Conservapedia - User contributions [en]

Founding Fathers

2010-04-22T21:39:43Z

Dasonk: Added truth.

[[File:Gilbert Stuart Portrait of George Washington.jpg|thumb|Portrait of George Washington by [[Gilbert Stuart]].]]
'''The Founding Fathers''' are the leaders who founded the [[United States]], especially the 40 dignitaries who signed the U.S. Constitution at the Constitutional Convention of 1787, and the 56 signers of the Declaration of Independence. Historians consider the most important founders to include [[John Adams]], [[Samuel Adams]], [[Benjamin Franklin]], [[Alexander Hamilton]], [[Thomas Jefferson]], [[James Madison]], and [[George Washington]]. Each has been studied in depth. Historians speak of Franklin's wide-ranging genius, Washington's charismatic leadership, Jefferson's paradoxical egalitarianism, Madison's brilliant constitutionalism, Hamilton's ambitious state-building, and Adams's quirkiness.

==Republicanism==
The Founding Fathers sought "Honor" --freedom from corruption, and a positive devotion to civic virtue. These were key elements of [[Republicanism]], and the Founding Fathers made republicanism the core values of the American system of government. The founding fathers were staunch believers in conservative policies and were exemplary in their tireless efforts to stamp out corrupt liberal influence.

[[Corruption]] was the great evil the Founding Fathers confronted. When Britain showed too much corruption, it was time to break free with the [[American Revolution]]. To overcome the temptations of corruption--such as luxury and bribery--in their own lives, the Founding Fathers cultivated the virtue of disinterestedness. That is, the made a conscious effort to not be the creature of his financial interests, and not give any sign to the public that they sought luxury or bribes. The goal was to be impartial, concerned only for the public good, not the advancement of friends or, still less, of party.

Even personal shame and humiliation was preferable to a tarnished honor or the hint of corruption. When Treasury Secretary Alexander Hamilton was accused of corruption for making secret payments to a man named James Reynolds, Hamilton revealed he had been set up and was paying blackmail to Reynolds following an affair with Mrs. Reynolds. Duels over honor were common in the era--Hamilton was killed in one, as was Hamilton's son.

== Signatories of the [[Declaration of Independence]] ==
{|
| valign="top" |
*[[John Adams]]
*[[Samuel Adams]]
*[[Josiah Bartlett]]
*[[Carter Braxton]]
*[[Charles Carroll of Carrollton|Charles Carroll]]
*[[Samuel Chase]]
*[[Abraham Clark]]
*[[George Clymer]]
*[[William Ellery]]
*[[William Floyd]]
*[[Benjamin Franklin]]
*[[Elbridge Gerry]]
*[[Button Gwinnett]]
*[[Lyman Hall]]
*[[John Hancock]]
*[[Benjamin Harrison V|Benjamin Harrison]]
*[[John Hart]]
*[[Joseph Hewes]]
*[[Thomas Heyward]]
| valign="top" |
*[[William Hooper]]
*[[Stephen Hopkins]]
*[[Francis Hopkinson]]
*[[Samuel Huntington]]
*[[Thomas Jefferson]]
*[[Francis Lightfoot Lee]]
*[[Richard Henry Lee]]
*[[Francis Lewis]]
*[[Philip Livingston]]
*[[Thomas Lynch, Jr.]]
*[[Thomas McKean]]
*[[Arthur Middleton]]
*[[Lewis Morris]]
*[[Robert Morris]]
*[[John Morton]]
*[[Thomas Nelson, Jr.]]
*[[William Paca]]
*[[John Penn]]
| valign="top" |
*[[Robert Treat Paine]]
*[[George Read]]
*[[Caesar Rodney]]
*[[George Ross]]
*[[Benjamin Rush]]
*[[Edward Rutledge]]
*[[Roger Sherman]]
*[[James Smith (signer)| James Smith]]
*[[Richard Stockton]]
*[[Thomas Stone]]
*[[George Taylor]]
*[[Matthew Thornton]]
*[[George Walton]]
*[[William Whipple]]
*[[William Williams]]
*[[James Wilson]]
*[[John Witherspoon]]
*[[Oliver Wolcott]]
*[[George Wythe]]
|}

== Signatories of the [[Articles of Confederation]] ==
{|
| valign="top" |
*[[Andrew Adams]]
*[[Samuel Adams]]
*[[Thomas Adams]]
*[[John Banister]]
*[[Josiah Bartlett]]
*[[Daniel Carroll]]
*[[William Clingan]]
*[[John Collins]]
*[[Francis Dana]]
*[[John Dickinson]]
*[[William Henry Drayton]]
*[[James Duane]]
*[[William Duer]]
*[[William Ellery]]
*[[Elbridge Gerry]]
*[[John Hancock]]
*[[John Hanson]]
*[[Cornelius Harnett]]
*[[John Harvie]]
*[[Thomas Heyward Jr.]]
*[[Samuel Holten]]
*[[Titus Hosmer]]
*[[Samuel Huntington]]
*[[Richard Hutson]]
| valign="top" |
*[[Edward Langworthy]]
*[[Henry Laurens]]
*[[Francis Lightfoot Lee]]
*[[Richard Henry Lee]]
*[[Francis Lewis]]
*[[James Lovell]]
*[[Henry Marchant]]
*[[John Mathews]]
*[[Thomas McKean]]
*[[Gouverneur Morris]]
*[[Robert Morris]]
*[[John Penn]]
*[[Joseph Reed]]
*[[Daniel Roberdeau]]
*[[Nathaniel Scudder]]
*[[Roger Sherman]]
*[[Jonathan Bayard Smith]]
*[[Edward Telfair]]
*[[Nicholas Van Dyke]]
*[[John Walton]]
*[[John Wentworth Jr.]]
*[[John Williams]]
*[[John Witherspoon]]
*[[Oliver Wolcott]]
|}

