The Runs Test for Random Sequences

The Runs Test for Random Sequences Given a sequence of data, one question that we may wonder is if the sequence occurred by chance phenomena, or if the data is not random. Randomness is hard to identify, as it is very difficult to simply look at data and determine whether or not it was produced by chance alone. One method that can be used to help determine if a sequence truly occurred by chance is called the runs test. The runs test is a test of significance or hypothesis test. The procedure for this test is based upon a run, or a sequence, of data that have a particular trait. To understand how the runs test works, we must first examine the concept of a run. Sequences of Data We will begin by looking at an example of runs. Consider the following sequence of random digits: 6 2 7 0 0 1 7 3 0 5 0 8 4 6 8 7 0 6 5 5 One way to classify these digits is to split them into two categories, either even (including the digits 0, 2, 4, 6 and 8) or odd (including the digits 1, 3, 5, 7 and 9). We will look at the sequence of random digits and denote the even numbers as E and odd numbers as O: E E O E E O O E O E E E E E O E E O O The runs are easier to see if we rewrite this so that all of the Os are together and all of the Es are together: EE O EE OO E O EEEEE O EE OO We count the number of blocks of even or odd numbers and see that there are a total of ten runs for the data. Four runs have length one, five have length two and one has length five Conditions With any test of significance, it is important to know what conditions are necessary to conduct the test. For the runs test, we will be able to classify each data value from the sample into one of two categories. We will count the total number of runs relative to the number of the number of data values that fall into each category. The test will be a two-sided test. The reason for this is that too few runs mean that there is likely not enough variation and the number of runs that would occur from a random process. Too many runs will result when a process alternates between the categories too frequently to be described by chance. Hypotheses and P-Values Every test of significance has a null and an alternative hypothesis. For the runs test, the null hypothesis is that the sequence is a random sequence. The alternative hypothesis is that the sequence of sample data is not random. Statistical software can calculate the p-value that corresponds to a particular test statistic. There are also tables that give critical numbers at a certain level of significance for the total number of runs. Runs Test Example We will work through the following example to see how the runs test works. Suppose that for an assignment a student is asked to flip a coin 16 times and note the order of heads and tails that showed up. If we end up with this data set: H T H H H T T H T T H T H T H H We may ask if the student actually did his homework, or did he cheat and write down a series of H and T that look random? The runs test can help us. The assumptions are met for the runs test as the data can be classified into two groups, as either a head or a tail. We keep going by counting the number of runs. Regrouping, we see the following: H T HHH TT H TT H T H T HH There are ten runs for our data with seven tails are nine heads. The null hypothesis is that the data is random. The alternative is that it is not random. For a level of significance of alpha equal to 0.05, we see by consulting the proper table that we reject the null hypothesis when the number of runs is either less than 4 or greater than 16. Since there are ten runs in our data, we fail to reject the null hypothesis H0. Normal Approximation The runs test is a useful tool to determine if a sequence is likely to be random or not. For a large data set, it is sometimes possible to use a normal approximation. This normal approximation requires us to use the number of elements in each category and then calculating the mean and standard deviation of the appropriate normal distribution.

Transitive Verbs

Transitive Verbs Transitive Verbs Transitive Verbs By Maeve Maddox The grammatical term â€Å"transitive verb† occurs in numerous posts on this site, usually with a reminder of what it means, but perhaps a dedicated post will be useful to readers who remain shaky on the concept. Note: To keep this post focused on the concept of transitive verbs and their direct objects, I am not going to mention terms that apply to other kinds of objects or verbs. The prefix trans occurs in many English words. It’s from Latin transire, a combination of the Latin preposition trans, â€Å"across† and the infinitive ire, â€Å"to go.† English words beginning with trans usually have something to do with moving something â€Å"across† to something or someone else. For example: transatlantic: passing or extending across the Atlantic Ocean. transcribe: to make a copy of something in writing; to copy out from an original, i.e., move the original writing â€Å"across† to another place. transfuse: to pour a liquid from one vessel or receptacle into another. In the case of blood, cause to flow from the donor or bag â€Å"across† to the recipient. The trans in â€Å"transitive verb† indicates that the action of an action verb carries across to a receiver of the action. The receiver that receives the action of a transitive verb is called its â€Å"direct object.† The dog bit the intruder. (Bit is an action verb. Intruder receives the action.) The batter hit the ball out of the park. (Hit is an action verb. Ball receives the action.) A flock of sheep halted traffic from here to the highway. (Halted is an action verb. Traffic receives the action.) Here’s how to decide if an action verb is transitive: First, identify the main action verb in the sentence. For example, in the first sentence, the main verb is bit. Then, ask the question, â€Å"Bit what?† The answer to â€Å"what?† will be the direct object: intruder. Not all action verbs are transitive. For example, the action verb kick may or may not have a receiver. For example, compare these sentences: 1. The girl kicked the football over the goal. 2. The baby kicked furiously in the bath. In the first sentence, when you ask â€Å"kicked what?† you find the answer â€Å"football.† In this sentence, kicked is a transitive verb because the action of kicking is received by the football. Football is the direct object of kicked. In the second sentence, when you ask â€Å"kicked what?† you do not find an answer to the question. The action does not travel across to any receiver. There is no direct object. In the second sentence, kicked is not transitive. Want to improve your English in five minutes a day? Get a subscription and start receiving our writing tips and exercises daily! Keep learning! Browse the Grammar 101 category, check our popular posts, or choose a related post below:50 Redundant Phrases to AvoidHomogeneous vs. Heterogeneous25 Idioms with Clean

