Zero tolerance policing free essay sample

Zero-resistance policing is a solid and definitive type of policing with a principle center around minor violations and open incivilities as open intoxication, spray painting, beggary. Police attentiveness is evacuated and supplanted by pummeling minor wrongdoings and the utilization of coercive force. This is required to cause a decrease in significant wrongdoings as robbery, theft and brutality. One of the principle instances of zero-resilience policing by and by is the arrangement of police magistrate William Bratton somewhere in the range of 1991 and 1997. During that period crime percentages declined to a great extent, this was viewed as a significant proof for the viability of zero-resistance policing. Albeit, other examination has demonstrated proof for additional, and perhaps progressively significant, clarifications of the gigantic decrease in wrongdoing. There was at that point a decrease in murder rates, the quantity of individuals utilizing rocks was declining, the medications showcase was evolving, insight drove policing was up and coming and there was an expansion in network wrongdoing counteraction (Bowling, 1999; Dixon, 1999). We will compose a custom article test on Zero resistance policing or on the other hand any comparable point explicitly for you Don't WasteYour Time Recruit WRITER Just 13.90/page Thinking about this, we can address if zero-resistance policing is as successful as guaranteed. To comprehend the impacts of zero-resistance policing, it is valuable to take a gander at it from an alternate perspective, a criminological perspective. There are numerous criminological hypotheses which advance zero-resistance policing, yet additionally a ton of speculations assaulting it. In this examination article the primary criminological hypotheses will be considered bringing about a decision around zero-resilience policing. The principle question is: To what broaden does zero-resistance policing decrease wrongdoing from a criminological perspective? Broken windows and broken windows-overhauled The most significant hypothesis which gives a base to zero-resilience policing is the wrecked windows hypothesis of Wilson and Kelling (1982). This hypothesis centers around the outcomes of minor wrongdoings and weakening of nature. On the off chance that the physical condition of a local decays and if there are conduct appearances of confusion, it will give a message of lack of engagement. This will give lawbreakers the inclination that the likelihood of identification is low (Bernasco Nieuwbeerta, 2003). Another outcome of the conduct and physical issue is that the individuals will have developing sentiments of instability and dread. O ‘Brien and Wilson (2011) contend thatâ individuals decide if an area is protected or not by searching for indications of turmoil as beggary or spray painting. The more incivilities they see, the less secure individuals will feel. As a result of the dread, there will be a lessening of casual social control. The low level of social union is required to bring about more wrongdoing, as once more, lawbreakers will get the inclination that danger of authorization is low (Bernasco Nieuwbeerta, 2003). A low level of social attachment can be appeared by an absence of collectivity, a high private versatility, free connections, minimal formal and casual control and inadequate social associations (Lanier Henry, 2010a). To put it plainly, physical turmoil and the nearness of minor wrongdoings will bring about more wrongdoing (Sampson Raudenbush, 2004). Zero-resistance policing is along these lines seen a decent technique to forestall wrongdoing since it will pummel the physical and social issue. Cops have no watchfulness so no exemptions would be made. The messed up windows hypothesis appears to be persuading yet when we investigate, are some faulty focuses. Sampson and Raudenbush (1999) have changed the messed up windows proposal and they accept that the minor wrongdoings are not the reason for increasingly genuine wrongdoing but rather there is another, fundamental factor that causes both minor violations and significant violations. The fundamental factor they mean is the level of collectivity and union in the area. Turmoil is viewed as an appearance of wrongdoing and consequently shows that there is a low level of social union. Additionally the social complication hypothesis of Shaw and McKay (refered to in Lanier Henry, 2009a, pp. 190 †251) contends that there will be more wrongdoing in neighborhoods with a low level of social union. To put it plainly, this implies the minor wrongdoings are not the fundamental driver of increasingly genuine violations, however it is the level of social attachment in an area. In this manner zero-resilience policing won't be successful in light of the fact that it doesn't concentrate on improving the social union and the feeling of collectivity in an area. The policing system is particularly centered around minor wrongdoings and no special cases can be made in light of the fact that the expulsion of the police watchfulness. This exacting arrangement is bound to make an antagonistic connection among police and open than to make a bond with the general public. As indicated by the changed broken windows hypothesis, policing techniques which depend on trust, correspondence and authenticity are relied upon to be the best (Burke 1998; Dixon, 1999). The hindrance impact of zero-resilience policing Another hypothesis