.' to detect an error, it is good to do some book keeping, to check the facts of all investments, and, find the best one, considering in out ratio or gross capital, depending which is more. this is relevant for investing and banking, of course, errors. this is economics mixed with math and philosophy if you were to ask me, holding true to my own definition, of course.

Now, detecting errors would become easier with 'research.' then, there is comparing known effects, and comparing old data. an error is where you have taken more and given less, so, giving more to the pessimism and less to the optimism is correct. if you were to round up for your income and down for your expenses, that is an error. this way, making errors will have no effect other than present surprises.

1) Your math is an error. 10% return on $500k of a small cap would be $50k in profits. But let's assume it's 20% and you return a $100k profit so that your premise isn't false.

What I believe you are describing seems to be the definition of "opportunity cost" - an economic term. To determine if Microsoft, in this example, is a good investment, the first question is what are you giving up by investing in Microsoft? Answer: The cash, for a period of time.

The next question is: what else could you have done with that money in that time? This is the Opportunity Cost: The difference between the other choice you could make and the choice you do make. It should be deducted from your profit, for comparison purposes.

There are a number of problems in calculating opportunity cost, and the stock market analogy is appropriate, as you can only refer to old data to predict future outcomes. There will always be a margin of error.

Also, there is another, much more difficult factor, which is "utility" - a way to quantify the happiness the money could have brought you from other sources. I.E. Going to Disney World, buying alcohol, giving to charity, etc. Whatever makes you happy. This is very difficult to do, of course, but there are ways. It gets easier to measure utility's worth when dealing with large groups of people by observing their spending habits.

I believe the error you are referring to is simply not taking into account all of the variables in Economics. Economics and Statistics do go hand in hand. My favorite class in College was Econometrics which blended the two very nicely.