Discussing Censorship and the First Amendment Essay

Discussing Censorship and the First Amendment - Essay Example It shows the US president how he played with the American people's sentiments after the terrorist attack in New York and Washington by fortifying his own agenda of oil manipulation. The movie depicts what manipulative tactics he did to win the Florida primaries the last deciding factor for president ship during 2001 elections. His family's relationship with various Arabic tycoons from around the world especially the Saudi royal family, his family stake on oil cartel market, relations to US biggest enemy's family the eminent Saudi fugitive billionaire etc. The first amendment clearly states the freedom for all to do or to say whatever he/ she may wish for. While as in the land of the free as this film was due for release Disney decided not to distribute "Fahrenheit 911". Miramax studios had been told by parent company Disney that it had decided to ban distribution of the film. The reason was according to Disney executive it was that it was not in the interest of any major corporation to be dragged into a highly charged partisan political battle. Moore said that he hoped that he would have been able to put his work out to the public without having to experience the profound censorship obstacles he has seen often seem to encounter," Moore wrote in the statement on his site. "Some people may be afraid of this movie because of what it will show," Moore wrote. "But there's nothing they can do about it now because it's done, it's awesome, and if I have anything to say about it, you'll see it this summer because, after all, it is a free country." Miramax had bought the film last May when Mel Gibson's Icon Pictures backed out, triggering complaints by conservatives to Disney. Overseas distribution rights have already had been sold. "Fahrenheit 911" was one of the movies at the Cannes film festival. Now people seem to ask what the sheer motivation to prevent its release was. The film portrayed deep resentments which prevailed in US society about the motives at which the Bush administration went to war over a lousy issue of weapons of mass destruction which turned out to be false as no weapons were found while young Americans continue to die everyday leading the toll to a massive 2200 soldiers. It shows interviews of GIs and of families of the fallen who live in utter miseries and now have to live with the fact that their loved one has died for a fallen cause. It shows the deep mistrust in joining the

3.2 The Internal Environment Research Paper Example | Topics and Well Written Essays - 750 words

3.2 The Internal Environment - Research Paper Example At present, Health Ascension is identified to follow an innovative organizational structure. The implementation of this structure facilitates the authorities of the healthcare organization to make decisions in a centralized manner. The corporate structure of the organization is clearly conveyed to every employee associated with the same. The organization has developed a new structure for managing operations in accordance with its business objectives as well as mission. In this context, the corporate structure is recognized to be consistent with the organizational objectives, policies and strategies among others (1Ascension Health, 2015). The changes in the organizational structure within Health Ascension as compared to BJC Healthcare has been quite different, as Health Ascension is focused on providing special attention to the patients based on the transformations observed in the healthcare system within the US (1Ascension Health, 2015; BJC Healthcare, 2015). Ascension Health is recognized to get developed based on a well-defined culture consisting of shared expectations, values and beliefs. The organization has developed a culture based on the principle of ‘Living the Mission and Values Awards.’ By following this principle, it can be found that the individuals associated with the aforesaid healthcare organization get support as well as become motivated for performing their respective operations in accordance with the organizational mission and values. The organizational culture of this healthcare firm is also recognized to be in alignment with ethics and workplace spirituality with the development in culture based on the legal healthcare provisions in the US (2Ascension Health, 2015). 1. Marketing. Ascension Health does not make any marketing initiative for its promotion. It must be mentioned in this context that the healthcare organization is involved in implementing sponsorship strategies in terms of clarity as well as responsibility to develop itself

The lessons in Vietnam war were forgotten in Iraq and Afghanistan Essay Example for Free