== Signatories of the [[United States Constitution]] ==
{|
| valign="top" |
*[[Abraham Baldwin]]
*[[Richard Bassett]]
*[[Gunning Bedford, Jr.]]
*[[John Blair]]
*[[William Blount]]
*[[David Brearly]]
*[[Jacob Broom]]
*[[Pierce Butler]]
*[[Daniel Carroll]]
*[[George Clymer]]
*[[Jonathan Dayton]]
*[[John Dickinson]]
*[[William Few]]
*[[Thomas Fitzsimons]]
*[[Benjamin Franklin]]
*[[Nicholas Gilman]]
*[[Nathaniel Gorham]]
*[[Alexander Hamilton]]
*[[Jared Ingersoll]]
| valign="top" |
*[[Daniel of St. Thomas Jenifer]]
*[[William Samuel Johnson]]
*[[Rufus King]]
*[[John Langdon]]
*[[William Livingston]]
*[[James Madison]]
*[[James McHenry]]
*[[Thomas Mifflin]]
*[[Gouverneur Morris]]
*[[Robert Morris]]
*[[William Paterson (jurist)|William Paterson]]
*[[Charles Cotesworth Pinckney]]
*[[Governor Charles Pinckney|Charles Pinckney]]
*[[George Read (signer)|George Read]]
*[[John Rutledge]]
*[[Roger Sherman]]
*[[Richard Dobbs Spaight]]
*[[George Washington]] (president of the Convention)
*[[Hugh Williamson]]
*[[James Wilson]]
*[[William Jackson (secretary)|William Jackson]] (Secretary)
|}

== Other Founding Fathers ==
{|
| valign="top" |
*[[Oliver Ellsworth]]
*[[Patrick Henry]]
*[[John Jay]]
*[[George Mason]]
*[[Thomas Paine]]
*[[Charles C. Pinckney]]
|}
==Further reading==
* Ellis, Joseph J. ''Founding Brothers: The Revolutionary Generation'' (2002), good overview of leading figures by top scholar [http://www.amazon.com/Founding-Brothers-Revolutionary-Joseph-Ellis/dp/0375705244/ref=cm_lmf_img_5_rdssss0 excerpt and text search]
* McClanahan, Brion. ''The Politically Incorrect Guide to the Founding Fathers'' (2009), popular book by conservative writer. [http://www.amazon.com/Politically-Incorrect-Founding-Fathers-Guides/dp/1596980923/ref=sr_1_1?ie=UTF8&s=books&qid=1251266508&sr=8-1 excerpt and text search]
* Wood, Gordon. ''Revolutionary Characters: What Made the Founders Different'' (2007), very good overview by leading conservative scholar [http://books.google.com/books?id=uOovRxek5AIC&dq=intitle:Revolutionary+intitle:Characters+inauthor:wood&lr=&as_drrb_is=q&as_minm_is=0&as_miny_is=&as_maxm_is=0&as_maxy_is=&num=30&as_brr=0 excerpt and text search]

== References ==

* [http://www.archives.gov/exhibits/charters/charters.html The Constitution from the National Archives]
* [http://www.foundingfathers.info/documents/constitution.html The Constitution of the United States of America]

== See also ==

*[[Gallery of American Heroes]]

== External Links ==

* [http://www.archives.gov/ The National Archives]
* [http://www.archives.gov/historical-docs/ The National Archives - Historical Documents]
* [http://patriotpost.us/histdocs/ The Patriot Post - Historical Documents]

=== Founding Fathers Quotes ===

* [http://www.marksquotes.com/Founding-Fathers/ Mark's Quotes: Founding Fathers Quotes]
* [http://www.dojgov.net/Liberty_Watch.htm USDOJ & Government Watch: Spirit of America Liberty Quotes]
* [http://www.eadshome.com/QuotesoftheFounders.htm Eads Home Ministries: Founding Fathers Quotes]

[[Category:Founding Fathers]]
[[Category:American Revolution]]
[[Category:Republicanism]]
[[Category:Conservatives]]
[[Category:Early National U.S.]]

Correlation

2010-04-13T00:45:23Z

Dasonk: /* Formal definition */ Added paragraph on independence with Normal random variables

'''Correlation''' describes the relationship of two factors to one another (see [[cause and effect]]). When two factors are found to go together, there are only three explanations. First, the two things may be entirely unrelated. Second, they may both be caused by a another factor. Third, one of the factors might be causing the other. It is the task of [[statistics]] to point out the existence of a correlation, but it is the task of science to discover what relationship, if any, exists.

==Unrelated factors==

Often [[cancer clusters]] have been said to indicate the existence of a biological hazard, but by the laws of chance in any group of people who get a rare disease (or win the lottery) there will always be some who live close together. This does not mean that something in their environment caused their tragedy or good fortune.

If you flip coins or throw dice, from time to time you will get runs of similar results like 4 heads in a row. You might try to find the cause for these runs in what you were thinking about at the time, hoping to find that you could influence the toss or roll. But this is nonsense.

When unrelated events occur, it is dismissed as a matter of coincidence.

==Factors which have a common cause==

Two commuters might happen to see each other on a train, not because either intended to meet the other, but simply because each happens to dislike crowded trains and prefer trains with dining cars. When the regular train is crowded or lacks a dining car, both may independently decide to take a later train. Seeing each other in the dining car of one would not be merely a coincidence, but would stem from the conditions on the earlier train.

