Howard Zinn

 https://www.howardzinn.org/collection/

http://web.archive.org/web/*/https://www.howardzinn.org/collection/

Effective hoaxes use prior implanted worldviews

Whereas the promoters of frauds, fakes, and scams devise them so that they will withstand the highest degree of scrutiny customary in the affair, hoaxers are confident, justifiably or not, that their representations will receive no scrutiny at all. They have such confidence because their representations belong to a world of notions fundamental to the victims' views of reality, but whose truth and importance they accept without argument or evidence, and so never question

http://web.archive.org/web/20220530222104/https://en.m.wikipedia.org/wiki/Hoax

Speaking Statutes and Preterism

And he had power to give life unto the image of the beast, that the image of the beast should both speak, and cause that as many as would not worship the image of the beast should be killed.

Revelation 13:15 KJV

http://web.archive.org/web/20111122173744/biblegateway.com/passage/?search=Revelation 13&version=KJV

 consulting statues through which a priest apparently spoke

https://en.m.wikipedia.org/wiki/Ancient_Egyptian_religion

Practices

Oracles

http://web.archive.org/web/20220617082230/https://en.m.wikipedia.org/wiki/Ancient_Egyptian_religion

The ancient festival has been survived by the present-day feast of Sheikh Yūsuf al-Haggāg, an Islamic holy man whose boat is carried around Luxor in celebration of his life

https://en.m.wikipedia.org/wiki/Opet_Festival

http://web.archive.org/web/20220524113604/https://en.m.wikipedia.org/wiki/Opet_Festival

Patterson Quantom Physics Abuse Reason

Steve Patterson Articles

Quantom Physics and the Abuse of Reason

we’re left with two mutually exclusive theories. On the one hand, you have a classically-determined universe, where motion is caused by concrete inputs. And on the other hand, you have the world of quantum indeterminacy, where motion is probabilistic and fundamentally random at the smallest levels. How do we resolve this conflict? We have several options.

http://web.archive.org/web/20220605151500/https://steve-patterson.com/quantum-physics-abuse-reason/

We could say, “Quantum phenomena are more fundamental than classical phenomena, and therefore the principle of indeterminacy is ultimately true. Macroscopic-level motion only appears to be determined, but in reality, it’s probabilistic.”

Or, we might say, “Classical mechanics more accurately describes reality, and the odd results of quantum experiments are due to a lack of sophisticated-enough equipment. We’re simply missing a variable in our experiments which causes the particles to behave in seemingly-unpredictable ways. Once we learn more and can measure more accurately, the missing variable will be found, and we will be able to correctly predict the motion of quantum particles.”

Another option might be to say both theories are inaccurate, and we need to come up with an altogether new theory

http://web.archive.org/web/20220605151500/https://steve-patterson.com/quantum-physics-abuse-reason/

The most obvious answer is the most accurate: the apparatus used to measure quantum phenomena in the double-slit experiment interferes with the results.

https://steve-patterson.com/quantum-physics-abuse-reason/

http://web.archive.org/web/20220605151500/https://steve-patterson.com/quantum-physics-abuse-reason/

Our Present Day Dark Age Part 1

http://web.archive.org/web/20220609224328/https://steve-patterson.com/our-present-dark-age-part-1/

Mind-Body Dualism | Solving the Interaction Problem

http://web.archive.org/web/20220607081659/https://steve-patterson.com/mind-body-dualism-solving-problem-interaction/

Quantum Computers Over Rated

 any problem solvable by a quantum computer is also solvable by a classical computer

http://web.archive.org/web/20220530025425/https://en.m.wikipedia.org/wiki/Quantum_computing

quantum computers cannot solve any problems that classical computers cannot already solve

http://web.archive.org/web/20220530025425/https://en.m.wikipedia.org/wiki/Quantum_computing

Group averages vs individual choices

Insurance company A sample size 200

Insurance company B sample size 200

A $300 per year for 100 people, B $400 per year for those same 100 people

A $400 per year for 100 people, B $300 per year for those same 100 people

If some person does a two tailed t test based on the sample results above to try to figure out if one company is cheaper than the other one on average they will find neither one is statistically significantly different

Insurance company A and Insurance company B have the same mean, sample size and standard deviation

People allowed to make individual choices switched companies if it saved them money and did not switch if it did not save them money

People who switched from A to B saved $100 per year on average

People who switched from B to A also saved $100 per year on average

It does not make sense to use a group average to make your decision as a individual

It makes more sense to look at your own individual results than the average results of other people when making life decisions

A statistical t test would be useless to make such a decision in this case

People wear shoe type A and shoe type B for one month each, each person trying both types of shoes

Shoe type A results in 70% of the people slipping on a workplace floor within a month

Shoe type B results in only 30% of people slipping on a workplace floor within a month

The 30% that slipped wearing type B did not slip wearing type A and the the 70% that slipped wearing type A did not slip wearing type B.  

There was no overlap in which someone did not slip wearing either type of shoe and no overlap in which someone slipped wearing both types of shoes

Statistically having a corporate or government policy of forcing everyone to wear shoe type B will result in which slipping incidents then forcing everyone to wear shoe type A

But it might make more sense to let the people decide on their own.  Those who did not slip with their individual results wearing type A shoes might choose to wear type A shoes and those that did not slip with their individual results wearing type B shoes might choose to wear type B shoes.  This might result in lower rates of slips and falls when they knew their individual results and could make choices than forcing those people to all wear the same shoe type based on whatever results had the least falls for the group even in cases in which it resulted in more falls for them as an individual.

Often in real life people who use group average results for other people make a mistake when they can access individual results for themself to make a decision

Since statistics provides no mechanism to explain results it is poor practice to enforce the best statistical results for a group of other people upon a single individual if one has a goal of the best good for a community in addition to being an violation of individual autonomy

Good practice is to find the mechanism that explains which people will have better results and which people will have worse results for making one choice instead of another choice and then to explain that mechanism to people and let them make their own choices

Good scientific practice is based on finding non probabilistic functions by which you can predict output for one set of variables by controlling the input of another set of variables not statistical probability tests which can not predict output as a function of input

Copyright Carl Janssen 2022 June 12

Some unlimited quantities are bigger than others

Infinity is not a whole number nor a real number but a concept or a symbol that has a certain meaning for what to do when put into mathematical operators or functions that use limits in calculus

Infinity is not a whole number

If you were to go to a hotel with an unlimited number of rooms starting at room 1 and each room having a door with a room number label that is 1 higher than the previous room number you would not know which room number to go to if you were told to go to the room with the number label of infinity because there is no whole number that is equivelent to the label of infinity

Infinity is not a real number either

Infinity is not a real number that is not a whole number

If starting at door number 2 each door with a room number label on it is the same distance from the previous door as it is from the next door and that distance is any positive number of meters you want to choose which is greater than zero but not a whole number.  Then if you were told to walk a distance of infinity meters from the first room number label to reach the room number label you are supposed to arrive at for your room then you still could not find the location of your room if you went a specific positive real number of meters that was not a whole number because there is no positive real number that is not a whole number that is equivelent to infinity.  And this would still be the case no matter what positive real number of meters greater than zero you select for the rooms to be apart from each other.

