Does a Normal Distribution Accurately Reflect the Empirical Distribution - Assignment Example

MANAGEMENT RESEARCH UNIT Part A Quantitative Analysis a. For the auction you have been assigned in describe the empirical results using the tools and techniques you have covered in the research methods unit b. Discuss, analyze and interpret your findings a) Does a normal distribution accurately reflect the empirical distribution? There is a difference between a normal distribution and an empirical distribution. The normal distribution, otherwise known as the Gaussian distribution is used in probability theory for continuous probability distributions that occur commonly, where a function describing the probability that some particular observation in a context, will fall between any two real numbers is referred to as the continuous probability distribution. Such distributions are of great importance in the statistical world where they are used in the social and natural sciences for unknown distributions of real-valued random variables. The normal distribution derives a lot of its usefulness from the central limit theorem. This theorem suggests that under insignificant conditions, most of the random variables have their mean drawn from the same distribution and are in this respect distributed approximately normally irrespective of what form the original distribution took. On the other hand, empirical distribution is equally as important in statistics, it is used as an estimator and as a result many statistical procedures depend on its performances. Empirical distribution is a kind of a staircase function with randomly placed locations of the drops. 1/n is usually the size of the drops without censoring, however, with censoring the size of the drops changes. The number of random observations that this empirical distribution is based of is ‘n’. With a growth in n, the empirical distribution gets closer to the true distribution. In the case of the data provided a normal distribution will not accurately reflect the empirical distribution. A normal distribution is expected to have a bell shaped curve with both ends edged out however; the graph of the data provided is skewed to the left as a result using a normal distribution in an effort to reflect empirical distribution will be misleading. b) Correlation between the auctioneers average estimate and the sales prices This is a situation in statistics where two sets of data are strongly linked together. The correlation is positive when values increase together and negative when one value decreases as the other increases. Below is the formula for calculating this correlation coefficient, Where: Σ is Sigma, the symbol for "sum up"  is each x-value minus the mean of x  is each y-value minus the mean of y However, given the data and will to use formulas provided in excel, the correlation coefficient was found to be 0.52408035. 1) Empirical and normal distribution is our first graph, where we can see the number of lots goes for what money. There should be two colors columns (it is very important), which will help us to analyze the empirical and standard and how it influences top lots ect. From the data provided in excel, we can see that the data is left skewed. There are two distinct colors depicting different curves. The normal curve follows the inclination of the frequency curve. Towards the left most end of the graph it is evident that a higher number of lots are acquired compared to the lots located towards the right side of the graph. There is primarily a very simple interpretation to this kind of behavior, a higher number of lots on the left side of the graph are acquired since they cost much less. As one progresses towards the right side of the graph, they notice that fewer lots are acquired and the reason behind this is cost oriented, these lots cost much more than those on the left side of the graph. 2) Please do the covariance (there must be a formula in excel), which is not the line of best fit. Covariance The variables used in calculating covariance for this research are the GBP, X and the Average Estimate, Y. Therefore the two random variables with the help of the data provided can be defined as: Cov [X, Y] = E[(X – E[X])(Y – E[Y])] From the formula in excel, the covariance was found to be 1,675,142,589. (1) Qualitative a. Provide a brief research plan of the qualitative methods you would use to further your understanding of your findings in Part 1. Qualitative research generally falls within scientific method processes. The description of these methods might include the data collection, the problem, the results, the hypothesis, and the discussion. Research commonly starts with the issue or problem, examination of literature in some way involved or related to the problem, posing questions, gathering data then analyzing them and developing their reports. These interconnected parts of the research process are what an inquirer tends to follow when engaging in the design of any qualitative study. A number of aspects vary from one study to the next an example being stances on the use of literature which vary on a very large scale as does the emphasis on using a theory. Such literature may have been entirely reviewed and used to inform questions asked, it may be reviewed later in the research process or may be used solely to document the importance of the research problem. The use of theory also varies in qualitative research where cultural theories form basic building blocks of any good qualitative ethnography (LeCompte&Schensul, 1999), in grounded theory however, theories are developed during the research process (Strauss & Corbin, 1990). The writing format also is of consideration as this varies considerably from scientific-oriented approaches, to performances, on to literary story telling e.t.c. Unlike in qualitative research there isn’t any one standard or accepted structure. Where other options exist they only point to varied uses of the literature in qualitative research. Steps in the Process Having already put these considerations in place we then begin by acknowledging the broad assumptions bringing us to qualitative inquiry and the interpretive lens to be employed. In addition to this we introduce a substantive area of investigation and have the literature about this particular