Hypothesis Testing With One-Sample t-Tests

Hypothesis Testing With One-Sample t-Tests Youve collected your data, youve got your model, youve run your regression and youve got your results. Now what do you do with your results? In this article we consider the Okuns Law model and results from the article How to Do a Painless Econometrics Project. One sample t-tests will be introduced and used in order to see if the theory matches the data. The theory behind Okuns Law was described in the article: Instant Econometrics Project 1 - Okuns Law: Okuns law is an empirical relationship between the change in the unemployment rate and the percentage growth in real output, as measured by GNP. Arthur Okun estimated the following relationship between the two: Yt - 0.4 (Xt - 2.5 ) This can also be expressed as a more traditional linear regression as: Yt 1 - 0.4 Xt Where:Yt is the change in the unemployment rate in percentage points.Xt is the percentage growth rate in real output, as measured by real GNP. So our theory is that the values of our parameters are B1 1 for the slope parameter and B2 -0.4 for the intercept parameter. We used American data to see how well the data matched the theory. From How to Do a Painless Econometrics Project we saw that we needed to estimate the model: Yt = b1 + b2 Xt Yt Xt b1 b2 B1 B2 Using Microsoft Excel, we calculated the parameters b1 and b2. Now we need to see if those parameters match our theory, which was that B1 1 and B2 -0.4. Before we can do that, we need to jot down some figures that Excel gave us. If you look at the results screenshot youll notice that the values are missing. That was intentional, as I want you to calculate the values on your own. For the purposes of this article, I will make up some values and show you in what cells you can find the real values. Before we begin our hypothesis testing, we need to jot down the following values: Observations Number of Observations (Cell B8) Obs 219 Intercept Coefficient (Cell B17) b1 0.47 (appears on chart as AAA)Standard Error (Cell C17) se1 0.23 (appears on chart as CCC)t Stat (Cell D17) t1 2.0435 (appears on chart as x)P-value (Cell E17) p1 0.0422 (appears on chart as x) X Variable Coefficient (Cell B18) b2 - 0.31 (appears on chart as BBB)Standard Error (Cell C18) se2 0.03 (appears on chart as DDD)t Stat (Cell D18) t2 10.333 (appears on chart as x)P-value (Cell E18) p2 0.0001 (appears on chart as x) In the next section well look at hypothesis testing and well see if our data matches our theory. Be Sure to Continue to Page 2 of Hypothesis Testing Using One-Sample t-Tests. First we’ll consider our hypothesis that the intercept variable equals one. The idea behind this is explained quite well in Gujarati’s Essentials of Econometrics. On page 105 Gujarati describes hypothesis testing: â€Å"[S]uppose we hypothesize that the true B1 takes a particular numerical value, e.g., B1 1. Our task now is to â€Å"test† this hypothesis.†Ã¢â‚¬Å"In the language of hypothesis testing a hypothesis such as B1 1 is called the null hypothesis and is generally denoted by the symbol H0. Thus H0: B1 1. The null hypothesis is usually tested against an alternative hypothesis, denoted by the symbol H1. The alternative hypothesis can take one of three forms:H1: B1 1, which is called a one-sided alternative hypothesis, orH1: B1 1, also a one-sided alternative hypothesis, orH1: B1 not equal 1, which is called a two-sided alternative hypothesis. That is the true value is either greater or less than 1.† In the above I’ve substituted in our hypothesis for Gujarati’s to make it easier to follow. In our case we want a two-sided alternative hypothesis, as we’re interested in knowing if B1 is equal to 1 or not equal to 1. The first thing we need to do to test our hypothesis is to calculate at t-Test statistic. The theory behind the statistic is beyond the scope of this article. Essentially what we are doing is calculating a statistic which can be tested against a t distribution to determine how probable it is that the true value of the coefficient is equal to some hypothesized value. When our hypothesis is B1 1 we denote our t-Statistic as t1(B11) and it can be calculated by the formula: t1(B11) (b1 - B1 / se1) Let’s try