supporting zero-resilience policing and its extreme and intense approach is the balanced decision hypothesis. This hypothesis depends on the possibility that individuals are reasonable creatures and they are free really taking shape of their choices. They will gauge the expenses and benefits and relying upon the result they choose what to do. Wrongdoing is viewed as a result of this objective decision whereby the advantages are greater than the expenses. The decision individuals make is unequivocally impacted by situational factors. To forestall wrongdoing it is in this manner essential to change the situational factors and give individuals the inclination that the expenses are higher than the advantages (Lanier Henry, 2009b). Zero-resilience policing can be viewed as a decent method to give individuals that sentiment of being controlled. At the point when the police endures no violations at all individuals will simpler choose to avoid carrying out a wrongdoing in light of the fact that the normal danger of assent is high. Notwithstanding this hypothesis, it is imperative to develop the idea of prevention. There are two types of discouragement, general prevention and explicit prevention, both with the treat of discipline as primary guideline. The previous is tied in with keeping the entire network from carrying out a wrongdoing by rebuffing a couple of them as model. The last spotlights on keeping one specific individual from perpetrating a wrongdoing by rebuffing the individual itself. Since the treat of discipline, the expenses of perpetrating a wrongdoing will be higher and in this manner individuals will be less inclined to violate the law. As turns out to be clear the discouragement viewpoint is firmly identified with the levelheaded decision hypothesis. A significant inquiry is, under which conditions is the obstacle impact ideal? There are a couple of conditions which are referenced by Jeremy Bentham (refered to in Ashworth, 1992, pp. 53-61), to be specific assurance, celerity and seriousness. Assurance is viewed as the most significant one and seriousness as the least significant one. It is hard to state if zero-resilience policing meets all the necessities to have a maximal obstacle impact. Unmistakably individuals turned out to be increasingly sure of being rebuffed for minor wrongdoings and since assurance is regularly observed as the principle condition, a critical impact is normal. For instance the stop and searches by cops will lessen road guiltiness in light of the fact that the anticipation of getting captured gets higher (Innes, 1999). Likewise zero-resistance policing meets the seriousness part since sanctions are higher. Demonstrating the celerity part is increasingly troublesome, quite possibly the punishmentâ process delays due to the over-burden of cases. On the opposite side the authorizing procedure might be finished all the more rapidly in view of its high need. To put it plainly, zero-resistance policing appears to produce a hindrance impact which lessens guiltiness in the city. Be that as it may, the hindrance impact appears to have its cutoff points and it is hard to demonstrate the effectivity of discouragement. From the outset it expect that guilty parties think soundly, yet generally they don't consider the outcomes while carrying out a wrongdoing. Moreover the prevention by the treat of discipline has absolutely not the greatest effect on the guilty party, different things like family are frequently discovered increasingly significant. Likewise, the hindrance impact has regularly got a little reach in light of the fact that not every person in the general public becomes more acquainted with which approvals are given (Ashworth, 1992). Along these lines, we can ask ourselves how compelling zero-resilience policing will be practically speaking on the grounds that the viability of discouragement is flawed. It is additionally critical to remember opposite symptoms, as I referenced previously, the normal decision hypothesis accept that intense arrangement and a significant level of control can stop individuals from perpetrating a wrongdoing. Be that as it may, a significant level of control won't generally affect the general population. The negative impacts of intense policing can be found in the results of the huge number of stop a nd searches in the UK. Each time somebody is halted and looked without a legitimate explanation, it harms the open certainty and its regard for the police. Further, the utilization of the stop and searches frequently ends up being lopsided in light of the fact that they for the most part centers around poor regions. Some ethnic minorities are bound to live in this poor zones which holds that they are all the more regularly focused by stop and searches. Imbalances like this can cause brutality and mobs, for instance the uproars in the UK in 2011. Youngsters felt outrage against the police and the lopsided utilization of stop and searches activated them to begin an uproar (Bowling, 2008). Authenticity and correspondence As turns out to be obvious from the case of the UK riots in 2011, it is extremely significant for the police to be seen as genuine, trustable and to have the option to speak with the regular people. Authentic policing isn't simply increasingly mainstream however it is additionally progressively successful in diminishing wrongdoing, on the grounds that the general population is all the more ready to give data and all the more ready to stand the la