topic reviewed so that we can conclusively say that the issue needs to be studied. The problem might be one that exists in the real world or alternatively a deficiency in the literature or investigations undertaken in the past and in some instances both. Qualitative research problems span topics in the human and social sciences whereby a hallmark of qualitative research today deeply involves issues of culture, gender and marginalized groups. These are topics close to human beings and practical too and to study such, comes the need to listen as a result of asking open ended questions. Developing quality questions will involve understanding the target group to be able to shape the questions to fit them and to do this it might be necessary to interview a few a few individuals just to get a clearer picture of what one should expect. This is a continuous process that ensures refinement of the questions being developed as a reflection of increased understanding of the problem. Various data sources will be used to collect information in the form of images or words. Basically, the four basic sources of qualitative information include document reviews, interviews, audiovisual materials and observations these traditional categorization has however been challenged by I new methods like social networking and email messaging. Data would simply be collected without an agenda or expectation of what to find. What follows is organization and storage of the collected data then an analysis of the same where analysts try to make sense of the collected data. Analyses of the qualitative data would be done by working inductively from particulars towards more general perspectives irrespective of whether they are themes, codes, dimensions or categories. Coming next would be working deductively in an effort to gather evidence that supports the interpretations and themes. An advisable way to go through this process would be to recognize it as operating through several levels of abstraction starting primarily with the raw data then forming wider and wider categories. This would lead to the recognition of highly interrelated sets of activities of data analysis, collection and report writing. During report writing, experimentation can be done which may involve making analogies and metaphors, developing tables and matrices and also using visuals in an effort to convey simultaneous data break down and their reconfigurations into new forms. The analyses can also be layered into increasing levels of abstractions from themes to codes to their interrelationship of themes to larger conceptual models. The data representation would be partly based on analysts own interpretation and partly on participants’ perspectives, never entirely escaping any personal hallmark on a study. Finally discussions on the findings would be conducted in a manner that compares analysts’ findings with their own personal views, with existing literature and with developing models which effectively convey the essence of the findings. In the end it would be very important for analysts to seek to have their account echo that of the participants and be an exact replication of what they said, to achieve this engaging in validation strategies would be of great importance. These are often numerous strategies that include triangulating data from a number of sources, employing other researchers to review the procedures used by the analysts and having the study reviewed and corrected by the participants. To asses the quality of the study, editorial board members for journals, participants, readers, graduate committees and reviewers of proposals are among individuals who will apply some standards to evaluate the quality of the study. Standards for assessing the quality of qualitative research are available (Howe &Eisenhardt, 1990; Lincoln, 1995; Marshall &Rossman, 2010).Researchers will employ demanding data collection processeswhere they would collect multiple data forms, give adequate summaries conceivably in tabular form, forms of data including details about the same and spend a considerable amount of time in the field. Researchers could frame the study within characteristics and assumptions of the qualitative approach to research which would include important characteristics like the presentation of several realities, an evolving design, the researcher as an instrument of data collection and focuses on the views of participants. . It is advisable to use a single recognized approach to qualitative inquiry as this improves the complexity and thoroughness of the research design. Furthermore it ensures the provision of some means to evaluate the qualitative study. The use of any particular approach will involve the researcher defining and identifying the approach, following the procedure outlined in the approach and citing studies that employ it. As much as the approach taken in the study may not thoroughly cover all elements of the approach, it is important for a beginning student of any qualitative research to get familiar with it by learning it and ensuring the study is kept brief and straightforward. Afterwards, especially in long and very intricate studies a number of approaches may be employed. Researchers or analysts begin with a single focus or perception which they explore. As much as qualitative examples may depict comparisons of groups or themes or factors, in ethnographies, it is important to begin a qualitative study focused on trying to understand a single idea or concept. During the progress of the study then associated factors and comparisons can now be assimilated. The study involves rigorous approaches to data analysis, data collection methods and report writing. Precision is witnessed for example when there is extensive data collection in the fields or when multiple levels of data analysis are conducted of course from the narrow themes or codes to much broader interrelated themes then to more abstract dimensions. Rigor also requires that any researcher validates the precision of the account using a variety of validation procedures which may include triangulating sources of data, member checking and using an external or peer auditor of the account. Multiple levels of abstraction are employed to analyze the data, for example, seeing researchers’ active work as they move from