this for our intercept data. Recall we had the following data: Intercept b1 0.47se1 0.23 Our t-Statistic for the hypothesis that B1 1 is simply: t1(B11) (0.47 – 1) / 0.23 2.0435 So t1(B11) is 2.0435. We can also calculate our t-test for the hypothesis that the slope variable is equal to -0.4: X Variable b2 -0.31se2 0.03 Our t-Statistic for the hypothesis that B2 -0.4 is simply: t2(B2 -0.4) ((-0.31) – (-0.4)) / 0.23 3.0000 So t2(B2 -0.4) is 3.0000. Next we have to convert these into p-values. The p-value may be defined as the lowest significance level at which a null hypothesis can be rejected...As a rule, the smaller the p value, the stronger is the evidence against the null hypothesis. (Gujarati, 113) As a standard rule of thumb, if the p-value is lower than 0.05, we reject the null hypothesis and accept the alternative hypothesis. This means that if the p-value associated with the test t1(B11) is less than 0.05 we reject the hypothesis that B11 and accept the hypothesis that B1 not equal to 1. If the associated p-value is equal to or greater than 0.05, we do just the opposite, that is we accept the null hypothesis that B11. Calculating the p-value Unfortunately, you cannot calculate the p-value. To obtain a p-value, you generally have to look it up in a chart. Most standard statistics and econometrics books contain a p-value chart in the back of the book. Fortunately with the advent of the internet, there’s a much simpler way of obtaining p-values. The site Graphpad Quickcalcs: One sample t test allows you to quickly and easily obtain p-values. Using this site, here’s how you obtain a p-value for each test. Steps Needed to Estimate a p-value for B11 Click on the radio box containing â€Å"Enter mean, SEM and N.† Mean is the parameter value we estimated, SEM is the standard error, and N is the number of observations.Enter 0.47 in the box labelled â€Å"Mean:†.Enter 0.23 in the box labelled â€Å"SEM:†Enter 219 in the box labelled â€Å"N:†, as this is the number of observations we had.Under 3. Specify the hypothetical mean value click on the radio button beside the blank box. In that box enter 1, as that is our hypothesis.Click â€Å"Calculate Now† You should get an output page. On the top of the output page you should see the following information: P value and statistical significance:The two-tailed P value equals 0.0221By conventional criteria, this difference is considered to be statistically significant. So our p-value is 0.0221 which is less than 0.05. In this case we reject our null hypothesis and accept our alternative hypothesis. In our words, for this parameter, our theory did not match the data. Be Sure to Continue to Page 3 of Hypothesis Testing Using One-Sample t-Tests. Again using site Graphpad Quickcalcs: One sample t test we can quickly obtain the p-value for our second hypothesis test: Steps Needed to Estimate a p-value for B2 -0.4 Click on the radio box containing “Enter mean, SEM and N.” Mean is the parameter value we estimated, SEM is the standard error, and N is the number of observations. Enter -0.31 in the box labelled “Mean:”. Enter 0.03 in the box labelled “SEM:” Enter 219 in the box labelled “N:”, as this is the number of observations we had. Under “3. Specify the hypothetical mean value” click on the radio button beside the blank box. In that box enter -0.4, as that is our hypothesis. Click “Calculate Now” P value and statistical significance: The two-tailed P value equals 0.0030By conventional criteria, this difference is considered to be statistically significant. We used U.S. data to estimate the Okuns Law model. Using that data we found that both the intercept and slope parameters are statistically significantly different than those in Okuns Law. Therefore we can conclude that in the United States Okuns Law does not hold. Now youve seen how to calculate and use one-sample t-tests, you will be able to interpret the numbers youve calculated in your regression. If youd like to ask a question about econometrics, hypothesis testing, or any other topic or comment on this story, please use the feedback form. If youre interested in winning cash for your economics term paper or article, be sure to check out The 2004 Moffatt Prize in Economic Writing