Cases of shark attacks correlate with sales of ice cream, but no one thinks that the bites make people buy ice cream, or that eating ice cream makes you vulnerable to sharks. Both things go up and down in an annual cycle, because people go to the beach more in the summer. They swim and buy ice cream because it's hot. Swimming exposes them to (rare) shark attacks.

==One thing causes another==

In scientific subjects like chemistry, physics and astronomy many laws of cause and effect have been discovered. Put two chemicals together, and they form a compound. Push something, and its momentum increases. The [[scientific method]] is useful in describing the relationship between events, especially when despite their best efforts, no one has been able to find an exception (see [[independent review]]).

==Terminology==

In common usage, it denotes an association of one variable with another in quite general terms; for example, one might say, "success is correlated with hard work". In mathematics, however, and in science and engineering, which make use of mathematical concepts, correlation is a technical term with a precise definition.

Correlation must be distinguished from causation (see article on [[correlation is not causation]]). When one factor changes and another factor changes with it, there is usually a direct relationship between the two factors, observed as a correlation. Alternatively, both changed could be the result of changes in a third factor. For example, the prices of two unrelated goods might increase during a period of [[inflation]]; the two price rises are correlated with each other but neither has caused the other.

Once a correlation is established, scientists may conduct research to determine causation. Are respiration deaths causing air pollution, or is it the other way around? It is easy to determine that sickness among the elderly does not cause air pollution. Rather, it is chemicals like sulfur dioxide (typically from coal burning [[power plant]]s) which are the culprits. Cities and states measure the amount of pollutants in the air and epidemiologists can use these data, comparing them to the number of people who develop respiratory diseases.

Regulations which restrict air pollution are made on the basis of these correlations, and on the cause and effect relationships which the correlations help scientists to discover. However, activists have sometimes created false correlations by selective use of data. [http://www.robinsoncurriculum.com/view/rc/s31p59.htm]

== Formal definition ==
''This section is at the level of advanced high school maths (e.g. A-level or Baccalaureat) and can be skipped by general readers.''

The '''correlation coefficient''', also known as '''Pearson's r''', is a statistical measure of association between two continuous variables. It is defined as:

'''r'''= ΣZxZy/n

Where: '''Zx'''= the Z-score of the independent variable X, '''Zy'''= the Z-score of the dependent variable Y, and '''n'''= the number of observations of variables X and Y.

Thus, Pearson's r is the arithmetic mean of the products of the variable Z-scores. The Z-scores used in the correlation coefficient must be calculated using the population formula for the standard deviation and thus:

'''Zx'''= (X-Mx)/SDx

Where: '''Mx'''= the arithmetic mean of the variable x and '''SDx'''= the standard deviation of the variable x.

'''SDx'''= Σ(X-Mx)2/n

Where: '''n'''= the number of observations of variables x and y

'''Zy'''= (Y-My)/SDy

Where: '''My'''= the arithmetic mean of the variable Y and '''SDy'''= the standard deviation of the variable Y.

'''SDy'''= Σ(Y-My)2/n

Where: '''n'''= the number of observations of variables X and Y

Pearson's r varies between -1 and +1. A value of zero indicates that no association is present between the variables, a value of +1 indicates that the strongest possible positive association exists and a value of -1 indicates that there is the strongest possible negative association. In a positive relationship, as variable X increases in value, variable Y will also increase in value (e.g. as number of hours worked (X) increases, weekly pay (Y) also increases). In contrast, in a negative relationship, as variable X increases in value, variable Y will decrease in value (e.g. as number of alcoholic beverages consumed (X) increases, score on a test of hand-eye coordination (Y) decreases).

It is important to note that while a correlation coefficient may be calculated for any set of numbers there are no guarantees that this coefficient is statistically significant. That is to say, without statistical significance we cannot be certain that the computed correlation is an accurate reflection of reality. Significance may be assessed using a variant on the standard [[Student's t-test]] defined as:

'''t'''= (r)√(n-2)/√(1-r2)

The results of this test should be evaluated against the standard t-distribution with degrees of freedom equal to n-2. As usual in significance tests, a result described as significant (i.e. a low value of ''P'' in the ''t'' test) means that the chance of getting a correlation coefficient at least as large (whichever the direction) as that observed, if there is in fact no correlation, is small. A statistically significant result can therefore arise if the actual correlation is strong, even if the dataset is small, or if the actual correlation is weak but many data are observed.

One should note that for most random variables a correlation of 0 does not imply that they are independent. However, if the two variables come from the [[Normal Distribution]] then it can be claimed that a correlation of 0 implies independence.

It is important to note that the correlation coefficient should not be calculated when either of the variables is not continuous. That is, when they do not vary continuously and have a meaningful zero. As such, correlating a dichotomous variable (e.g. sex) with a ratio variable (e.g. IQ) is inappropriate and will return uninterpretable results.

Additionally, correlation estimates a linear relationship between X and Y. Thus, an increase in variable X is assumed to exert the same influence on Y across all values of X and Y.

==Correlation and Causation==

''Main article: [[Correlation is not causation]]''

Correlation is a linear statistic and makes no mathematical distinction between [[independent variable|independent]] and [[dependent variable]]s. As a consequence, it is impossible to assert [[causation]] based on a correlation even if that correlation is statistically significant. Therefore, when a significant correlation has been identified it is possible that X -> Y (i.e. X causes Y), Y -> X (i.e. Y causes X), or that X <- Z -> Y (i.e. Both X and Y are caused by an additional variable, Z). Caution must be exercised in asserting causation using correlation and claims to this effect must be viewed with considerable skepticism.