Although infinity is not a real number there can be an unlimited amount for a measurement

There are two types of directions, translational directions and rotational directions

N is a positive real number

If you choose coordinates one coordinate being N meters in one translational direction from where you are and the other being N meters in the opposite translational direction from where you are there would be no limit to the maximum distance between how far apart those two points could be, no matter how large a value could be assigned to N, there could be a larger value assigned to N thus the potential distance between those two points is unlimited

The universe has unlimited length in any direction measured or direction and it's opposite measured and unlimited volume whether the amount of mass in the universe is limited or unlimited although if the amount of mass in the universe is limited then the smallest section of the universe that contains all mass in the universe inside it or the combined volume of all the sections of the universe that contain mass might have a finite volume

One can measure the distance between the coordinates of two parts of the universe that both contain empty space without mass if the universe has a limited amount of mass in it which is confined within borders of a limited volume, limited surface area and limited distance between the two farthest apart points within those borders

There is an unlimited distance in any translational direction that coordinate points can be set apart from each other, such as being N meters apart from each other no matter how large N is and still have a known location, but two coordinate points can not be set a distance of infinity length units apart from each other such as infinity meters apart from each other and still have a known location because infinity is not a number

Infinity plus one is not equal to the number of infinity

Infinity plus one is undefined because infinity is not a number

Infinity times two is not equal to the number of infinity 

Infinity times two is undefined because infinity is not a number

Infinity plus a number other than zero is not equal to itself 

Infinity plus a number is undefined because infinity is not a number

Infinity times a number other than one is not equal to itself

Infinity times a number is undefined because infinity is not a number

It is wrong to use infinity as an excuse to claim you can add a quantity greater than zero to another quantity greater than 0 without increasing the quantity

It is wrong to use infinity as an excuse to claim you can multiply a positive non zero quantity by a number greater than 1 without increasing the quantity

It is wrong to use infinity as an excuse to claim you can multiply a positive non zero quantity by a number greater than 0 and 1 than one without decreasing the quantity

Doubling a positive amount of an unlimited positive quantity will double that quantity

I am not claiming such objects physically exist in real life.  But, a object that is 2 inches by 8 inches but goes on forever in both a third direction and it's opposite, has twice the volume of a object that is 2 inches by 4 inches but goes on forever in both a third dimension and it's opposite, both objects have unlimited volume but neither object has a volume of infinity cubic inches nor infinity cubic inches times a constant that is a real number

N is a positive real number

For real numbers

Each even number except for 0 is twice one and only one odd number

Each odd number except for 0 is twice one and only one odd number

So excluding 0 there are exactly the same number of odd and even numbers

Twice 0 is 0 and half 0 is also 0 and 0 is an even number

So there is exactly one more even number than the number of odd numbers

When 0 is excluded there are either two more odd number than even numbers or an equal number of odd and even numbers between negative N and positive N

When 0 is included there is either one more odd number than even numbers or one more even number than odd numbers between negative N and positive N

The limit as N approaches positive infinity of the number of odd numbers divided by the number of even numbers approaches 1 from below

The limit as N approaches positive infinity of the number of even numbers divided by the number of odd numbers approaches 1 from above

M is a whole number

For real numbers

The number of numbers that are muliples of M excluding 0 is equal to twice the number of non zero integers divided by M

The number of numbers that are muliples of M excluding 0 is equal to twice the number of odd numbers divided by M

The number of numbers that are multiples of 2 excluding 0 is equal to twice the number of odd numbers divided by 2

N is a positive real number

For real numbers

The limit as N approaches infinity of the number of prime numbers divided by the number of composite numbers approaches 0 from above

The big bang makes no sense because the universe has unlimited volume and must be eternal.  

The total momentum of an entire universe of finite mass within each and every non accelerating reference frame is constant for each such reference frame and does not change with time due to conservation of momentum therefore the universe must be eternal according to the known laws of physics if there was a point in time in which the universe did not exist and then suddenly did exist that would violate the conservation of momentum for all non accelerating reference frames in which the total momentum of the universe was not zero.  The total momentum would change from zero or undefined before the universe existed to a non zero number after it existed which would violate conservation of momentum for such a non accelerating reference frame.  Therefore the universe must have eternally existed and not existed for only a finite or limited time unless the known laws of physics are violated.

No object with mass can travel faster the the speed of light in any reference frame according to special relativity.  The limit as the amount of kinetic energy of that object approaches infinity joules of the objects speed approaches the speed of light from below.  Although special relativity has already been disproven by me, we are going to assume no object travels faster than the speed of light.

http://teachingthenarrowway.blogspot.com/2022/03/fat-runner-paradox-test-for-special.html

A universe that has 100% of all the mass of non photon objects within a border of finite volume and that has a finite chemical and finite kinetic energy and finite mass within that border from a specific non accelerating reference frame would emit photons outside that border traveling at a faster speed than the non photon mass inside that border can travel.  

Electrons drop energy levels and photons are emitted some of them leaving the border resulting in a decrease in the total chemical energy or a loss of total kinetic energy of all particles added together as measured within a non accelerating reference frame in the finite boundary that contains all the mass of non photon particles in the universe unless compensated by nuclear reactions which result in a loss of mass within that boundary

Some photons which were emitted during loss of one type of energy might transfer energy from one type to another occassionally instead of leaving the boarder but some of them will leave the boarder without ever returning to the boarder because they leave at the speed of light and will never contact any object within the boundry again because the objects inside the boundary move slower than the speed of light resulting in a permanent and irreversible loss of the total kinetic energy plus chemical energy plus mass times the speed of light squared inside the boundary

Through nuclear reactions the total chemical energy in the border containing all the mass of non photon particles in the universe can increase at an amount less than or equal to the amount of mass of non photon particles lost in the universe times the speed of light squared.  It is less than or equal to the loss in mass times the speed of light squared because some photons will be emitted that leave the finite border containing all the mass within the universe.  

The absolute temperature is the mean average kinetic energy per molecue.  Thermal kinetic energy is equal to the mean average absolute temperature per mole of molecues times the number of moles of molecues.  The total chemical energy in the boundary of the universe containing all the mass of non photon particles can also increase by an amount less than or equal to the decrease in the total of the mean average absolute temperature per mole times the number of moles in the universe.  It is less than or equal to the loss in mean average temperature per mole of molecues times the number of moles of molecues because some photons will be emitted that leave the finite border containing all the mass within the universe.

 The chemical energy within the boundary can increase by less than or equal to the loss of mass within the boundary times the speed of light squared plus the loss of thermal kinetic energy within the border.  It is less than or equal to because of photons emitted outside the border.

The thermal kinetic energy within the boundary can increase by less than or equal to the loss of mass within the boundary times the speed of light squared plus the loss of chemical energy within the border.  It is less than or equal to because of photons emitted outside the border.  

The mass times the speed of light squared within the boundary can increase by less than or equal to the loss of thermal kinetic energy plus the loss of chemical energy within the border.  It is less than or equal to because of photons emitted outside the border.  

The mass times the speed of light squared plus the kinetic energy plus the chemical energy inside the border would decrease over time at a decreasing rate in any non accelerating reference frame due to emitting photons that leave outside that border.   The farther back in time you look the higher the rate of energy in photons that are emitted outside the border per time.  Looking backwards in time with no limit to how far back in time you go results in an unlimited quantity of mass times the speed of light squared plus the kinetic energy plus the chemical energy inside the border within any non accelerating reference frame.

If the mass times the speed of light squared plus the kinetic energy plus the chemical energy inside the border decreases over time then the mass although it might sometimes increase over time when compared between two short time periods through a decrease in the total chemical plus kinetic energy inside the boundary will in the long run decrease over time within the boundary because it can only increase by a decrease in the total chemical plus kinetic energy inside the boundary which when added to the mass times the speed of light squared inside the boundary is decreasing over time through the expulsion of photons outside that border moving at a faster speed than objects inside that border can move.

This means you can not start with a universe of finite starting mass all enclosed within a finite boundry that did not exist before a finite amount of time ago without violating the known laws of physics.  Any big bang theory involving a universe of finite starting mass violates the known laws of physics.  Any universe of unlimited mass that can not all be contained within a finite border can not expand anywhere and since the big bang is the claim that the universe is expanding such a universe is incompatible with the big bang.

