Example of ANOVA Calculation

One factor analysis of variance, also known as ANOVA, gives us a way to make multiple comparisons of several population means. Rather than doing this in a pairwise manner, we can look simultaneously at all of the means under consideration. To perform an ANOVA test, we need to compare two kinds of variation, the variation between the sample means, as well as the variation within each of our samples. We combine all of this variation into a single statistic, called the ​F statistic because it uses the F-distribution. We do this by dividing the variation between samples by the variation within each sample. The way to do this is typically handled by software, however, there is some value in seeing one such calculation worked out. It will be easy to get lost in what follows. Here is the list of steps that we will follow in the example below: Calculate the sample means for each of our samples as well as the mean for all of the sample data.Calculate the sum of squares of error. Here within each sample, we square the deviation of each data value from the sample mean. The sum of all of the squared deviations is the sum of squares of error, abbreviated SSE.Calculate the sum of squares of treatment. We square the deviation of each sample mean from the overall mean. The sum of all of these squared deviations is multiplied by one less than the number of samples we have. This number is the sum of squares of treatment, abbreviated SST.Calculate the degrees of freedom. The overall number of degrees of freedom is one less than the total number of data points in our sample, or n - 1. The number of degrees of freedom of treatment is one less than the number of samples used, or m - 1. The number of degrees of freedom of error is the total number of data points, minus the number of samples, or n - m.Calculate the mean square of error. T his is denoted MSE SSE/(n - m).Calculate the mean square of treatment. This is denoted MST SST/m - 1.Calculate the F statistic. This is the ratio of the two mean squares that we calculated. So F MST/MSE. Software does all of this quite easily, but it is good to know what is happening behind the scenes. In what follows we work out an example of ANOVA following the steps as listed above. Data and Sample Means Suppose we have four independent populations that satisfy the conditions for single factor ANOVA. We wish to test the null hypothesis H0: ÃŽ ¼1 ÃŽ ¼2 ÃŽ ¼3 ÃŽ ¼4. For purposes of this example, we will use a sample of size three from each of the populations being studied. The data from our samples is: Sample from population #1: 12, 9, 12. This has a sample mean of 11.Sample from population #2: 7, 10, 13. This has a sample mean of 10.Sample from population #3: 5, 8, 11. This has a sample mean of 8.Sample from population #4: 5, 8, 8. This has a sample mean of 7. The mean of all of the data is 9. Sum of Squares of Error We now calculate the sum of the squared deviations from each sample mean. This is called the sum of squares of error. For the sample from population #1: (12 – 11)2 (9– 11)2 (12 – 11)2 6For the sample from population #2: (7 – 10)2 (10– 10)2 (13 – 10)2 18For the sample from population #3: (5 – 8)2 (8 – 8)2 (11 – 8)2 18For the sample from population #4: (5 – 7)2 (8 – 7)2 (8 – 7)2 6. We then add all of these sum of squared deviations and obtain 6 18 18 6 48. Sum of Squares of Treatment Now we calculate the sum of squares of treatment. Here we look at the squared deviations of each sample mean from the overall mean, and multiply this number by one less than the number of populations: 3[(11 – 9)2 (10 – 9)2 (8 – 9)2 (7 – 9)2] 3[4 1 1 4] 30. Degrees of Freedom Before proceeding to the next step, we need the degrees of freedom. There are 12 data values and four samples. Thus the number of degrees of freedom of treatment is 4 – 1 3. The number of degrees of freedom of error is 12 – 4 8. Mean Squares We now divide our sum of squares by the appropriate number of degrees of freedom in order to obtain the mean squares. The mean square for treatment is 30 / 3 10.The mean square for error is 48 / 8 6. The F-statistic The final step of this is to divide the mean square for treatment by the mean square for error. This is the F-statistic from the data. Thus for our example F 10/6 5/3 1.667. Tables of values or software can be used to determine how likely it is to obtain a value of the F-statistic as extreme as this value by chance alone.

The Importance Of Religious Practices In International...