==References==

Aron, Arthur, Elaine N. Aron and Elliot J. Coups. 2008. ''Statistics for the Behavioral and Social Sciences: A Brief Course.'' 4/e. Upper Saddle River, New Jersey: Prentice Hall.

[[Category:statistics]]

Talk:Correlation

2010-04-13T00:42:43Z

Dasonk: suggestion.

Okay, Tory, you take it from here. :-) --[[User:Ed Poor|Ed Poor]] [[User talk:Ed Poor|Talk]] 16:22, 13 October 2007 (EDT)

== Maths restored ==

I've restored the mathematical section, which is useful for those who want to know the maths. I've also done some general tidying and clarification. Note that the definition that a correlation is only valid if the two variables are ratio variables is too strict; they only need to be continuous variables. [[User:HSpalding|HSpalding]] 16:57, 5 January 2009 (EST)

The unrelated factors section seems to be of very poor quality altogether and I say we just do a full rewrite of the section. Anybody opposed to this suggestion? [[User:Dasonk|Dasonk]] 7:43 12 April 2010 (CST)

Talk:Correlation

2010-04-13T00:42:14Z

Dasonk: suggestion.

Statistics

2010-04-07T12:55:30Z

Dasonk:

{{statistics}}

''This article is about mathematical statistics. For statistics regarding [[Conservapedia]], see [[Special:Statistics]].''

'''Statistics''' can be described as "the practice or science of collecting and analysing numerical data in large quantities, especially for the purpose of inferring proportions in a whole from those in a representative sample."<ref>Soanes, C. and Stevenson, A. (eds.) (2005) 'Oxford Dictionary of English (2nd edition revised)' Oxford University Press, Oxford, U.K.</ref> It involves all stages of data collection and processing from the initial collection, to the analysis and ultimately to the conclusions and interpretations of the data. It is used in all research oriented disciplines from physics, chemistry and biology to economics, anthropology and psychology as well as many thousands of other fields. It is also used in businesses and governments.

Statistics analyzes data in two primary ways, the first is called [[descriptive statistics]] which describes and summarizes the data. Often this will include things like: [[mean | the mean]], [[standard error]], or [[standard deviation]] each of these is an example of a [[statistic]]. Also statistics can attempt to infer relationships between the data collected and various hypothesis or populations, this is called [[inferential statistics]]. Both descriptive and inferential statistics comprise applied statistics. There is also a discipline called mathematical statistics, which is concerned with the theoretical basis of the subject.

Statistics takes its name from the fact that it was traditionally taught to monarchs to enable them to manage affairs of state.

==Frequentist Approaches==

[[Frequency probability | Frequentist]] approaches are often referred to as classical approaches because it is the oldest and most used method of statistical analysis. The heart of this approach is to try and understand data as a relative frequency or ratio of a particular occurrence out of a total possible number of occurrences. For example, a frequentist would describe the number of times a coin turns up heads as a ratio of total number of heads out of total number of flips.

===Descriptive statistics===

Frequentist approaches to descriptive statistics mostly involve averaging. For example, the mean of a sample is calculated as the total value of all observations divided by total number of trials, and the standard error is calculated by taking the total error size for all samples and dividing by total number of trials.

These methods stem from the view of data as ratios probabilities.

===Inferential statistics===

Frequentist approaches to inferential statistics primarily involve trying to compare descriptive statistics of two data sets to determine if they are [[statistically significant | significantly]] different. One of the most common approaches is to test a given data set against a [[null hypothesis]] or the data set that would be created if the values were the result of random chance alone. For example, if a given head came up 9 times as heads and 1 time as tails you would compare the number of heads, 9, to the number of heads that would be expected if chance alone was operating, or 5.

Testing against the null hypothesis is sometimes referred to as an [[omnibus]] test since it is testing the idea that a given data set is the result of anything other than chance. Often it is much more desirable to test specific data sets against each other.

===Common frequentist methods===

[[Linear model]]

[[Analysis of variance]]

[[Chi-Square test]]

[[Students t-test]]

[[Z test]]

[[Linear regression]]

[[Multiple Regression]]

[[Pearson product-moment correlation coefficient]]

==Bayesian Approaches==

[[Bayesian inference | Bayesian statistics]] is a method of applying [[Bayes theorem]] to data analysis. One of the biggest difference between Bayesian approaches and frequentist approaches is that Bayesians attempt to determine the probability that a given hypothesis is true given the data, while frequentist attempt to define the probability of getting the data given that a particular hypothesis is true.

Bayesian approaches are becoming more and more popular in science because what most people are interested in is the probability of the proposed hypothesis, not the probability of the data. It also does not need to make prior assumptions about the data such as [[Normal distribution | normality]] and [[homogeneity of variance]]. However, Bayesian methods have come under fire from many frequentist proponents. This has led to very heated debate in statistical circles, though this has largely died now, about the respective validity of both methods. The primary complaint leveled at Bayesian statistics is that it must use a [[prior probability]] of a hypothesis in its analysis. This prior is intended to build contextual information into the analysis, but it may be seen by its critics as subjective or arbitrary. Commonly used prior distributions include the [[uniform distribution]] and [[beta distribution]].