Copyright Carl Janssen 2022

http://web.archive.org/web/20220612042252/https://whichiscorrect.com/boundary-or-boundry/

http://web.archive.org/web/20220624181413/https://linguaholic.com/linguablog/other-than-vs-other-then/

Letting you enemies abort themselves

I never opposed abortion if getting an abortion would save the mother's life and not getting an abortion would result in the death of the mother.  But I supported outlawing abortions after the development of brain cells and possibly also earlier in the past.

Maybe I was wrong in opposing abortion and here is why I might have been wrong.  I am not saying I was definitely wrong but I might have been wrong.

Let's presuppose abortion is an act of killing and in some cases it is more specifically an act of murder.

Most Democratic Candidates support legalized abortion.  Now someone who votes Democrat is more likely to teach their children to vote Democrat and to have the value systems very often that go with voting Democrat including supporting abortion.

There are some exceptions of Democratic Candidates that do not support abortion

https://web.archive.org/web/20030614103243/https://www.ontheissues.org/OH/Jim_Traficant_Abortion.htm

After the Republicans took control of the House in 1995, Traficant tended to vote more often with the Republicans than with his own party. On the issue of abortion, Traficant voted with the position of the National Right to Life Committee 95% of the time in the 105th Congress, and 100% of the time in the 106th and 107th Congresses.If someone who votes democrat does not get an abortion and raised children they would not have raised if they got an abortion their children would be more likely to vote to legalize abortion

https://web.archive.org/web/20220412003322/http://en.wikipedia.org/wiki/James_Traficant

When I talk about Democrats through the rest of the article I am not talking about the rare exceptions but for people who primarily support taxpayer funding of abortion, more taxes, taxpayer funding of public schools, forced hiring policies controlling the percent of employees based on race, religion, gender identity and sexual orientation, taxing carbon dioxide emissions, internet censorship of viewpoints that do not agree with the democratic party viewpoints and forcing people who do not want to live in a communist society to be coerced to do work for other people through taxation, the right for public school teachers to persuade children under 18 years old that they are transgender without parental permission, the right to surgically remove children under 18 years old anatomical parts without parental consent if the children are persuaded by public school teachers that they are transgender, the right to fine or imprison people who do not call you by the gender pronoun you desire them to, taxing people to pay insurance benefits for monogamous homosexual married couples, arresting police who use force to try to stop black on black violence, open border immigration for people with HIV AIDS, open border immigration for people without background checks to see if they committed violent crimes, etc.

Talking Democrats out of getting abortions or outlawing abortions for Democrats would only spread abortion in the next generation

Democrats tend to support taxing people to spend money on Public Schools.  Public Schools tend to instill in people the Democratic Party value system.

The Democratic Party Value system supports war against people who should not have war waged against them and supports using violent to redistribute wealth, even if they give lip service to opposing war, by supporting tax payer funded schools that teach blind faith in government Democrats support unjust wars.

If people were made fully aware that abortion is killing or murder but not prevented from getting abortions then people who do not value human life would be more likely to choose to get abortions, but people who do value human life would be less likely to choose to get abortions.  Hopefully this would result in the next generation having a lower percentage of people that do not value human life and a higher percentage of people that do value human life.  This might not happen if those who got abortions adopted later and still raised children with their anti life value system.  Also hypothetically if someone got A abortions but still gave birth to X children and raised X children but would have given birth to and raised Y children if they did not get any abortions then if X is greater than or equal to Y then allowing them to get an abortion does not make the situation better in terms of preventing people with anti life value systems from raising children

When people with anti life value systems teach their children an anti life value system those children are more likely to grow up to become murderers or commit other violent acts against non violent people.

Allowing people to voluntarily set up a communal wealth system is not a problem and many voluntary communal societies have successfully worked when the society was allowed to reject members who would not contribute labor to help others in the community such as working to provide food for the community or provide services for the community members which the community members agree are valuable enough to let them stay without producing food in exchange for the food.

New Book: Bernie Sanders Was Kicked Off Vermont Commune for Loafing

https://web.archive.org/web/20160420123527/https://www.jewishpress.com/news/breaking-news/new-book-bernie-sanders-was-kicked-off-vermont-commune-for-loafing/2016/04/20/

Imposing communism by force has had a track record of multiple holodomores in which massive numbers of people starved.  

In 1932–1933, a famine known as the Holodomor killed 3.3–3.9 million people in the Ukrainian Soviet Socialist Republic

https://web.archive.org/web/20220429172547/https://en.wikipedia.org/wiki/Holodomor_genocide_question

https://web.archive.org/web/20220502021057/https://en.wikipedia.org/wiki/Holodomor

Democrats support policies that lead to holodomores in which massive numbers of people starve to death

If Democratic parents raise children who vote and more importantly behave like Democrats more people would be murdered if the parents did not abort the children and successfully instilled Democrat value systems in the children then the number that would be murdered if the parents aborted the children and did not give birth to or adopt any children to replace the children they murdered through abortion

Now not all children that are raised by Democratic parents choose the value system of their Democratic parents so this reasoning might not hold in practice

Although there is an unlimited amount of money since money is created by belief there is a finite amount of food mass per volume in any section of the world of a given volume.  I am not opposed to people receiving welfare if they are offered it but I am opposed to people using violence to force other people to do slave labor work to give them welfare.  Someone can choose to take food stamps while simultaneously voting against any tax that is justified with the excuse of raising funds for food stamps.  

Currently men when looked on as a group as a whole are net tax payers and women looked on as a group as a whole are net tax receivers.  Traditionally women would have children and receive net resources of food from her husband but not from other women's husbands.  The husband who provides the food for his wife's children would get to instill his value system in her children, whether they are both of their biological or adopted children or children she had from a previous marriage in the case of a widow or sometimes in the case of a divorced woman depending on custody arrangements.  

Now some single mothers are exceptions to this but the following applies to the net effect of most single mothers as a group.  Now single mothers will tax men she is not married to, to give food to them without letting that men paying the tax raise her children and teaching them their value system.  These single mothers do not do the work of raising their children because they do not earn the food to feed the children, do not baby sit their own children and do not morally educate their own children instead they send their children to public schools that babysit the children and to public schools to immorally educate the children and tax men they are not married to, to pay for their children's food.  These single mothers tend to vote Democrat and the Public schools they send their kids to tend to teach a Democrat value system.  If voting actually worked there is not way to solve this problem by voting.  The problem can not be solved by voting because single mothers tax men who are not married to them.  This means that married men who try to have as many children as they can support in order to teach them other value systems than the Democrat value system are are limited in how many children they can support because they have to pay taxes to support children of single mothers who vote Democrat, but single mothers who vote Democrat have no limit to how many children they can have and raise to vote Democrat because the more children they have the more tax they can take from men they are not married to.  This is a positive feedback loop that can only be stopped if single mothers no longer can tax men they are not married to.  This positive feedback loop of an ever increasing percent of the population of people who do not work for food taxing an ever decreasing percent of the population who work to produce food tends to lead towards mass starvation.  The only reason it has not yet reached a state of mass starvation in the United States yet is because technology improves over time so one man can potentially produce more food per time now than in the past.

Suddenly Hermes and La Barbara have returned from Spa 5. He had made the labor camp so efficient that they only needed one Australian man to perform the labor.

https://web.archive.org/web/20220503233255/https://futurama.fandom.com/wiki/How_Hermes_Requisitioned_His_Groove_Back

The only way to stop the positive feedback loop that will lead to starvation is to stop taxing men to pay for other men's children which will never happen as long as net tax receivers can vote to tax net tax payers.  This positive feedback loop could be slowed down by letting single mom's get abortions if single mom's would have less children and thus raise less children who vote to tax people to fund net tax receivers.