their specific religious practices. The hamburgers (and all food items for that matter) must be Halal, and in fact, they do not call the burgers hamburgers as such, instead they call them beef burgers so as to make it clear that there is no ham in them. (The Travel Almanac n.d) So taboos and preferences have to be explored before entering a religious society and trade with partners who are religious believers.Whereas in developing economics foreign brands have status value, when countries develop, people tend to focus more on their historical national preferences. In the early 1990s anything Western sold in Russia, but since 1996 international companies such Coca-Cola and Nestle have been localizing their messages in†¦show more content†¦On the other hand, another important institution in China is the family and the mutual dependency of its members.In Chinese societies, such relationships are governed by what is termed guanxi, which is a bond between people, on the basis of which friends are expected to look after each others wellbeing. (Bargiela-Chiappini and Harris 1997: 42) The complexities of interpersonal relations bothered a large number of western businessmen, since most Chinese businessmen prefer to trade with friends or friends friends and relatives, who are thought to be more trustful due to the special guanxi between them.So, exploring the social institution of the destination countries is very useful for businessmen to trade in different societies efficiently. A famous study of cultural dimensions, which can provide a more clear view of the impacts of culture on international business.Dimensions of cultural differences are very necessary for organizations especially those who operate internationally to understand and cope with such differences that can manifest themselves in terms of different standards, values and expectations in the various countries in which they operate. (Johnson, Scholes, Whittington 2008: 190) Here I have to mention one of the most effective studies of cultural dimensions, Hofstedes cultural dimensions, which are consisted of power distance, uncertainty avoidance, individualism and collectivism, masculinity-femininity, andShow MoreRelatedReligion and Spirituality in the Workplace Essay1680 Words   |  7 PagesToday there are over 900 religious employee resource groups, according to the International Coalition of Workplace Ministries (Caà ±as Sondak, 2010). 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Nonsmokers A Prospective Study Free Essays

In 2006, Rudolf bertagnoli and his team published a study investigating the effects of smoking on patients who have undergone Lumbar total disc arthroplasty. â€Å"Smoking has always been considered to a negative predictor for fusion surgery.† (Bertagnoli. We will write a custom essay sample on Nonsmokers: A Prospective Study or any similar topic only for you Order Now R, 2006) Not many studies have been undertaken to observe effects of smoking on the procedure of Total arthroplasty and the recovery afterwards in smoking and non smoking patients. Some research suggests that smoking prevents or reduces the bones ability to grow into the prosthesis. Delay in recovery and decrease in over all success of the implantation procedure have also been blamed on smoking. (ProDisc Total Disc Replacement, 2008) â€Å"The aim of the study was to evaluate the changes in functional and disability outcomes within a period of two years minimum in smoking and nonsmoking patients who have undergone the artificial disc replacement therapy.† (Bertagnoli. R, 2006) The Null hypothesis and the Alternate hypothesis proposed were as follows. Null Hypothesis: Smoking has no detrimental effect on success of artificial disc replacement (ADR). Alternate Hypothesis: â€Å"Smoking has a detrimental effect on the success of artificial disc replacement (ADR).† (Bertagnoli. R, 2006) A cohort study was conducted with an initial sample of 110 patients between March 2000 and April 2002. The inclusion criteria for the sampling included, smokers and non smokers, age between 18-65 years, â€Å"disabling low back pain and some radicular pain secondary to single-level lumbar spondylosis† (Bertagnoli. R, 2006) , patients undergoing minimum of 2 year follow up and assessment, and lastly failure of medical treatment. They excluded â€Å"patients with spinal stenosis, osteoporosis, prior fusion surgery, chronic infections, metal allergies, facet arthrosis, inadequate vertebral endplate size, more than one level of spondylosis, neuromuscular disease, pregnancy, Workers’ Compensation, spinal litigation, body mass index greater than 35, and/or any isthmic.