The lessons in Vietnam war were forgotten in Iraq and Afghanistan Essay A lot of lessons were learned throughout the Vietnam War but those lessons were not carried out in the Iraq and Afghanistan war. Australia’s involvement in the Vietnam War, caused by fears of communism and the fact that since the USA was our allied country we had to join forces, was one of the most disastrous episodes in our past. The lessons learned from the Vietnam War were forgotten when Australia decided to join the United States of America, who were planning the invasion of Iraq and Afghanistan. The American soldiers and the Australian soldiers went through and are still going through some of the same circumstances that happened in the Vietnam War. Some of those circumstances are that the American/Australian soldiers don’t know the terrain as well as the enemies do and the enemies are blending amongst innocent civilians and they plan ‘attack and run/booby traps’ which harm/kill the innocent civilians and the soldiers like the Vietcong did in the Vietnam war. The number of American/Australian deaths in Iraq and Afghanistan are 1/10. Some people would say that the USA/Australian forces in Iraq and Afghanistan are completely pointless, ‘Like Vietnam, this war cannot be won’. Some people however disagree. People argue that the reason why our efforts in Vietnam failed where due to the lack of support towards the America/Australian Military defence forces. In World War 2, the United States were not fighting against Japanese and German soldiers in and attempt to make those countries better places. The goal was to defeat there military forces, destroy their capacity and keep fighting, just as what the North Vietnamese were trying to do to the South Vietnamese. World war ll was a much simpler war than Vietnam. There enemies were easier to identify and the United States felt obligated to use firepower at its disposal and kill innocent people. Suddam Hussein (the fifth president of Iraq), had ‘weapons of mass destruction’. Hussein ordered the Iraqi troops to attack the country of Kuwait. The United States defended Kuwait in the Persian War against Iraq. On March 19th, 2003, the United States attacked Iraq. The United States used national security as an excuse for fighting. Afghanistan had terrorist training camps run by the Taliban government. Also, Hussein supposedly had ‘Mass Weapons of Destruction’. Due to Australia being allied with the United States, it was Australia’s right to help America out. This is where they all went wrong; it was going to turn into another Vietnam War again. Two countries stepping onto foreign land, fighting against foreign people, who were hard to identify and who were also hard to find. Over time, especially in Iraq and Afghanistan, the united states/Australian soldiers are trying to win wars while appearing to help people and are fighting against enemies who are hard to identify against the civilians, just as they did in Vietnam. With such unrealistic goals, it may be impossible to ever declare victory in Iraq and Afghanistan.

Valuing a Website Before You Sell :: Sell Websites Buy Websites

Valuing a Website Before You Sell Reprinted with permission of VotanWeb.com There is probably no part of the buying process that worries a potential buyer more than overpaying for a website. While this is understandable (who wants to pay more than something is worth), it has more to do with misinformation and one's total approach to buying a website than it does to being an expert at appraisals. The truth is, value is completely subjective. After all, what one website may be worth to you is entirely different from what it is worth to the next person. While there are cases where people may not negotiate the best price possible for a good website you must know that no price is cheap enough if you buy the wrong website. In time, a good website will always justify the purchase price whereas a bad one may not ever allow you to recover financially. What is Value? In a nutshell, value must be measured by what you are getting in return for your money. You have to equate the purchase price against the benefits you will derive over the term in which you can realistically expect to own the website. As an example, you cannot simply measure the purchase price against the income that you will derive from a specific website. What about the daily enjoyments you will get from being your own boss? Or, the sense of accomplishment you will feel from building something? Maybe, it's the gratification that you will get from contributing to the lives of others (i.e. employees). Perhaps it will come from knowing that from the toils of your labor you have been able to provide certain things for your family that you could never even consider if you were working for somebody else. A good website will provide abundant rewards for you so in order for you to truly measure a website’s value you have to consider all of the benefits that you stand to gain. Also, you must factor in what you could never have achieved if you don't go into business for yourself. Think of it this way: the average person takes 30 years to payoff a mortgage and 4 years to pay off a car. Neither one of these will pay you a salary. While they both have their benefits, neither one comes close to what you can derive from a good website as far as overall benefits are concerned.