Democrats also support open borders which when combined with allowing net tax receivers to tax net tax payers will result in mass starvation.  Communal societies only work with border restrictions.  Forced communism plus open borders leads to mass starvation, because you can not close the borders to keep out people who will refuse to produce food but will demand to receive food through the violent imposition of communism.  When these non food producers enter the border and have children they can persuade their children to vote for the value system that will tax the net food producers leading to mass starvation.  Allowing the immigrants who want to violently force other people to produce food for them to get abortions can slow down the positive feedback loop that would lead to mass starvation if non net tax paying immigrants would have less children and thus raise less children who vote to tax people to fund net tax receivers.

Getting an abortion is still killing so I am not suggesting people who oppose the Democrats anti life value system go out and get jobs as professional abortionists.  I am suggesting maybe we should let people know abortion is the killing of a life, and let people who do not value human life get abortions without stopping them.  We should still stop forced abortions of mothers who do not want abortions and who would not die as a result of not getting an abortion.

Presuming the reader is on my team, now we should encourage people on our team to not get abortions.  But on the team that supports all the bad things I listed above that Democrats support, preventing them from getting abortions might lead to an increase in their numbers resulting in mass starvation of both or all teams in the long run and increased violence in future generations in the short run.  We can try to persuade them to change teams and then persuade them not to get an abortion if they switch to our team, but if they will not switch to our team preventing them from getting an abortion might increase the numbers of an army of evil.  

I still maintain that Paul Hill and Scott Roeder committed third party defense and not murder when they executed abortionists, but Paul Hill was executing someone from the enemies team to defend someone else who would likely be recruited to the enemies team which might have increased the number of abortions in the long run even though it decreased the number of abortions in the local geographic area in the short run.  Although Paul Hill technically committed defense it might not have been a wise decision because he may have increased the population of the anti life team by preventing a member of the anti life team from aborting potential recruits of the anti life team who have anti life parents who would try to raise them in anti life values.

Letting the antilife team completely exterminate themselves would result in less abortions in the long run then letting the antilife team procreate more members who will get future abortions.  Perhaps allowing the antilife team to grow in population relative to the prolife team by temporary forcing antilife people not to get abortions instead of allowing them to naturally exterminate themselves would allow them to grow in numbers enough to be powerful enough to not only change the law in the future and resume abortions but also to force abortions on the prolife team as has been done in China with the one child policy. 

But someone might object the Bible opposes abortion.  The Bible classifies causing a parent who should not receive an abortion to have an abortion as murder but actually has prescribed abortions for wicked people or executing the children of wicked people in some cases.

I am not saying we should enforce old testament laws or execute people based on old testament laws in a different geographical location than ancient Israel and a different time period.  I am not saying whether or not people should obey the Bible but simply explaining this for those who object to what I say on the grounds of the Bible.

Exodus 21:22-24 describes up to the death penalty for a man who injures the baby of a pregnant woman with the death penalty in the case of an abortion that results from hitting a pregnant woman but the following exceptions in the Bible in which there is no death penalty for abortion must be considered

Deuteronomy 20:10-18 

Deuteronomy 20:10-11 prescribes not to kill people who make peace with you,

Deuteronomy 20:12-14 prescribes  to execute men only and take the cattle, women and children of people who do not make peace with you 

except those people from specific groups listed in Deuteronomy 20:16-17 who you are to leave nothing alive of not even the cattle, women nor children

The groups described in Deuteronomy 20:16-17 may have committed human sacrifice, incest and bestiality in Leviticus 18 and Leviticus 20 and because of that leaving any of them alive even their offspring may have resulted in a spread of stds and genetic defects leading unto future generations, and leaving the adults alive may have spread the teachings of the practices of incest, bestiality and idol worship

Leviticus 20:20-21 prescribes the execution of people who committed a specific type of incest and for them to die childless.  They were not to be given an abortion and allowed to live but to be executed.  The execution would result indirectly in an abortion unless the execution was delayed and the woman was allowed to give birth prior to being executed.  However Leviticus 20:20-21 prescribes for them to die childless hence an indirect abortion through the execution of the mother.

Numbers 5 Prescribes giving a woman suspected of adultery drink a solution and if she has committed adultery the result of the solution will result in her having an abortion but if she has not committed adultery the solution will not result in her having an abortion.

Deuteronomy 22 Execution of an adulteress woman would result in an abortion unless the woman is required to have her execution delayed until she gives birth which is not mentioned in the text

The difference between Numbers 5 and Deuteronomy 22 is in Deuteronomy 22 understood in the context of the books of Moses a further degree of proof is required before executing the woman involving a proper court trial with witnesses but in Numbers 5 the proof is insufficient and the solution is given upon suspicion of adultery

Starting in Exodus 11 and continuing in later parts of Exodus, God warns he will slay the firstborn sons of the Egyptians who were supporting Pharaoh in enslaving the Israelites, except perhaps hypothetically for any Egyptians who changed sides to the Israelites side and performed the same passover ritual Israelites were required to perform to prevent their firstborn from being executed.  This would be post birth abortions and might potentially have included pre birth abortions of any Egyptians who were pregnant with their first son but have not yet given birth

Copyright Carl Janssen 2022 May 9

Evolutionary biologists implying birds are reptiles

If all birds are dinosaurs and all dinosaurs are reptiles then all birds are reptiles

But if all birds are not reptiles then not all dinosaurs are reptiles and or all birds are not dinosaurs

If some birds are not reptiles then not all dinosaurs are reptiles and or not all birds are dinosaurs

Copyright Carl Janssen 2022 April 15

"Modern taxonomy classifies all dinosaurs as reptiles."

http://web.archive.org/web/20210617054043/https://www.worldatlas.com/articles/were-dinosaurs-reptiles.html

"Modern classification considers all dinosaurs to be reptiles"

http://web.archive.org/web/20220415082239/https://adventuredinosaurs.com/2019/09/18/dinosaurs-were-reptiles-heres-why/

"What Category Is A Dinosaur?

Since dinosaurs have anatomical features that are similar to living reptiles, they have always been classified as reptiles.

Are Dinosaurs Not Reptiles?

The modern taxonomy classifies all dinosaurs as reptiles, not birds or mammals"

http://web.archive.org/web/20220415082458/https://www.animalpicturesarchive.com/is-dinosaur-a-reptile-or-an-amphibian/

Using more modern classification techniques, we’ve also found out that not only are dinosaurs reptiles, but birds are too.

http://web.archive.org/web/20220314141928/activewild.com/are-dinosaurs-reptiles/

"birds are reptiles"

http://web.archive.org/web/20211204145747/https://askabiologist.asu.edu/questions/birds-dinosaurs-reptiles

"In the Linnaean system, organisms are grouped by characteristics regardless of their ancestry. So a reptile is an animal that is ectothermic and has scales, and birds would not be reptiles. In the 1940's, a biologist named Willi Hennig came up with another classification system that he called phylogenetics. In this system, organisms are grouped only by their ancestry, and characteristics are only used to discover the ancestry."

http://web.archive.org/web/20211204145747/https://askabiologist.asu.edu/questions/birds-dinosaurs-reptiles

https://duckduckgo.com/?q=are+all+dinosaurs+reptiles&ia=web

"birds are literally dinosaurs"

http://web.archive.org/web/20220408070301/birdlife.org/news/2021/12/21/its-official-birds-are-literally-dinosaurs-heres-how-we-know/

https://duckduckgo.com/?q=are+all+birds+dinosaurs&ia=web

birds are considered a separate class to reptiles

http://web.archive.org/web/20220403071650/https://en.m.wikipedia.org/wiki/Reptile

https://duckduckgo.com/?q=are+birds+reptiles&ia=web

Percentage of greater values between two distributions

Importance of raw data in knowing practical or clinical significance as opposed to statistical significance

Sometimes a t test is very useless to achieving real life goals yet it is incredibly popular to publish t tests comparing two sets of data without showing the raw data in medical science.  Although it could make sense to remove some parts of raw data in order to keep patient data confidential someone could simply replace identifying data such as patient name with unidentifiable information such as id numbers from which the patient name can not be determined.  This would not be possible in all cases such as studying if there is a correlation between the latitude or longitude of primary location of residence address and health conditions but would probably have been possible in most cases that occurred in the past.