===Descriptive statistics===

Bayesian methods all use Bayes' equation, this applies for both descriptive and inferential statistics. To find such things as the mean and standard deviation first a prior probability for all means and standard deviations must be assigned. In practice this usually means assigning uniform probabilities to values equally spaced between what we think is the minimum and maximum values for the statistic we are interested in (the number of values depends on the grid density, which is proportional to accuracy and inversely proportional to computation time). Then a likelihood of each value is then calculated based on the data and then Bayes equation is used to assign a [[posterior probability]] for each value. These posterior probabilities can be plotted as a [[probability density function]] (PDF) to see the various probabilites for the value given the data, or often simply the value with the highest posterior probability is simply chosen.

===Inferential statistics===

Inferential statistics in Bayesian methods looks much the same as descriptive statistics since both use the Bayes equation and the same basic approach. To compare to means you would calculate the PDF for each data set then subtract them from each other to figure out the probability that they differ.

In order to compare hypothesis [[Bayesian model selection]] is often used. This is when each hypothesis you want to test is assigned a prior probability, and then the likelihood of the data given each hypothesis being test is calculated. You can then us Bayes equation to determine the relative probabilities that each hypothesis is correct. This method is almost always testing relative probabilites since to calculate an absolute probability would require knowing every possible hypothesis. Usually this is not possible, but sometimes the subset is finite enough it can be tested.

Because of the large number of calculations needed for model selection Bayesian approaches have only became practical and popular with the advent of computers. But even with the most modern computers available many Bayesian models remain computational intractable. Recent developments in applying [[Markov chain]] [[Monte Carlo method | Monte Carlo methods]] to these problems have led to promising results.

==Non-parametric and Bootstrapping methods==

One of the greatest problems in frequentist approaches to statistics is that it often relies on making prior assumptions about how the data looks and was collected. Most commonly the data must be a normal distribution and have homogeneity of variance. Different statistical methods are more or less robust to violations of these assumptions, and some techniques have attempted to avoid them all together. The end result though is usually a significant loss of power and increased likelihood of error.

[[Non-parametric statistics]] are any one of many methods that attempt to define descriptive characteristics or make inferential claims with out the need of tightly confined parameters. The main goals is to try and eliminate the need for assumptions without sacrificing power and accuracy.

[[Bootstrapping statistics]] is a particularly popular non-parametric approach. Bootstrapping is computationally costly and has only recently become feasible for most data sets. It involves [[sampling with replacement]] from the given data set perhaps as many as 100,000 times in order to determine mean, error, best fits and comparisons of data sets.

==Misuse of statistics ==

Statistical data can often be manipulated to make it seem like it proves a certain hypothesis, whereas in actuality it does not. Because of the advanced mathematics involved in computing some statistics, people can sometimes be deceived by this. This type of deceit has been used by politicians and their supporters to give a false impression of voter preferences, for example. It can also be used by scientists with their own agendas (e.g. atheistic) to try to "prove" various otherwise unsupported theories (e.g. [[evolution]]).

==References==
<references/>

[[Category:Probability and Statistics]]

Pac-Man

2010-04-06T23:36:09Z

Dasonk: minor rewording

'''Pac-Man''', formerly known as '''Puckman''', is a classic maze [[video game]] series ([[ESRB]] ratings: E). It was first released in 1979 in [[Japan]] and later released in [[United States|America]] in 1980 by [[Namco]]. The game is completely non-violent so it can be considered clean and [[family friendly]] fun for all ages.

==Inspiration==
The game's creator, Toru Iwatani, says he came up with the idea for Pac-Man's design while eating [[pizza]]. When he saw a pizza with one missing slice, Pac-Man was born.

Also according to him, this game was originally designed to appeal to female gamers. One of those factors were the four ghosts that chased Pac-Man. However, the game was a hit with gamers of both sexes.

==Gameplay==
Players play as the title character, a yellow, pie-shaped character whose objective to eat all the dots in the maze. Pac-Man is chased by four ghosts named Blinky, Pinky, Inky, and Clyde, who chase him with an intention of making the player lose a life. Pac-Man can eat the ghosts after eating one of four energizers (Power Pellets), located near the corners surrounding the maze, which turn the ghosts blue for a short time.

Pac-Dots are worth 10 points, Power Pellets are worth 50 points. When Pac-Man eats the ghosts, he first ghost is 200 points, the second ghost is 400 points, the third 800 points, and the fourth 1600 points. Also, after Pac-Man eats a specific number of dots, a bonus fruit appears in the center of the maze. They give bonus points.

==Legacy==
Since this game was very successful, many sequels and spinoffs have followed. These include (but are not limited to) Ms. Pac-Man, Pac-Man Plus, Jr. Pac-Man, and platformers like Pac-Man World.

[[Category: Video Games]]
[[Category: Japan]]

Jesse Owens

2010-04-06T23:30:41Z

Dasonk: removed visible tags

[[Image:Jesse Owens.jpg|right]]
'''James Cleveland Owens''' (b. September 12, 1913, Oakville, [[Alabama]] - March 31, 1980) American athlete; he won four gold medals at the 1936 [[Olympics|Olympic Games]] in Nazi [[Berlin]].

The media and spectators paid special attention was paid [[Jesse Owens]] (1913-1980), the black American track and field star. Owens, who craved the chance to compete, resisted the [[NAACP]]'s pleas that he support the boycott. He won four gold medals and was enthusiastically cheered in the face of Nazi propaganda about "Negro inferiority." The film "Olympia" (1938), made by Nazi producer-director [[Leni Riefenstahl]] set the modern standard for high quality documentaries, and prominently featured Owens. He was miffed that not only Hitler did not congratulate him, but neither did President Roosevelt.