particulars to much more general levels of abstraction. More often than not, studies will be presented in stages or layered analyses from the particular to the general, themes and codes derived from the data might show ordinary, predictable and surprising ideas. The best qualitative studies however, present themselves as analyzed in terms of shadow sides of exploring their unusual viewpoints. The best qualitative studies have the concept of verisimilitude where the writing is engaging, clear and full of unexpected ideas, stories captured build their realism correctly reflecting complexities that exist in the real life. Justification of the approach The qualitative analyses methodologies are a complex undertaking marred by a variety of uncertainties. To be able to tackle then accurately and conclusively assuring full satisfaction it is important for the researcher or analyst to adopt a singular method during the primary stages. Doing so will help the analyst/researcher to understand fully the field of study and its associated variables after which s/he can now incorporate a variety of other methodologies to manipulate the data he now clearly understands. Adopting a variety of methodologies at the preliminary stages can be very risky since one does not have a clear understanding of the data and their interrelationships and associations as a result, researchers may be blindly led by some bias towards making a conclusion therefore tailoring the data collected towards achieving pre-specified results. GENERAL DESCRIPTION OF THE ORGANISATION The Global Art Affairs Foundation is the organization of choice. This organization was founded in New York, USA in 2002. The foundation relocated its headquarters in 2009 to Leiden in the Netherlands. The permanent exhibition venue however is in Venice Italy, the “Palazzo Bembo”. The year 2012 saw the establishment of the “Global Art Centre Foundation (GAC)”, also a non-profit organization with a new exhibition site “Palazzo Mora”. The Global Art Affairs Foundation formed a strategic partnership with the “Asia Art Centre”, a Chinese art organization with their objectives being heightening awareness about Asian artists and architects and also getting to be the leading international and intercultural platform that links Eastern and Western art.The Global Art Affairs Foundation has organized up to 6 symposia and 24 contemporary exhibitions in Germany, Netherlands, Japan, Italy and USA. This Foundation makes extensive publications about all their enterprises in magazines and art books. They also promote and support as well as facilitate creation of artworks by a number of artists and participate in joint projects with them. Global Art Affairs Foundation is represented and legally advised and supported in Italy, Venice by Francesco Adami from Studio Legale Palmer and in the Netherlands, Haarlem, by notary AdriaanHelmig.The Global Art Centre Foundation (GAC) is also a non-profit organization registered under the number 56220189 in Leiden by the Dutch Chamber of Commerce. Legal advisory is provided by notary Haarlem Adriaan Helming in the Netherlands Being non-profit organizations, both the Global Art Centre Foundation and the Global Art Affairs Foundation aim towards heightening the understanding about the more philosophical themes in present day art and in particular: Existence, Space, Time, to replicate the heterogeneity and homogeneity of today’s world experience under very wide ranges of geographical, cultural and social environment. The curatorial theme brought about by this exhibition aims not only to provide supporting and exchanging platforms between artists globally but also between artists and their audiences. The primary concept of these two foundations is to break away from beliefs and ideas claiming that arts are merely static ornaments but that they should continuously interrelate with our everyday life and society. Both Foundations collaborate with major art institutions and world museums. In addition to working hand in hand with internationally recognized contemporary artists, the Global Art Centre Foundation is much more committed to seeking supportive opportunities with potential though less exposed artists. They have projects that have been accepted and approved by the Venice Biennale Committee for two successive years as authorized categories in the Collateral Events. The mission of the Global Art Centre Foundation is to ensure that it becomes the intercultural “meeting point” where artworks, artists, audiences come across all the continents to share different thoughts. In an effort to encourage cross-cultural and interdisciplinary debate the Global Art Centre Foundation organizes frequent artist symposium and forum and also spreads knowledge through extensive publications. - What does your chosen art world organization do in terms of the research it conducts? When it comes to conducting research these two foundations, the Global Art Centre Foundation and the Global Art Affairs Foundation prefer to use the same approach. During the preliminary stages of data collection, they will conduct interviews, review documents relevant to the study area, distribute questionnaires and get them back for analysis and they will also employ data collection by the use of audiovisual means. Since technology has developed drastically, the two organizations have found it important to recognize this and as a result they have also decided to collect data by use of electronic mail and from social media platforms as this is fast becoming the way of conducting business with technologies such as video conferencing revolutionizing the world. Needless it is to say that implementing technology in conducting any form of research is quite effective and efficient. Later after completing these preliminary stages the data is stored then analyzed using state of the art tools to generate the required information at very high speeds. At this stage the two foundations can independently make decisions that affect their business based of the information they have acquired from the research they have conducted. Bibliography Darrell, Huff. "How to lie with statistics." Penguine Business Journals (1991(first printed in 1954)). Derek, Rown Tree. "Statistics without Tears." 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