In many cases it maybe more useful to know what each of two distributions look like rather than if two distributions are statistically significantly different by a certain alpha value or if one distribution is statistically significantly greater than the other by a certain alpha value

In many cases the question of practical significance or clinical significance is more important than statistical significance.  A question of practical significance could be, what is the probability that a single specific choice will result in a value that is acceptable for my goal.  Other times a question of practical significance could be out of all the available choices which choice has the highest probability of resulting in a value acceptable for my goal.

In such a case it might make more sense to simply look at the raw data of a study and count the number of cases in which the desired value was greater than the minimum value acceptable and less than the maximum value acceptable and then divide that number by the total number of cases.

For example if someone is comparing two treatments for blood pressure someone and wants to decrease a patients blood pressure by at least 10 units but by no more than 50 units it would make more sense to figure out the frequency at which each treatment in a study resulted in a decrease of more than 10 units but less than 50 units than to use a t test.  This would be done by counting the number of cases that result in a decrease of at least 10 units but no more than 50 units then dividing by the total number of cases for each distribution.  Next the person choosing the two treatments figures out which treatment has a higher percentage of acceptable results and chooses that treatment.  

This can not be done without the raw data which is commonly removed from scientific journal articles that give the results of a t test comparing two sets of raw data but removes the raw data.  It might be possible however if the raw data was removed but both sets of raw data were given a standard deviation and mean, to use that information, to estimate the percentage or frequency of cases for each of two choices that produced a decrease of at least 10 units but no more than 50 units in the example above, by using the mean and standard deviations published to construct a distribution to represent each choice based on the assumption of a normal distribution for each of the two treatments that were used.  This however would be a very bad idea if no results for tests of having a normal distribution were presented in the scientific journal article.  I would not be surprised if it is very common never to show the results of any tests showing that the two distributions were actually normally distributed before conducting a t test.  I would like to see a study looking at the percentage of studies in which normal distribution was not checked for but a t test was performed.

Sometimes a question of practical significance might not be so delicate as to have both a upper and lower limit in desired outcomes.  For example if someone wanted a fire arm that could shoot at least a distance of 200 units but did not worry if it could shoot too great a distance.  It would make more sense to look at the raw data for each of the different firearm choices and calculate the percent frequency that exceeded a firing distance of 200 units for each firearm choice's distribution than to conduct a t test on the raw data to determine if each of two firing distribution choices available produced statistically significant different results for an alpha value or if one test produced statistically significant greater results for an alpha value

Sometimes a question of practical significance is yet another degree even less delicate than that and someone might not even care if a at least a minimal number of units were produced but only want to know which of two choices produced greater results the most often.  Someone might say, now we can finally use a t test legitimately.  And in such a case you could use a t test but it still would not be the best choice for at least two reasons.

Firstly, a t test would not be the best choice because the question was not which choice had a greater mean but which choice produced greater results than the other available choice most often.  Secondly, a t test would not be the best choice because you can not know if the results of both distributions will be normally distributed before conducting the test.

I am going to write a possibly new statistics test I thought of which may or may not have already been created by someone else under another name.  I will name this test the "Percentage of greater values between two distributions" test.

Test steps

This test works for ordinal, interval or ratio data and it does not matter if the two sets of data being compared have equal sample sizes or not or if they have odd or even sample sizes.

After collecting data from two samples order the values of the data for each sample in a list in ascendimg or descending order.

Pick one of the two lists

For each value on the chosen list count the number of values on the other list that are below that value as 1 point each, the number of data points exactly equal to that value as 0.5 points each and the number of data points higher than that value as 0 points each.  Each value on the chosen list will have a certain score or sum total of points.  If there are more than one data points on the list other than the chosen list that have that value count that data point multiple times.  Add up the total number of points for each value on the chosen list together for all the values on the chosen list and divide it by the product of the sample size of the chosen list and the sample size of the other list.  If a value on the chosen list occurs multiple times then count or use that value multiple times when adding up the points for all of the values.  You can swap lists next and get a score for each list.  The final value for each list should give you the percent of time that a value randomly selected from the population that one list was sampled from should be greater than another value randomly selected from the population the other list was sampled from.  In some cases involving data with discrete quantized values it maybe better to set the 0.5 points each values to 0 points instead as long as you do so consistently for both lists, I choose them to be 0.5 points based on the assumption of non quantized data in which it could have a 50% chance of being above and 50% chance of being below the other data point if a very small measurement difference was made such as one data point being 1.49999 and the other being 1.50001 instead of both being 1.5 when measured to two significant digits each.

Examples

I will use this possibly new test to compare two such sets of random uniform data each with a sample size of five, one between 0 and 1 and the other between 0.1 and 1.1 both to 4 decimal places from

https://www.random.org/decimal-fractions/

https://web.archive.org/web/20220402133005/https://www.random.org/decimal-fractions/ 

I will add 0.1 to the second set of numbers between 0 and 1 to get a range between 0.1 and 1.1  

( I was hoping this would increase the likelihood of the results for the two distributions looking different but unfortunately the distribution which has 0.1 added to it had a lower mean and median and the opposite of intended results were produced)

In order to compare this test with a t-test I will assume the p value for the possibly new data is one minus the percent that a randomly selected value from one list will be greater than a randomly selected value from another list, even though this does not line up the same way as a t test because a t test only compares if one mean is likely to be greater than another.  I will also look at the percent of values from one list that are less than or less than or equal to the mean and median of the other list ( four combinations choice of mean or median and choice of less than or less than or equal to. )

Here are your random numbers:

0.8349
0.3538
0.8425
0.2781
0.5241 

Timestamp: 2022-04-11 00:42:01 UTC

List A (sample A in order from least to greatest)

0.2781

0.3538

0.5241

0.8349

0.8425

Sample B before adding 0.1

Here are your random numbers:

0.1081
0.3479
0.4587
0.7225
0.3923

Timestamp: 2022-04-11 00:46:43 UTC

0.1081

0.3479

0.3923

0.4587

0.7225

List B ( sample B in order after 0.1 is added)

0.2081

0.4479

0.4923

0.5587

0.8225

Start of example for "Percentage of greater values between two distributions" test

Value B, Value A, points ( 1 if A<B, 0.5 if A=B, 0 if A>B)

0.2081, 0.2781, 0

0.2081, 0.3538, 0

0.2081, 0.5241, 0

0.2081, 0.8349, 0

0.2081, 0.8425, 0

0.4479, 0.2781, 1

0.4479, 0.3538, 1

0.4479, 0.5241, 0

0.4479, 0.8349, 0

0.4479, 0.8425, 0

0.4923, 0.2781, 1

0.4923, 0.3538, 1

0.4923, 0.5241, 0

0.4923, 0.8349, 0

0.4923, 0.8425, 0

0.5587, 0.2781, 1

0.5587, 0.3538, 1

0.5587, 0.5241, 1

0.5587, 0.8349, 0

0.5587, 0.8425, 0

0.8225, 0.2781, 1

0.8225, 0.3538, 1

0.8225, 0.5241, 1

0.8225, 0.8349, 0

0.8225, 0.8425, 0

Total points 10

Sample Size A * Sample Size B = 5 * 5 = 25

Total Points / Sample Size = 10 / 25

estimated 40% of random value from population B being greater than value from population A

one tailed P value = 1 - 0.40 = 0.60 used for comparing with one tailed t test if population B > A