† (Bertagnoli. R, 2006) Patient’s smoking status was recorded through questionnaires. Preoperative aspects of the lumbar anomaly were recorded radiographically. Outcome measurements were recorded at 3rd, 6th, 12th and the 24th month after undergoing the procedure. The procedure success and recovery progression was noted using the Visual Analog Score (VAS) and the Oswestry Disability Index (ODI). Questionnaires recording the back pain, pain drugs usage and patient satisfaction were also used. Preoperative and postoperative radiographical assessment of the back was also used to observe the recovery progression in both, the smoking and non smoking group of patients. Dependent variables included Smoking and Non smoking group. Whereas the independent variables included VAS, ODI, patient satisfaction, leg pain, work rates (postoperative), and drugs used postoperatively. Statistical analysis was done as it was found that even though there was significant changes between preoperative and postoperative variable like VAS, ODI, patient satisfaction, relief of leg pain work rate etc but no statistically significant differences were found between these outcomes of smoking patients when compared with nonsmokers. Therefore, the study fails to reject the null hypothesis, which still stands, i.e. â€Å"Smoking has no detrimental effect on success of artificial disc replacement (ADR).† (Bertagnoli. R, 2006) The research was conducted in a controlled manner excluded many bias.   But further studies need to be conducted with larger sample sizes to further explore the role of smoking if any, in the success of disc replacement. Also there is need for exploring the link between blood levels of nicotine and success of procedure as well as the effects of smoking and indicators of bone adherence to the prosthesis needs to be further conducted. Couple of questions that come to mind, if nicotine plays such great inhibiting effect on the bone and collagen growth as the study claims, then why wasn’t the effect of smoking   on growth factors and their monitoring not included in the study. Also, if as the researchers claim, that nicotine has an analgesic effect on patient, was it not included as a component in the study? REFERENCES Bertagnoli. R., Yue. J.J., Kershaw.T, Shah.R, V., Pfeiffer. F, Fenk-Mayer, A, et al. (2006). Lumbar Total Disc Arthroplasty Utilizing the ProDisc Prosthesis in Smokers versus Nonsmokers: A Prospective Study with 2-Year Minimum Follow-up. Spine, 3, 992-997. ProDisc Total Disc Replacement (2008).   Spine Service- Sydney, Australia, retrieved on February 29th, 2008, from http://www.spine-service.org/dr.html ; ; ; ; ; How to cite Nonsmokers: A Prospective Study, Essay examples

Logistics and Supply Chain Management Products and Information

Question: Discuss about the Logistics and Supply Chain Management for Products and Information. Answer: Introduction Logistic management refers to a supply chain management that is used to meet the demands of the customers with the help of planning, implementation of effective movement and storage of products and information from the point of source to the point of destination (Abbasi Nilsson, 2016). Logistic management is an important element for a business and the importance of logistic management has transcended the sky. In the age of international trade, it is important that logistic management is given special attention and stress to ensure smooth functioning of the business. Logistics decides the smoothness of the flow of the goods from the point of source to the point of destination. The following report critically analyzes the challenges faced by OMEGA for transporting refined products from Singapore to Townsville, Mackay and Bundaberg. The application of logistics management and concepts are useful and critical in analyzing the challenges faced by a company regarding logistics. Logistic Goals and Objectives The goals of logistics are to efficiently handle materials and reduce cost. It intends on reducing the variable cost, which is related to the movement and storage of goods. Another objective of logistics is to reduce the level of investment involved in logistics and at the same time it intends to increase the return on the assets of logistics. At the same time it intends n improving the service to the company and the firm. The evaluation of the goals and objectives of logistics paves the way to the challenges faced by logistics of OMEGA. Logistic Challenges faced by Omega The purpose of the logistics is to plan and manage the movement and storage of refined products from one place to another. In the age of globalization the logic aspect of OMEGA has to face various challenges in order to survive in the competition. There are various factors that affect the logistics of OMEGA, especially the macro environment factors. Some of the elements that pose a challenge to the logistics to OMEGA are: Tariffs Tariffs are a tax or duty that is imposed on import and export of goods. They are macro environment element that affects international trade. They restrict trade as they limit the volume of flow of goods across the borders. From the viewpoint of OMEGA, tariffs are a major source of hindrance for the company. It includes the charges of the product for OMEGA. It affects the overall growth of the company and impacts the smooth flow of goods from the point of source to the point of destination (Selviaridis Norrman, 2015). Increased demand and customer satisfaction In the age of globalization and international trade, one fact that needs to be noted is that there is increasing demand and the need of customer satisfaction is integral and critical. In the case of OMEGA, one of the challenges that the company has to face to meet the increasing demands of the customer. In