Characteristics of Sam as an Employee Essay Example | Topics and Well Written Essays - 3500 words - 1

Characteristics of Sam as an Employee - Essay Example First of all, Sam does not know if the client really complained against him, or if it is the trick played by his employers to get rid of him, because Sam, under the presented circumstances, would not dare to sue them legally, as there is a possibility of a sexual abuse cropping up against him. He would be frightened, or he would also be humiliated to face such charges and hence, the employers even after dismissing him from service are safe. Here is a very strong possibility of the employers plotting against an employee who could be dismissed in a devious way, and at the same time, could be unable to retaliate against them. If they had dismissed Sam from the job without a sexual abuse complaint in the background, he would have definitely sued them for unlawful dismissal and they would have been forced to compensate him for the money and the career prospectus that he had lost due to their dismissal. As a grave charge of sexual assault is made here, Sam is unable to knock at the legal d oor. In any job, job security is of paramount importance without which the mental, physical wellbeing of the worker could be ruined combined with a disastrous career route. â€Å"The employee who loses his or her job in an economy which uses market exchanges to direct labour towards remunerative employment is immediately deprived of his or her major source of wealth, and will possibly suffer long-term impoverishment as a result of unemployment. At the same time the worker is excluded from the workplace which is likely to constitute a significant community in his or her life,† Collins (1992, p.15). The worker loses his dignity and self-confidence to find another job. Even he gets an alternative job; he would find it difficult to work freely in that post being haunted by the earlier unsavoury memories. There are psychological cases where the person was scarred for life. The importance of job security is so high that almost all the governments have chosen to pass as many laws as possible to create an atmosphere of security for the worker.

Where Am I Now Essay Example | Topics and Well Written Essays - 1250 words

Where Am I Now - Essay Example Although college was challenging, I graduated from the University of Peru with a degree in Communication. Using my degree, I published a 400-page book of nonfiction about preserving nature: I called it The Dream of the Dolphins. After this, I found a job with IBM selling large, mainframe computers to banks. In 1999, I met and later married my husband who I met at an IBM advertising conference. We married six months after the conference and we moved to the United States. Currently, we live in a small, friendly, community in Norwich, Vermont. Our home is on a farm, and we have four horses, four dogs and four children. I am currently working full-time as a graphic designer at a very successful advertising agency in Woodstock, Vermont. In addition, during my free time, I enjoy reading a good book and working out in the gym. Some of my hobbies include skydiving, hiking and horseback riding. One challenging issue for me is the fact that English is my second language. This means that I ofte n have to use an editor in order to make sure that I am writing the words correctly. What many people do not realize is that students with English as their second language have to use other ways of learning English that natural English speakers. According to Yau-hau Tse (2011) â€Å"students used six dimensions of language learning strategies: cognitive, social, association, compensation, assistance and constructive strategies† (p. 33). ... I notice that I basically ask many questions in class to make sure that I understand what is going on. I learn best through hands on learning, face to face and lectures. These methods suggest that I am a visual, kinesthetic and auditory learner (Fleming, 2011). This means that I need to hear and see what I am learning on one level and if the course adds some type of hands on ability, it allows me to totally engage in the learning of that subject. I find that if I have more than one way to approach a subject I have a better understanding of what I need to do to be successful with that subject. Luu Trong (2011) states that understanding the learning styles is important in order to engage students into specific learning. He calls learning styles â€Å"a consistent way of functioning which reflects cultural behavior patterns †¦Ã¢â‚¬  (p. 291) which means that because learning styles are based within cultures, they also can be stretched to accommodate more styles as they are develo ped. I am not sure that I am developing new learning styles yet, but perhaps this will happen later. Barnes, Marateo and Ferris (2007) suggest that there are many different styles to consider when working with learners and students today are part of a generation that they call The Net Generation. They say that this generation is very interested in education and that they are brought up in education from a very young age. I see myself as part of this particular generation and I do believe that my education is very important to my future goals. As they state, I have been involved with the Internet for a very long time and have and I understand my learning style very well. As a teacher/counselor/mentor/leader, I