100% - 40% = 60% 

estimated 60% of random value from population A being greater than value from population B

one tailed P value = 1 - 0.60 = 0.40 used for comparing with one tailed t test if population A > B

Value A, Value B, points ( 1 if B<A, 0.5 if B=A, 0 if B>A)

0.2781, 0.2081, 1

0.2781, 0.4479, 0

0.2781, 0.4923, 0

0.2781, 0.5587, 0

0.2781, 0.8225, 0

0.3538, 0.2081, 1

0.3538, 0.4479, 0

0.3538, 0.4923, 0

0.3538, 0.5587, 0

0.3538, 0.8225, 0

0.5241, 0.2081, 1

0.5241, 0.4479, 1

0.5241, 0.4923, 1

0.5241, 0.5587, 0

0.5241, 0.8225, 0

0.8349, 0.2081, 1

0.8349, 0.4479, 1

0.8349, 0.4923, 1

0.8349, 0.5587, 1

0.8349, 0.8225, 1

0.8425, 0.2081, 1

0.8425, 0.4479, 1

0.8425, 0.4923, 1

0.8425, 0.5587, 1

0.8425, 0.8225, 1

Total points 15

Sample Size A * Sample Size B = 5 * 5 = 25

Total Points / Sample Size = 15 / 25

estimated 60% of random value from population A being greater than value from population B

one tailed P value = 1 - 0.60 = 0.40 used for comparing with one tailed t test if population A > B

100% - 60% = 40% 

estimated 40% of random value from population B being greater than value from population A

one tailed P value = 1 - 0.40 = 0.60 used for comparing with one tailed t test if population B > A

End of test example for "Percentage of greater values between two distributions" test

Comparing with t - test

One tailed t-test to determine if population A > B

https://www.socscistatistics.com/tests/studentttest/default2.aspx

p-value is .351604

Comparing with percent of values above and below mean and median of data from other list

Percent of values in one list that are less than or greater than mean or median of values from other list

List B ( sample B in order after 0.1 is added)

0.2081

0.4479

0.4923

0.5587

0.8225

median = 0.4923

mean = 0.5059

list of values from sample A that are less than mean of sample B ( 0.2781, 0.3538 )

list of values from sample A that are greater than mean of sample B ( 0.5241, 0.8349, 0.8425 )

no values from sample A that are equal to the mean of sample B

list of values from sample A that are less than median of sample B ( 0.2781, 0.3538 )

list of values from sample A that are greater than median of sample B ( 0.5241, 0.8349, 0.8425 )

no values from sample A that are equal to the median of sample B

60% of values from A are greater than or equal to the mean of B

60% of values from A are greater than the mean of B

60% of values from A are greater than or equal to the median of B

60% of values from A are greater than the median of B

https://www.calculatorsoup.com/calculators/statistics/average.php

https://web.archive.org/web/20220324192741/https://www.calculatorsoup.com/calculators/statistics/average.php

List A (sample A in order from least to greatest)

0.2781

0.3538

0.5241

0.8349

0.8425

median = 0.5241

mean = 0.56668

list of values from sample B that are less than mean of sample A ( 0.2081, 0.4479, 0.4923, 0.5587 )

list of values from sample B that are greater than mean of sample A ( 0.8225 )

no values from sample B that are equal to the mean of sample A

list of values from sample B that are less than median of sample A ( 0.2081, 0.4479, 0.4923 )

list of values from sample B that are greater than median of sample A ( 0.5587, 0.8225 )

no values from sample B that are equal to the median of sample A

20% of values from B are greater than or equal to the mean of A

20% of values from B are greater than the mean of A

40% of values from B are greater than or equal to the median of A

40% of values from B are greater than the median of A

Start of example for "Percentage of greater values between two distributions" test

Sample E

0.1081

0.3479

0.4587

0.7225

0.3923

List E

0.1081

0.3479

0.3923

0.4587

0.7225

Calculating scores for list E

Value B, Value A, points ( 1 if A<B, 0.5 if A=B, 0 if A>B)

0.1081, 0.2781, 0

0.1081, 0.3538, 0

0.1081, 0.5241, 0

0.1081, 0.8349, 0

0.1081, 0.8425, 0

0.3479, 0.2781, 1

0.3479, 0.3538, 0

0.3479, 0.5241, 0

0.3479, 0.8349, 0

0.3479, 0.8425, 0

0.3923, 0.2781, 1

0.3923, 0.3538, 1

0.3923, 0.5241, 0

0.3923, 0.8349, 0

0.3923, 0.8425, 0

0.4587, 0.2781, 1

0.4587, 0.3538, 1

0.4587, 0.5241, 0

0.4587, 0.8349, 0

0.4587, 0.8425, 0

0.7225, 0.2781, 1

0.7225, 0.3538, 1

0.7225, 0.5241, 1

0.7225, 0.8349, 0

0.7225, 0.8425, 0

Total points 8

Sample Size E * Sample Size B = 5 * 5 = 25

Total Points / Sample Size = 8 / 25

estimated 32% of random value from population E being greater than value from population A

one tailed P value = 1 - 0.32 = 0.68 used for comparing with one tailed t test if population E > A

100% - 32% = 68% 

estimated 68% of random value from population A being greater than value from population E

one tailed P value = 1 - 0.68 = 0.32 used for comparing with one tailed t test if population A > E

End of example for "Percentage of greater values between two distributions" test

Comparing with other tests

one tailed t-test for mean of population A > mean of population E

P value = 0.163344

https://www.socscistatistics.com/tests/studentttest/default2.aspx

Copyright Carl Janssen 2022 April 10

Custom Distribution Statistical Hypothesis Test

This might not be mathematically accurate in terms of probability theory I am experimenting with the results of doing different things with numbers.  These assumptions I am using do contradict with reality as do all probability based statistical hypothesis tests but possibly in different ways than some others.

I am literally making up this statistical test and calling it the custom distribution statistical hypothesis test.  I do not know if someone already made a test like this before me and called it a different name

Goal :  The probability distribution model that best represents data collected from the population that corresponds to real life samples is not known before collecting the data therefore it is erroneous to assume it will be a normal distribution before analyzing the sample data.  I am trying to create a model that creates a custom model for frequency distribution to represent the population that corresponds to data collected from a sample then create a possibly new type of statistical test.  I will call this possibly new type of statistical test a, "custom distribution statistical hypothesis test."

A "custom distribution statistical hypothesis test" is similar to a replacement for two sample independent unpaired t tests only with the assumption of a "custom distribution" instead of a normal distribution.

This statistics test includes determining the probability that the median of one sample of  data would be at least the distance it is measured to be in a specific direction from the median of another sample of data based on using the "custom frequency distribution" to represent the population of the sample from the other set of data.  This is done twice once for each sample of data compared to the other one.

By similar I do not mean the mathematical definition of the word similar.  The shape of the "custom frequency distribution" is empirically determined in a custom manner for each sample of data simply by using a cumulative frequency table plus certain additional assumptions and it is assumed that the population has a similar shape to the "custom frequency distribution" determined by a table except that it is modeled as continuous instead of discrete.  

The shape of the normal distribution used in t tests however is not determined empirically by the actual sample data but presumed to represent something "close enough" to the true shape of the population's probability distribution from which a sample is collected when running a t test.  Although the standard deviation or variance and mean of a normal distribution used for a t test is determined empirically the shape is not.  For example the shape of a set of data could appear to be uniform (or any other shape than a normal distribution) based on someone rational looking at a empirical probability plot or empirical probability table for a set of data but would still be treated as a normal distribution shape for a t test.