Should English Be the Medium of Instruction in Sri Lankan Universities

Should English be the medium of instruction in Sri Lankan Universities Medium of instruction is a language used in teaching. It may or may not be the official language of the country or territory. Where the first language of students is different from the official language, it may be used as the medium of instruction for part or all of schooling and universities Bilingual or multilingual education may involve the use of more than one language of instruction. UNESCO considers that â€Å"providing education in a child's mother tongue is indeed a critical issue†Native-language instruction is the practice of teaching schoolchildren in their native language instead of in the official language of their country of residence. An English medium education system is one that uses English as the primary medium of instruction – in particular where English is not the mother tongue of the students. Because a working knowledge of English is perceived as being valuable, many states thro ughout the world where English is not the predominant language encourage or mandate the use of English as the normal medium of instruction.Bilingual education involves teaching academic content in two languages, in a native and secondary language with varying amounts of each language used in accordance with the program model. There are two ways of Bilingual education. First one is Transitional Bilingual Education. This involves education in a child's native language, typically for no more than three years, to ensure that students do not fall behind in content areas like mathematics, science, and social studies while they are learning English.Research has shown that many of the skills learned in the native language can be transferred easily to the second language later. The goal is to help students transition to mainstream, English-only classrooms as quickly as possible, and the linguistic goal of such programs is English acquisition only. In a transitional bilingual program, the stu dent's primary language is used as a vehicle to develop literacy skills and acquire academic knowledge. It is used to develop literacy and academic skills in the primary language. Second one is â€Å"Two-Way† or Dual Language Immersion Bilingual Education.These programs are designed to help native and non-native English speakers become bilingual and bi-literate. The two-way bilingual immersion program has 90% of the instructions in grade 1 in minority language which is less supported by the broader society and 10% in the majority language . This proportion gradually changes in the majority language until the curriculum is equally divided in both the language by 5th grade. The two-way bilingual immersion program is based on the principle of clear curriculum separation of the two languages of instruction.Teachers do not repeat or translate the subject matter in second language but strengthen concepts taught in one language across the two languages in a spiral curriculum in orde r to provide cognitive challenge. The languages of instructions are alternated by theme or content area. This type of immersion is required to develop the dual language proficiency, as social language can be mastered in couple of years, but a higher level of competency is required to read social studies texts or solve mathematics word problems, roughly around 5 to 7 years.This essay attempts to take into account of divergent views to deal with â€Å"Should English be the medium of instruction in Sri Lankan Universities†. . The debate on English as a medium of instruction in tertiary level education was always carried out among the Sri Lankan society. Majority claims that â€Å"who can never speak English with the degree of adequacy or fluency is not survived in the job arena of the white collar’s. † Almost the private sector investors’ basic requirement is the employees should be able to communicate with the mediation language of the globe.When we conside r about trading with other countries, tourism, IT Sector and the other areas of high salary paying employment opportunities govern by the people with the command in English. Or at least they know how to deal with the language and the opportunity they involved with. And jobs in the private sector which require functioning knowledge of English have enabled migration across the globe. However, one can point out the flaw in the system which restricts the benefits of the migration to 8-10% English speaking elite and middle class of the total population in Sri Lanka.Some view English as an elitist urban cultural value, derived from the west, which is imposed on the nation. This argument sees English as a language left behind by the whites and claims that cultural and linguistic authenticity is tied to thinking, speaking and writing only in vernacular languages. The argument also suggests that if the academia shifts to English it might sound the death knell for native languages as there wi ll be fewer and fewer literary works in native languages.The general obsession with English and with the notion of â€Å"sophistication† attached to the language has been a major cause of increasing divisions and psychological distress among the youth. University drop out rates can potentially increase among the students with weaker English skills. The above arguments tend to draw their inspiration from the fact that countries like Japan have done remarkably well in spite of a resolute emphasis on retaining their native languages even among children of the internet age.However, most works of science and human studies have, unfortunately, not been documented in Sri Lankan national languages to place complete reliance on the local medium even if we were to agree with the above arguments to do away with English. Developing our languages to impart higher education is important but depriving people of the access to the knowledge systems in English is not correct. It is important t o invest in education in our country to create resources to impart the language skills required to fully utilize the educational opportunities offered in English.To take a pragmatic view, introduction of English at an early stage in children’s education is necessary without being overbearing on the native languages. Perhaps we should look to the European Union in this regard, to develop multilingual skills without compromising on the native character of individual nation. Some Sri lankans are firmly convinced that the only way to learn English properly is to learn everything else through English.This is contrary to logic and evidenced both in Sri lanka and around the world. Children in every country today learn English, but they learn it as a foreign language, and learn it well, in all countries where English is not the native tongue. Consider countries like Korea, Japan, Germany, Sweden, Russia, Brazil and China. They have economies that are better than most. Their schools t each English, but employ their own mother tongues as the medium of instruction. Korea's population is equal to Sri Lanka.The Scandinavian countries are comparable, less in population size, to Sri Lanka Their languages remain vibrant, they create new knowledge and literature in their own languages and produce Nobel prize winners and world-beating companies. Of course, they also learn English, the de facto world language. Except in colonized Sri Lanka, nowhere do people believe that unless they abandon their mother tongue and embrace English as the sole language of instruction, their future is doomed.