In 1976, Jesse was awarded the highest honor an American civilian can receive. President [[Gerald R. Ford]] awarded him with the Medal of Freedom. [http://www.jesseowens.com/biography/]

''"Perhaps no athlete better symbolized the human struggle against [[tyranny]], [[poverty]] and [[racial bigotry]]. His personal triumphs as a world-class [[athlete]] and record holder were the prelude to a career devoted to helping others. His work with young athletes, as an unofficial ambassador overseas, and a spokesman for [[freedom]] are a rich legacy to his fellow Americans".'' President [[James Carter]]. [http://www.jesse-owens.org/about5.html]

== External links ==

*[http://www.jesse-owens.org/about1.html Who is Jesse Owens]
==Further reading==
* Jeremy Schaap, ''Triumph: The Untold Story of Jesse Owens and Hitler's Olympics,'' (2007) 272 pp.

====references====
<references/>

[[Category:Sports]]
[[Category:New Deal]]

Median

2010-03-21T02:47:03Z

Dasonk: Added links to references

A '''median''' is the middle [[number]] in an ordered numerical [[sequence]]. If there are two middle numbers (i.e. there is an even number of terms in the sequence), then the median is found by taking the [[mean]] of the two middle numbers.

So in an example of the following numerical values:

:2, 4, 5, 11, 13

The median is 5, as there are 2 values less than 5 and 2 values greater than 5.

The median is sometimes preferred as a measure of centrality over the mean due to the fact that is isn't as affected by [[outliers]] as the mean is.

==See Also==

*[[Mean]]
*[[Mode]]

[[category:Probability and Statistics]]
[[category:Statistics]]

User:Dasonk

2010-03-20T23:53:23Z

Dasonk: Added Useful links

Set

2010-03-20T05:02:33Z

Dasonk: Minor rewording and clarification

A '''set''' is a collection of objects. Sets are the subject of [[set theory]]. Two sets are the same if they contain the same elements, regardless of the order they are in. Sets are written in set notation, such as {1,2} indicating the set containing the elements 1 and 2. This is the same as the set {2, 1} because order does not matter when comparing sets.

Also, repetition of elements is irrelevant, so the set {1, 2, 2} is the same as the set {1, 2}.

An important concept in set theory is [[cardinality]]. In the case of finite sets, this is simply the number of elements of the set. So {1, 2} has a cardinality of 2. However, the theory is more complicated in the case of infinite sets.

It was thought that an informal concept of sets ([[Naive set theory]]) was sufficient, however [[Russell's Paradox]] shows that this can lead to a contradiction if sets are allowed to contain themselves. Modern set theory is more formal, and disallows such paradoxical sets.

Compare:
*[[multiset]]

==See also==
*[[union (set theory)]]
*[[intersection]]

[[Category:Mathematics]]

Mode

2010-03-20T04:58:15Z

Dasonk:

The '''Mode''' is a summary of data that reports the value that occurs most frequently in a dataset.

For the following data:

:1, 3, 3, 3, 3, 5, 7, 9, 19

The mode is "3" because "3" occurs 4 times and no other value occurs 4 or more times.

The mode can be used to describe [[categorical data]] as well.

For the following categorical data:

:Blue, Blue, Blue, Green, Green, Yellow, Orange

The mode would be "Blue"

==See Also==

*[[Median]]
*[[Mean]]

[[Category:Probability and Statistics]]

Mode

2010-03-20T04:57:50Z

Dasonk: Clarification and expansion.

The '''Mode''' is a summary of data that reports the value that occurs most frequently in a dataset.

For the following data:

:1, 3, 3, 3, 3, 5, 7, 9, 19

The mode is 3 because "3" occurs 4 times and no other value occurs 4 or more times.

The mode can be used to describe [[categorical data]] as well.

For the following categorical data:

:Blue, Blue, Blue, Green, Green, Yellow, Orange

The mode would be "Blue"

==See Also==

*[[Median]]
*[[Mean]]

[[Category:Probability and Statistics]]

Median

2010-03-20T04:52:59Z

Dasonk: Aesthetic change. Rewording of final sentence. Added Category.

A '''median''' is the middle number in an ordered numerical sequence. If there are two middle numbers (i.e. there is an even number of terms in the sequence), then the median is found by taking the [[mean]] of the two middle numbers.

So in an example of the following numerical values:

:2, 4, 5, 11, 13

The median is 5, as there are 2 values less than 5 and 2 values greater than 5.

The median is sometimes preferred as a measure of centrality over the mean due to the fact that is isn't as affected by outliers as the mean is.

==See Also==

*[[Mean]]
*[[Mode]]

[[category:Probability and Statistics]]
[[category:Statistics]]

Completing the square

2010-03-19T13:52:04Z

Dasonk: added category:algebra

'''Completing the square''' is a method for solving for the roots of the general [[quadratic equation]]:

<math>ax^2 + bx + c = 0</math>, where <math>a \ne 0</math>

It is first taught using equations with "friendly" numbers in place of ''a'', ''b'', and ''c'' to get the student used to the process.

:What one does is add and multiply by various carefully chosen constants to create an equation of the form:

:<math>d^2x^2 + 2dex + e^2 = f</math> where ''d'', ''e'' and ''f'' are constants expressed in ''a'', ''b'', and ''c''.