This test should work with ordinal, interval or ratio data when there is a odd sample size for both samples.  When there is a even sample size for one or both samples one can use a mean to get the median for interval or ratio data but the test results should be less trustworthy than with a odd sample size.  When there is a even sample size for one or both samples and the data is ordinal it does not work to use a mean to estimate the median unless you are taking the mean of two identical values.  However, it might be possible in the case of an even number sample size to create a fictitious rank in between the two values that are closest to where the median would be that you would normally take the mean of to get the median with interval or ratio data and use that fictitious rank in place of the median.  For example if the median would be between "10th street" and "11th street" you could create a fictitious rank of "the street that is less than 11th street but greater than 10th street" or if the median was between "3rd degree" and "4th degree" you could create a fictitious rank of "the degree that is more than 3rd degree but less than 4th degree" but you should not use 14th street as a replacement for the median that is in between 12th street and 16th street because there might be a real 14th street that is not located at the mean of the coordinates or positions of 12th and 16th street and you should not use 7th degree to represent a median that is in between 5th degree and 9th degree because 7th degree might be a real rank that is not the same as the mean of 5th degree and 9th degree.

Comparing the medians of two different samples with the probability distributions of the other sample to estimate the probability that the median of one population is greater than the median of the other population.

Assumption 1 :  The sample which is expected to have a greater median is named sample B and the one expected to have a lower median is named sample A.

Assumption 2 : If two values collected from a sample have no collected values taken from a sample found between them then the probability of obtaining or being above a third value that is in between them when collecting a sample with a sample size of one from that population shall be inclusively between the probability of obtaining or being above each of the two values that were collected from the sample.

Assumption 3 : If two values collected from a sample have no collected values taken from a sample found between them then the probability of obtaining or being below a third value that is in between them when collecting a sample with a sample size of one from that population shall be inclusively between the probability of obtaining or being below each of the two values that were collected from the sample.

How I am defining "inclusively between"

2 <= X <= 3 in this example X is inclusively between 2 and 3

2 < X < 3  in this example X is exclusively between 2 and 3

Assumption 4 : The median of a population shall be estimated to be the median of the sample taken from that population.  Sample A is a sample taken from population A and sample B is a sample taken from population B.

Assumption 5 : If both the median of sample A is lower than the median for the population estimated from sample B and the median of sample B is higher than the median for the population estimated from sample A, both for the same alpha level, then the median of population B is higher than the median of population A for that alpha level.  If exactly one of those two conditions are met but not both then it is unclear if the median of population A is lower than the median of population B for that alpha level.  If neither of those conditions are met then the median of population A is not lower than the median of population B for that alpha level.

Null Hypothesis 1 : Median of sample B <= Median of population A

Alternative Hypothesis : Median of sample B > Median of population A

Null Hypothesis 2 : Median of sample A => Median of population B

Alternative Hypothesis : Median of sample A < Median of population B

Null Hypothesis 3 : Median of population B <= Median of population A

Alternative Hypothesis 3 : Median of population B > Median of population A

If Null Hypotheses 1 and 2 are both rejected then null hypothesis 3 is rejected.  If exactly one of Null Hypotheses 1 and 2 are rejected but not both of them then it is unclear if Null Hypothesis 3 is rejected or not.  If Null Hypothesis 1 and 2 both fail to be rejected then then Null Hypothesis 3 fails to be rejected.

Assumption 6 : The P value of rejecting Null Hypothesis 1 shall be one minus the cumulative frequency distribution as calculated from left to right of achieving the median of Sample B on the probability distribution table for Sample A.  In the case where no value from sample A exists with the same value as the median of Sample B this shall be estimated by using the closest value above and the closest value below the median of sample B from the probability distribution table on sample A as explained in assumption 2.  In the case where a value exists on sample A which is the same as the median of sample B the cumulative frequency distribution for the value already on the chart of the cumulative frequency distribution for  sample A shall be used with the frequency greater than or equal the value instead of the greater than only option

Assumption 7 : The P value of rejecting Null Hypothesis 2 shall be one minus the cumulative frequency distribution as calculated from right to left of achieving the median of Sample A on the probability distribution table for Sample B.  In the case where no value from sample B exists with the same value as the median of Sample A this shall be estimated by using the closest value above and the closest value below the median of sample B from the probability distribution table on sample B as explained in assumption 3.  In the case where a value exists on sample B which is the same as the median of sample A the cumulative frequency distribution for the value already on the chart of the cumulative frequency distribution for  sample B shall be used with the frequency less than or equal to the value instead of the less than only option

Examples 1-4

Comparing results between t tests and custom distribution statistical hypothesis tests for uniform distributions in which both samples have equal variance and independent unpaired samples are used

Example 1

sample A = (1, 2, 3, 4, 5)

sample B = (2.5, 3.5, 4.5, 5.5, 6.5)

custom distribution statistical hypothesis test

sample A = (1, 2, 3, 4, 5), median = 3

value, frequency=value, frequency <= value, frequency < value

0.5, 0, 0, 0, 0

1, 1/5, 1/5, 0

1.5, 0, 1/5, 1/5

2, 1/5, 2/5, 1/5

2.5, 0, 2/5, 2/5

3, 1/5, 3/5, 2/5

3.5, 0, 3/5, 3/5

4, 1/5, 4/5, 3/5

median of sample B 4.5, 0, 4/5, 4/5

5, 1/5, 1, 4/5

5.5, 0, 1, 1 

1-1  <= P <= 1 - 4/5

0 <= P <= 0.2 for the median of sample B being higher than the estimated median of population A  

sample B = (2.5, 3.5, 4.5, 5.5, 6.5) median = 4.5

value, frequency=value, frequency => value, frequency > value

7, 0, 0, 0

6.5, 1/5, 1/5, 0

6, 0, 1/5, 1/5

5.5, 1/5, 2/5, 1/5

5, 0, 2/5, 2/5

4.5, 1/5, 3/5, 2/5

4, 0, 3/5, 3/5

3.5, 1/5, 4/5, 3/5

median of sample A 3, 0, 4/5, 4/5

2.5, 1/5, 1, 4/5

2, 0, 1, 1

1-1  <= P <= 1 - 4/5

0 <= P <= 0.2 for the median of sample A being lower than the estimated median of population B

for alpha > P reject the null hypothesis

for alpha < P fail to reject the null hypothesis

for one tailed alpha > 0.2 the median of sample A can be considered lower than the median of population B

and

for one tailed alpha > 0.2 the median of sample B can be considered higher than the median of population A

therefore

for one tailed alpha > 0.2 the median of population B can be considered greater than the median of population A

0 < one tailed alpha < 0.2 the median of sample A can not be considered conclusively if it is lower than the median of population B

and

0 < one tailed alpha < 0.2 the median of sample B can not be considered conclusively if it is higher than the median of population A

therefore

0 < one tailed alpha < 0.2 the median of population B can not be considered conclusively if it is greater than the median of population A

t - test

Null Hypothesis : mean of Population B <=  mean of Population B

Alternative Hypothesis : mean of Population B > mean of Population A

sample A = (1, 2, 3, 4, 5), mean = 3, n = 5

sample variance = [ ( 5 -3 ) ^ 2 + ( 4-3 ) ^ 2 + ( 3 - 3) ^2 + ( 2 - 3 ) ^2 + (1-3) ^2 ] / ( 5 - 1 )

sample variance = ( 4 + 1 + 1 + 4 ) / 4 = 10 /4 = 2.5

sample std = sample variance ^ 0.5 = 2.5 ^ 0.5 = approx 1.58113883008

sample B = (2.5, 3.5, 4.5, 5.5, 6.5), mean = 4.5, n = 5

sample v =[ ( 6.5 -4.5 ) ^ 2 + ( 5.5-4.5 ) ^ 2 + ( 4.5 - 4.5) ^2 + ( 3.5 - 4.5 ) ^2 + (2.5-4.5) ^2 ] / ( 5 - 1 )

sample variance = ( 4 + 1 + 1 + 4 ) / 4 = 10 /4 = 2.5

sample std = sample variance ^ 0.5 = 2.5 ^ 0.5 = ( 5 / 2 ) ^ 0.5

mean sample B - mean sample A = 4.5 - 3 = 1.5

in this case Sp = sample std A = sample std B because the sample sizes and variance are exactly equal

t = ( mean sample B - mean sample A ) / ( Sp *[ (1/na) +(1/nB) ] ^ 0.5 )