Research Topic For Logistics Topics For Research Paper

Research Topic For Logistics Topics For Research PaperIf you are currently attending university in the United Kingdom, one of the logistics topics for research paper is probably article writing. This is an area in which a lot of students fail because they lack the interest and the ability to write well. In order to be successful as a writer, you have to know a bit about your topic and how to write a good article. In this article, we will look at some of the other topics that are associated with logistics.The logistics topics for research paper are ones that you must think about before you write. If you have already written a research paper, then you must ask yourself if you are truly interested in the topic. Is the topic related to the point you want to make?There are two other logistics topics for research paper, which are popular with a large number of students. One of these is 'Logistics and Customer Service'. There are many topics that deal with logistics, which includes shipping and storing, logistics of customers, managing supplies, and even logistics of customers' goods.The other logistics topics for research paper are related to transportation and logistics management. As with the topic of storing and inventory management, this involves problems in the movement of goods from one place to another. Transport logistics involves moving different types of materials such as trucks, trains, boats, planes, and trains.Many students also choose to write about the logistical topics that are not mentioned above. If you are involved in a business in which you are providing logistics services, you can choose to write about the topic of business logistics. If you own a company that provides logistics services, you can choose to write about the topic of company logistics. Whatever topic you choose, you must include both the companies' clients.Before writing your logistics topics for research paper, you must first decide what exactly you are writing about. If it is rela ted to a specific industry, then you can include that industry. However, if it is not related to any industry, then you can choose to cover just one aspect of logistics, which could be time management or supply chain management. If you have worked in this industry before, then you might be able to include information that you learned from the experience.When writing your logistics topics for research paper, it is important to make sure that you give a concise and clear explanation of what you are trying to say. Also, you should include both company and client information, although they should be related to each other. The content should be so easy to understand that it will not leave any room for any misinterpretation. Lastly, you should be clear about the purpose of the article and if it is related to a company's business objectives.

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The Newly Leaked Secrets to Researchable Argumentative Essay Topics Uncovered

The Newly Leaked Secrets to Researchable Argumentative Essay Topics Uncovered Argumentative arguments are only arguments that are written back on paper. So, the objective of an argument essay isn't to ultimately proved that you're right, instead it is to produce a wholesome debate on the special topic that you're writing on and permit the reader to form their own opinion too. It's recommended not to choose reflective essay that cannot be convinced during the arguments. An argumentative essay is a kind of thesis or composition in which you have to present your view and endeavor to convince others your facts and arguments are correct. When you develop this kind of essay, you should make your claims by your composition so it will be open fordebate. Before you import evidence, you should be certain your facts are accurate and right to the point. You should back up your viewpoint with well-researched facts and data too. There's a huge possibility that you come out the task a specialist in the topic. Controversial issues are happening all of the time, all you have to do is turn on the news and you'll be able to locate a huge choice of topics to select from. A great method to tell if your topics is an argument topic is to see whether you can debate your topic employing the info you find. If you select the incorrect subject, you might get stuck with your writing and have a difficult time moving forward. Bear in mind you may make funny argumentative essays if you do a few things. You should begin by letting the reader understand what you hold as true about this issue. One of the greatest methods to make writing a research paper easier is to opt for a topic which you're passionate about. Choose from popular topics that folks are passionate about. The essay ought to have a little bit of structure, unlike a normal essay. Your essay should consist of recent statistics and data from reliable sources. Just adhere to the fundamentals of composition writing and you'll have your argumentative essay ready. An argumentative essay requires you to choose a topic and have a position on it. Argumentative essay topics cover a wide number of subjects, and can be quite persuasive if an excellent essay represents them. You could also see concept essays. Argumentative essays have to be well-organized. Generally, they are not similar to othertypes of essays. Creating an excellent argument essay starts with a list of argumentative essay topics. Below you'll find specific instructions about how to compose an argumentative essay on any topic, which is well written and are going to have excellent opportunity to have a good grade. Quite frequently, the ideal topic is one which you truly care about, but you also will need to get ready to research it. First you discuss the very first subject. Never utilize words of which you don't know the specific meaning. In order to give an in-depth understanding about the argumentative essay, it's better to examine some of the greatest examples of argumentative essay. To write a superb argumentative essay, there are four key pieces of the essay you're likely to have to know about. If you're new to writing argumentative essays, there are a number of essential factors which you can learn that may help you compose a greater argumentative essay. The Benefit A persuasive essay grants you the advantage of digging through a problem. Bear in mind that what you include as facts ought to be such they can be authenticated by objective ways. Brutus sacrificed relationships as a way to look after the people.