:This resolves to:

::<math>(dx+e)^2 = f</math> (grouping)
::<math>dx + e = \pm \sqrt{f}</math> (take square root)
::<math>dx = -e \pm \sqrt{f}</math> (subtract e)
::<math>x = \frac{-e \pm \sqrt{f}}{d}</math> (divide by e)

By then applying the process to the general equation, we can derive the [[quadratic formula]]:

:<math>ax^2 + bx + c = 0</math> (given)

:<math>4a^2x^2 + 4abx + 4ac = 0</math> (multiply by 4a)

:<math>4a^2x^2 + 4abx = -4ac</math> (subtract 4ac)

:<math>4a^2x^2 + 4abx + b^2 = -4ac + b^2</math> (add b^2)

:<math>(2ax + b)^2 = b^2 - 4ac</math> (group each side)

:<math>2ax + b = \pm \sqrt{b^2 - 4ac}</math> (take sqaure root, allow for both roots)

:<math>2ax = -b \pm \sqrt{b^2 - 4ac}</math> (subtract b)

:<math>x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}</math> (divide by 2a)

We can now determine the real or imaginary roots of any quadratic equation by simply inserting ''a'', ''b'', and ''c'' into the formula.
[[category:mathematics]]
[[category:algebra]]

Complete the square

2010-03-19T13:49:09Z

Dasonk: Creating a redirect

#Redirect[[Completing the square]]

Quadratic equation

2010-03-19T13:44:09Z

Dasonk: Corrected an incorrect statement.

A '''quadratic equation''' can take two forms. The general formula, written as a function of <math>x</math>, <math>y=f(x)</math>, is:

:<math>y = ax^2 + bx + c</math>

The graph of a quadratic equation is a [[parabola]], one of the [[conic section]]s. (In some cases, the parabola collapses, most obviously when <math>a = 0</math>)

The points where this curve crosses the x axis are represented by the second form of the equation:

:<math>ax^2 + bx + c = 0</math>

These are solved for using the [[quadratic formula]], which will not only solve for [[real number|real]] roots, but result in the [[imaginary number|imaginary]] roots if the parabola does not actually cross the y axis (this is when <math>4ac</math> is greater than <math>b^2</math>).

Quadratic equations are very important in calculating the motion of bodies under constant [[acceleration]], i.e., [[gravity]] (when close to the earth's surface).

The [[derivative]] of a quadratic equation is a simple [[linear function]]:

:<math>\frac{dy}{dx} = 2ax + b</math>

[[category:mathematics]]

Algebra

2010-03-19T13:30:55Z

Dasonk: /* Basic Algebra */ Clarification on the solutions to the equation.

'''Algebra''' is a major branch of [[mathematics]] that analyzes the relationships between quantities or items. In higher math the principal fields of algebra are [[linear algebra]], which focuses on matrices, and [[group theory]].<ref>The name algebra comes from the [[Arabic]] word ''al jebr'', which means reduction or "reunion of broken parts" [http://dictionary.reference.com/browse/algebra Algebra] as mentioned in a book ''Hisab al-jabr w'al-muqabala'' translated as ''Science of the Reunion and the Opposition''. This text was written in in about 830 AD by [[Muhammad ibn Mūsā al-Khwārizmī| Mohammad ibn-Musa al-Khwarizmi]] of [[Baghdad]]. See the [http://www.sjsu.edu/depts/Museum/alkhwa.html Biography of Al-Khwarizmi]</ref>

== Basic Algebra ==

Algebra is a generalization of [[arithmetic]] in which letters stand for numbers in order to accomplish this purpose. Ordinary arithmetic deals with ''specific'' numbers, treated individually: 4 + 7 = 11.

Algebra generalizes these operations by using variables or letters instead of specific numbers. These letters are called [[unknown]]s. For example,

:x + y = 11

By using unknowns, algebra can go beyond individual number facts and express general relationships between ''sets'' of numbers. Thus, the equation above represents ''every pair'' of numbers that add up to 11:
*x could be 4 and y could be 7,
*x could be 5 and y could be 6,
*x could be 10 and y could be 1.

There are 12 such pairs where both x and y are non-negative integers. If solutions are not restricted to non-negative integers then an infinite number of solutions to this equation exist.

==Notes and references==
<references/>

[[Category:Algebra]]
[[Category:Mathematics]]

Statistics

2010-03-18T15:20:16Z

Dasonk: /* Frequentist Approaches */

{{statistics}}

''This article is about mathematical statistics. For statistics regarding [[Conservapedia]], see [[Special:Statistics]].''

'''Statistics''' "the practice or science of collecting and analysing numerical data in large quantities, especially for the purpose of inferring proportions in a whole from those in a representative sample."<ref>Soanes, C. and Stevenson, A. (eds.) (2005) 'Oxford Dictionary of English (2nd edition revised)' Oxford University Press, Oxford, U.K.</ref> It involves all stages of data collection and processing from the initial collection, to the analysis and ultimately to the conclusions and interpretations of the data. It is used in all research oriented disciplines from physics, chemistry and biology to economics, anthropology and psychology as well as many thousands of other fields. It is also used in businesses and governments.

Statistics analyzes data in two primary ways, the first is called [[descriptive statistics]] which describes and summarizes the data. Often this will include things like: [[mean | the mean]], [[standard error]], or [[standard deviation]] each of these is an example of a [[statistic]]. Also statistics can attempt to infer relationships between the data collected and various hypothesis or populations, this is called [[inferential statistics]]. Both descriptive and inferential statistics comprise applied statistics. There is also a discipline called mathematical statistics, which is concerned with the theoretical basis of the subject.

Statistics takes its name from the fact that it was traditionally taught to monarchs to enable them to manage affairs of state.