1/na + 1/nB = 1/5 + 1/5 = 2/5

t = 1.5 / [ (5/2) ^ 0.5 * (2/5) ^ 0.5 ] = 1.5

degrees of freedom = df = nA + nB -2 = 5 + 5 -2 = 8

one tailed p value = .086002

https://www.socscistatistics.com/pvalues/tdistribution.aspx

one tailed p value = 0.08600

https://www.statology.org/t-score-p-value-calculator/

for one tailed alpha > 0.086 the mean of population B can be considered greater than the mean of population A

for one tailed alpha < 0.086 the mean of population B can not be considered greater than the mean of population A

Example 2

sample A = (1, 2, 3, 4, 5)

sample B = (2, 3, 4, 5, 6)

sample A = (1, 2, 3, 4, 5), median = 3

value, frequency=value, frequency <= value, frequency < value

1, 1/5, 1/5, 0

2, 1/5, 2/5, 1/5

3, 1/5, 3/5, 2/5

3.5, 0, 3/5, 3/5

4, 1/5, 4/5, 3/5

median of sample B 4, 1/5, 4/5, 3/5

4.5, 0, 4/5, 4/5

5, 1/5, 1, 4/5

5.5, 0, 1, 1

P = 1 - 4/5

P = 0.2 for the median of sample B to be greater than than estimated median of population A

custom distribution statistical hypothesis test

Null Hypothesis : Median of sample B <= Median of population A

Alternative Hypothesis : Median of sample B > Median of population A

Null Hypothesis : Median of sample A => Median of population B

Alternative Hypothesis : Median of sample A < Median of population B

t - test

Null Hypothesis : mean of Population B <=  mean Population B

Alternative Hypothesis : mean of Population B > mean of Population A

t = 1

one tailed P = 0.173297

https://www.socscistatistics.com/tests/studentttest/default2.aspx

one tailed P = 0.17330

https://www.statology.org/t-score-p-value-calculator/

Example 3

sample A = (1, 2, 3, 4, 5, 6)

sample B = (2.5, 3.5, 4.5, 5.5, 6.5, 7.5)

custom distribution statistical hypothesis test

Null Hypothesis : Median of sample B <= Median of population A

Alternative Hypothesis : Median of sample B > Median of population A

Null Hypothesis : Median of sample A => Median of population B

Alternative Hypothesis : Median of sample A < Median of population B

t - test

Null Hypothesis : mean of Population B <=  mean of Population B

Alternative Hypothesis : mean of Population B > mean of Population A

Example 4

sample A = (1, 2, 3, 4, 5, 6) 

sample B = (2, 3, 4, 5, 6, 7) 

custom distribution statistical hypothesis test

Null Hypothesis : Median of sample B <= Median of population A

Alternative Hypothesis : Median of sample B > Median of population A

Null Hypothesis : Median of sample A => Median of population B

Alternative Hypothesis : Median of sample A < Median of population B

t - test

Null Hypothesis : mean of Population B <=  mean of Population B

Alternative Hypothesis : mean of Population B > mean of Population A

Example 5

Comparing custom distribution statistical hypothesis test with unpaired independent t test for the following triangular shaped distributions

sample A = ( 1, 2, 2, 3, 3, 3, 4, 4, 5 )

sample B = ( 2, 3, 3, 4, 4, 4, 5, 5, 6 )

custom distribution statistical hypothesis test

Null Hypothesis : Median of sample B <= Median of population A

Alternative Hypothesis : Median of sample B > Median of population A

Null Hypothesis : Median of sample A => Median of population B

Alternative Hypothesis : Median of sample A < Median of population B

t - test

Null Hypothesis : mean of Population B <=  mean of Population B

Alternative Hypothesis : mean of Population B > mean of Population A

Example 6 

custom distribution statistical hypothesis test with unequal sample sizes

sample A = ( 1, 2, 3, 4, 5, 6, 7, 8)

sample B = ( 3, 4, 5, 6, 7 )

Null Hypothesis : Median of sample B <= Median of population A

Alternative Hypothesis : Median of sample B > Median of population A

Null Hypothesis : Median of sample A => Median of population B

Alternative Hypothesis : Median of sample A < Median of population B

Copyright Carl Janssen 2022

https://en.m.wikipedia.org/wiki/Student%27s_t-test

http://web.archive.org/web/20220307082135/https://en.m.wikipedia.org/wiki/Student's_t-test

https://duckduckgo.com/?q=independent+t+test+equal+variance+and+equal+sample+size&ia=web

https://www.real-statistics.com/students-t-distribution/two-sample-t-test-equal-variances/

http://web.archive.org/web/20200804112708/https://www.real-statistics.com/students-t-distribution/two-sample-t-test-equal-variances/

https://duckduckgo.com/?q=unpaired+t+test+equal+variance+and+equal+sample+size&ia=web

https://tungmphung.com/unpaired-two-sample-t-test-independent-t-test/

http://web.archive.org/web/20210423122739/https://tungmphung.com/unpaired-two-sample-t-test-independent-t-test/

https://www.khanacademy.org/math/statistics-probability/summarizing-quantitative-data/variance-standard-deviation-sample/a/population-and-sample-standard-deviation-review

http://web.archive.org/web/20220323223702/https://www.khanacademy.org/math/statistics-probability/summarizing-quantitative-data/variance-standard-deviation-sample/a/population-and-sample-standard-deviation-review

https://duckduckgo.com/?q=standard+deviation+sample+vs+population+formula&ia=web

https://www.statology.org/population-vs-sample-standard-deviation/

http://web.archive.org/web/20210824024007/https://www.statology.org/population-vs-sample-standard-deviation/

https://duckduckgo.com/?q=test+statistic+and+critical+value+calculator&ia=web

https://duckduckgo.com/?q=p-value+and+alpha&ia=web

https://duckduckgo.com/?q=+hypothesis+one+tail+t+test+example&ia=web

https://duckduckgo.com/?q=t+test+percentile&ia=web

https://duckduckgo.com/?q=t+test+p+value+calculator&ia=web

https://www.socscistatistics.com/pvalues/tdistribution.aspx

https://web.archive.org/web/20211011165105/https://www.socscistatistics.com/pvalues/tdistribution.aspx

https://www.socscistatistics.com/tests/studentttest/default2.aspx

https://web.archive.org/web/20211011072830/https://www.socscistatistics.com/tests/studentttest/default2.aspx

https://duckduckgo.com/?q=p+value+t+test+chart&ia=web

https://www.statology.org/how-to-calculate-a-p-value-from-a-t-test-by-hand/

https://web.archive.org/web/20211123175421/https://www.statology.org/how-to-calculate-a-p-value-from-a-t-test-by-hand/

https://www.statology.org/t-score-p-value-calculator/

https://web.archive.org/web/20210306170506/https://www.statology.org/t-score-p-value-calculator/