Japanese Pornographic Animation Essay Example for Free

Japanese Pornographic Animation Essay Susan J. Napier’s â€Å"The Frenzy of Metamorphosis: The Body in Japanese Pornographic Animation† describes how both female and male bodies are depicted in Japanese animated pornography. Napier explains how male dominance over women is portrayed in the different animated films she has cited, where gender-specific roles are usually restored in the end of each film or series. For example, the female lead character in the animated film Wicked City is portrayed as a better warrior than the male lead character, but in the end she assumes the traditional role of damsel-in-distress and mother of the child that would bring peace to their city and its parallel, the Black World. Napier further highlights the often problematic and complicated depiction of male-female relationships in these films. The fantasy behind every transformation a male or female character’s body undergoes in the animated film subliminally illustrates underlying cultural backgrounds, as well as frustrations, of the Japanese. In these films, the female characters are commonly fantastically proportioned with massive breasts and hips, and tiny waists, while the male characters are similarly fantastically sexually endowed and lustful. Such depictions appear to reflect heavy Western influences. The metamorphosis of female bodies is described by Napier as â€Å"controlled† in that they are rather reflective of traditional roles and perceptions towards females in Japanese culture. Meanwhile, the metamorphosis of male bodies is described as more of â€Å"demonic dominance and comic frustration. † While they are subversive to the patriarchal culture of Japan, male bodies are portrayed in the opposite of how female bodies are portrayed. Male bodies are portrayed as either grotesquely demonic-looking or ridiculously child-like. Napier maintains that males do not always come out as the dominant character in Japanese animated pornography. I find this rather arguable as most if not all of the examples highlighted in the reading suggest the presence of a male figure whose role is either to dominate the female character or to support it. Culturally, Japanese are of control-minded and patriarchal culture where every female is traditionally submissive to a male partner. The presence of a male character, no matter how comic or demonic as depicted in the film, can be attributed to an attempt to balance out the portrayal of powers where the protagonist is a female; hence, whether the dominant role belongs to the male or female remains problematic. The presence of the male support character suggests that female characters cannot achieve great power over her adversary without him. An example of this is La Blue Girl where the lead character, a female ninja, is supported by her male ninja sidekick who is portrayed as constantly lusting after her. Napier also cites that male orgasms are depicted far less than male frustrations in these films because orgasms are viewed as a loss of patriarchal control. Patriarchal control can also be seen in the way that female orgasms are almost always depicted in these films, regardless of whether these orgasms are the result of traditional lovemaking or of sexual torture. I find that this is because of socio-cultural factors given the changes in roles of men and women in modern Japanese society. The Japanese male ego seems to be affected by this change so much that their frustration is reflected even in their animated pornographic films. Hence, Japanese animated pornography tend to portray female characters as young and non-threatening (high school girls, commonly) while male characters are either comically lustful (young or old voyeurs) or powerfully demonic. Many of the strong male characters in Japanese animated pornography are depicted as demons, making them appear threatening and ultimately powerful over the females. Even if the female lead characters are able to overcome these demonic male antagonists at the end of the film, these females are still portrayed as traditionally vulnerable to sexual violence.