==Frequentist Approaches==

[[Frequency probability | Frequentist]] approaches are often referred to as classical approaches because it is the oldest and most used method of statistical analysis. The heart of this approach is to try and understand data as a relative frequency or ratio of a particular occurrence out of a total possible number of occurrences. For example, a frequentist would describe the number of times a coin turns up heads as a ratio of total number of heads out of total number of flips.

===Descriptive statistics===

Frequentist approaches to descriptive statistics mostly involve averaging. For example, the mean of a sample is calculated as the total value of all observations divided by total number of trials, and the standard error is calculated by taking the total error size for all samples and dividing by total number of trials.

These methods stem from the view of data as ratios probabilities.

===Inferential statistics===

Frequentist approaches to inferential statistics primarily involve trying to compare descriptive statistics of two data sets to determine if they are [[statistically significant | significantly]] different. One of the most common approaches is to test a given data set against a [[null hypothesis]] or the data set that would be created if the values were the result of random chance alone. For example, if a given head came up 9 times as heads and 1 time as tails you would compare the number of heads, 9, to the number of heads that would be expected if chance alone was operating, or 5.

Testing against the null hypothesis is sometimes referred to as an [[omnibus]] test since it is testing the idea that a given data set is the result of anything other than chance. Often it is much more desirable to test specific data sets against each other.

===Common frequentist methods===

[[Linear model]]

[[Analysis of variance]]

[[Chi-Square test]]

[[Students t-test]]

[[Z test]]

[[Linear regression]]

[[Multiple Regression]]

[[Pearson product-moment correlation coefficient]]

==Bayesian Approaches==

[[Bayesian inference | Bayesian statistics]] is a method of applying [[Bayes theorem]] to data analysis. One of the biggest difference between Bayesian approaches and frequentist approaches is that Bayesians attempt to determine the probability that a given hypothesis is true given the data, while frequentist attempt to define the probability of getting the data given that a particular hypothesis is true.

Bayesian approaches are becoming more and more popular in science because what most people are interested in is the probability of the proposed hypothesis, not the probability of the data. It also does not need to make prior assumptions about the data such as [[Normal distribution | normality]] and [[homogeneity of variance]]. However, Bayesian methods have come under fire from many frequentist proponents. This has led to very heated debate in statistical circles, though this has largely died now, about the respective validity of both methods. The primary complaint leveled at Bayesian statistics is that it must use a [[prior probability]] of a hypothesis in its analysis. This prior is intended to build contextual information into the analysis, but it may be seen by its critics as subjective or arbitrary. Commonly used prior distributions include the [[uniform distribution]] and [[beta distribution]].

===Descriptive statistics===

Bayesian methods all use Bayes' equation, this applies for both descriptive and inferential statistics. To find such things as the mean and standard deviation first a prior probability for all means and standard deviations must be assigned. In practice this usually means assigning uniform probabilities to values equally spaced between what we think is the minimum and maximum values for the statistic we are interested in (the number of values depends on the grid density, which is proportional to accuracy and inversely proportional to computation time). Then a likelihood of each value is then calculated based on the data and then Bayes equation is used to assign a [[posterior probability]] for each value. These posterior probabilities can be plotted as a [[probability density function]] (PDF) to see the various probabilites for the value given the data, or often simply the value with the highest posterior probability is simply chosen.

===Inferential statistics===

Inferential statistics in Bayesian methods looks much the same as descriptive statistics since both use the Bayes equation and the same basic approach. To compare to means you would calculate the PDF for each data set then subtract them from each other to figure out the probability that they differ.

In order to compare hypothesis [[Bayesian model selection]] is often used. This is when each hypothesis you want to test is assigned a prior probability, and then the likelihood of the data given each hypothesis being test is calculated. You can then us Bayes equation to determine the relative probabilities that each hypothesis is correct. This method is almost always testing relative probabilites since to calculate an absolute probability would require knowing every possible hypothesis. Usually this is not possible, but sometimes the subset is finite enough it can be tested.

Because of the large number of calculations needed for model selection Bayesian approaches have only became practical and popular with the advent of computers. But even with the most modern computers available many Bayesian models remain computational intractable. Recent developments in applying [[Markov chain]] [[Monte Carlo method | Monte Carlo methods]] to these problems have led to promising results.

==Non-parametric and Bootstrapping methods==

One of the greatest problems in frequentist approaches to statistics is that it often relies on making prior assumptions about how the data looks and was collected. Most commonly the data must be a normal distribution and have homogeneity of variance. Different statistical methods are more or less robust to violations of these assumptions, and some techniques have attempted to avoid them all together. The end result though is usually a significant loss of power and increased likelihood of error.

[[Non-parametric statistics]] are any one of many methods that attempt to define descriptive characteristics or make inferential claims with out the need of tightly confined parameters. The main goals is to try and eliminate the need for assumptions without sacrificing power and accuracy.

[[Bootstrapping statistics]] is a particularly popular non-parametric approach. Bootstrapping is computationally costly and has only recently become feasible for most data sets. It involves [[sampling with replacement]] from the given data set perhaps as many as 100,000 times in order to determine mean, error, best fits and comparisons of data sets.

==Misuse of statistics ==

Statistical data can often be manipulated to make it seem like it proves a certain hypothesis, whereas in actuality it does not. Because of the advanced mathematics involved in computing some statistics, people can sometimes be deceived by this. This type of deceit has been used by politicians and their supporters to give a false impression of voter preferences, for example. It can also be used by scientists with their own agendas (e.g. atheistic) to try to "prove" various otherwise unsupported theories (e.g. [[evolution]]).

==References==
<references/>

[[Category:Probability and Statistics]]