addition to this, the company also has to provide value to the customers so that it meets the customer satisfaction level. As OMEGA is trying to reduce sourcing cost and component cost, the customers interest will only be pertaining to the landed cost and the quality of the product and its overall value (Caunhye Nie Pokharel, 2012). So the major challenge for OMEGA is to reduce the cost involved with logistics and at the same time maintain the quality of the product that it provides. Therefore, one of the major challenges is to provide value and reduce landed cost. Maintenance of the velocity of supply chain Another factor that needs careful evaluation and understanding is the need to maintain the various elements in a supply chain. The company tries to increase the velocity of the product and at the same time tries to reduce cost by reducing the storage time and the damage that could be caused before the dispatching of the good. However, the extended time taken in transit has an adverse effect on the supply chain management of the company. The distance between Singapore and Australia is a long distance and in such circumstances border delays and unnecessarily extended time while the goods are in transit increase the perils of damage to the goods and it reduces the product velocity that the company aims to achieve. It makes the maintenance of the velocity of the supply chain difficult in such circumstances (Schulenberg, 2014). Maintenance of the visibility of supply chain Visibility in the supply chain is a major requirement for a company. It is important for manufacturers and companies to keep a track of the product that is in transit and which goes through multiple channels. It is important to track the time of arrival of product. Since OMEGA deals in international trade, one of the things that will be noticed is that there will be multiple carriers and it will got through multiple chains after its dispatchment from Singapore until it reaches the ports of Townsville, Mackay and Bundaberg. Therefore, since it involves multiple channels, it becomes important that tracking of shipment is done in a more proactive way. The increased supply chain variations present fresh challenges for the company. Increased documentation and the role of government in cross border trade Documentation is an important element in international trade. The flow of documents is an important feature in international trade. There are various documents that are required for international trade and more than 100 documents are required for cross border shipment. Some of the important documents that are required are Certificate of origin, commercial invoice, shippers export declaration and shippers letter of instruction. Australian Biosecurity follows the document requirement policy. As per this policy, there is minimum number of documents that is required to be submitted to the AQIS (Dekker Bloemhof Mallidis 2012). The failure to do so could create hindrance in the transit. The increased number of documentation makes it challenging for the company to discharge smooth functioning of the flow of goods and adds increased layer and wastage of time involved in documentation. The logistics will have to have through excess level of regulations that will constrict the functioning of the company. At the same time there are significant roles of government in international trade. The policies are made by the government. In the case of OMEGA, there is a significant role played by the Australian government. There are standards and requirements set according to the Australian biosecurity requirements. There are two regulatory acts as per the biosecurity requirements. These are Quarantine Act 1908 and the Quarantine regulations. As per the requirements, the goods need to be packaged and careful inspection and scrutiny of the good is required. Inspection if good is compulsory as per the biosecurity requirements. The Quarantine Act puts special emphasis on avoiding all those elements that may cause adverse effect on human beings and the surroundings. According to the biosecurity requirement, if there is a specific treatment of goods that is required, then it should use an accredited provider before the product moves for shipment (Zijm, 2016). A lot of stress is given on the quality o f product. The terms of sale, also known as incoterms also analyses the various logistics channels. The role of government is important in logistics. Government shutdown adversely affects logistics. The lack of funding of road highways and airports or ports might obstruct the smooth functioning of these strategic points. Border crossings of trucks could become difficult because of custom border patrol that would create priorities between the products and cause unnecessary delays. The Singapore government shutdown could pose a major hindrance to the security of air and traffic control due to the lack of funds of the government (Selviaridis Norrman, 2015). Legislations and rules of the government also affect the logistic process. The recent cases of Oil spills have resulted in stringent laws and regulations been implemented to offset the adverse impact and implement conservation practices. These might spring up challenges for logistics, which they need to tackle. Wave management Wave management is another challenge that OMEGA has to face in the logistics sector. Wave management refers to the arrangement of freight in an order that would allow the company to meet the requirements of the customers in an efficient and economical way and would utilize labour in an effective and efficient way. There are 72 cities in South Australia, with more than 100 companies in the arrangement of freight and cargo. OMEGA might face certain challenges regarding wave management. Economic condition and cyclical trend Another fact that needs to be kept in mind is the economy of a country. Cyclical trend of economy has a major impact on logistics. Australia is in the grip of a major global financial crisis. This could heavily impact the import of refined products (Christopher, 2016). As a result, logistics might have to adjust their supplies accordingly and the product in transit could be majorly impacted. As a result of global financial crisis, there could be major fluctuation in the currency value and consequently the market size would be adversely impact by evil of negative cyclical trend. Supply Chain Vulnerability The vulnerability related to supply chain is another factor that needs to be evaluated. The perils of destruction of goods during transit can result in loss for the company and major obstructions for the logistics. The supply chain vulnerability is an obstruction for the company (Fernie Sparks, 2014). Conclusion On concluding the report, it can be seen that OMEGA has certain objectives and goals to fulfil. There are certain challenges that OMEGA has to fulfil. Vulnerability of the product, economic factors, tariff issues, visibility and velocity of the product in the supply chain are some of the issues faced by the company. The company has to overcome these issues so that the operations can be carried out smoothly and without any hassle. The company has to identify these issues regarding the economic issues and the government regulations that hinder the process of the logistics of the company. Recommendations Some recommendations to overcome challenges in logistics are: The supply chain needs to be assessed and the network should be maintained in a more optimum and intricate details need to be noted. To company needs to focus on more fulfilment of order in a more efficient way and it should be done without increasing the cost of operation The process involved in the logistic department should be assessed to secure reduction in the cost and increase efficiency of operation Wave management and lean management should be practiced in amore better and effective way. Better technology and warehouse management should be done efficiently. Reference List Abbasi, M., Nilsson, F. (2016). Developing environmentally sustainable logistics: Exploring themes and challenges from a logistics service providers perspective.Transportation Research Part D: Transport and Environment,46, 273-283. Caunhye, A. M., Nie, X., Pokharel, S. (2012). Optimization models in emergency logistics: A literature review.Socio-economic planning sciences,46(1), 4-13. Christopher, M. (2016).Logistics supply chain management. Pearson Higher Ed. Dekker, R., Bloemhof, J., Mallidis, I. (2012). Operations Research for green logisticsAn overview of aspects, issues, contributions and challenges.European Journal of Operational Research,219(3), 671-679. Dekker, R., Fleischmann, M., Inderfurth, K., van Wassenhove, L. N. (Eds.). (2013).Reverse logistics: quantitative models for closed-loop supply chains. Springer Science Business Media. Fernie, J., Sparks, L. (2014).Logistics and retail management: emerging issues and new challenges in the retail supply chain. Kogan Page Publishers. Leiras, A., de Brito Jr, I., Queiroz Peres, E., Rejane Bertazzo, T., Tsugunobu Yoshida Yoshizaki, H. (2014). Literature review of humanitarian logistics research: trends and challenges.Journal of Humanitarian Logistics and Supply Chain Management,4(1), 95-130. Rushton, A., Croucher, P., Baker, P. (2014).The handbook of logistics and distribution management: Understanding the supply chain. Kogan Page Publishers. Sarraj, R., Ballot, E., Pan, S., Montreuil, B. (2014). Analogies between Internet network and logistics service networks: challenges involved in the interconnection.Journal of Intelligent Manufacturing,25(6), 1207-1219. Schulenberg, J. L. (2014). Systematic social observation of police decision-making: the process, logistics, and challenges in a Canadian context.Quality Quantity,48(1), 297-315. Selviaridis, K., Norrman, A. (2015). Performance-based contracting for advanced logistics services: challenges in its adoption, design and management.International Journal of Physical Distribution Logistics Management,45(6), 592-617. Sundin, E., Dunbck, O. (2013). Reverse logistics challenges in remanufacturing of automotive mechatronic devices.Journal of Remanufacturing,3(1), 1. Taniguchi, E., Thompson, R. G., Yamada, T. (2016). New opportunities and challenges for city logistics.Transportation Research Procedia,12, 5-13. Zijm, H. (2016). Trends and challenges in logistics and supply chain management.ERCIM news,2016(105), 3.