Research in Motion Coursework Example | Topics and Well Written Essays - 1500 words

Research in Motion - Coursework Example The Blackberry telephones spearheaded the period of advanced mobile phones in spite of the fact that the opposition has developed in the ongoing years from different stages, for example, Android, iPhone and Windows. The interest for Blackberry telephone has altogether expanded in light of the fact that most organizations have received endeavor innovations and there is a developing worry of representatives who need to access corporate information safely while out of office. Most cell systems give information benefits thus the Blackberry telephone fits superbly in the environment. Request has likewise been fuelled by the developing changes in buyers’ inclinations. The advanced cell showcase is currently significantly dependent on stage as opposed to equipment and this has expanded the applications accessible to the purchaser henceforth expanding the interest for the PDAs. The cell phones have become a focal piece of an individual’s life consequently purchasers require a g adget that can offer additional highlights (Baumol and Blinder, 2011). The client base has likewise become fundamentally because of an expanding working class who are pulled in to purchase the Blackberry telephones. The expanded interest has brought about the exponential increment in deals and benefits. The flexibly of PDAs has additionally expanded because of innovative progressions that have made it simpler and less expensive to deliver them. They are numerous organizations creating advanced mobile phones and as such the quantities of telephones made is high. From the previously mentioned, we understand that the gracefully has expanded after some time. Along these lines, it is apparent that more units must be offered to achieve benefit. Cell phone request development The market structure of Blackberry telephones can be portrayed as an oligopoly. The primary players in the advanced mobile phone advertise are Apple (iPhone), Nokia (Symbian), Google (Android) and Microsoft (Windows P hone). The item offered by these contenders is separated through different changes to the working framework. The boundaries to section in the advanced cell showcase are high. Infact, an organization needs to lay a tremendous capital speculation and amazingly forceful showcasing strategies so as to begin in this market. The valuing in this section is genuinely uniform and high. The advanced cell advertise is portrayed by consistent development if just to stay serious. The turnover of customers is high since purchasers would wish to evaluate the new and extravagant applications in the distinctive advanced cell stages. Piece of the pie Comparison (January 2012) In request for Blackberry to keep succeeding in this market, there is requirement for constant development and propelling of new item. The market of cell phones is dynamic and this necessitates an organization remains on the cutting edge of advancement. The other pattern that has a promising future is the (applications) showcase . The purchasers need applications in their telephones that make their lives simpler and loaded with fun. To thrive in this fragment, Blackberry should try to have a vigorous network of engineers through giving of motivating forces. The ongoing information blackouts experienced ought to be a relic of days gone by as this may prompt mass migration of current clients of the administrations (Redo, 2008). The center datacenters ought to be sponsored up and numerous fall flat over components set up to ensure supporters administration accessibility. Blackberry telephones have extremely low value versatility. This suggests regardless of whether the value transforms, it has almost no impact on request. With more salary, there is a probability of more purchasers of the

How to Write a Thank You Writing Paper

How to Write a Thank You Writing PaperA thank you writing paper can be an opportunity to express your gratitude for the favor that has been done for you. Thank you cards give many people a way to express their appreciation. This can be both simple and creative and it can make you feel better after someone has made you feel really appreciated.Gratitude is not about what you have not done for someone. It is an expression of thanks for all the wonderful things that someone has done for you. Thank you cards are an easy way to show someone how much you appreciate their efforts.However, when people are trying to determine how to write thank you notes, they tend to be overwhelmed by the task at hand. There are so many things to think about and there are so many options to choose from. Some people even write thank you notes for many different people. This can make the task of choosing a card very overwhelming.Creative people tend to use words to express what they want to say in a clear manne r. A thank you writing paper should include plenty of pictures can really add a personal touch to a note. Whether it is an actual picture of the person that gave you the gift or a picture that represents the item or service that you received, that picture will mean something to the recipient.Thank you cards come in many styles. They can be simple, with just the recipient's name on the front and a thank you note inside. Alternatively, they can be elegant, having all of the recipient's name on the front along with fancy envelopes and tie dye ribbons. They can also be pretty in their own right, which might be more suited to an event that is more formal in nature.These days, people seem to be less hesitant to use thank you cards. In fact, many stores now sell them as business gifts. Some people prefer them to not only be personalized but also be a little fancier than the typical card. This makes them great if you are looking for a way to thank a person who helped you out in your profess ional life.Thank you for writing paper can help you express how grateful you are for a gift or the service that was given to you. For example, consider how to write a thank you note for a baby shower. You can take pictures of the new mother and put them into a thank you card for the baby shower, or perhaps you can find a photograph of the baby for the new mother to put on the thank you card. If you are someone who offers services to another person, be sure to put a specific image of that person on the thank you card.Thank you for writing paper is something that should be fun to write and to print. It is a great chance to include pictures and to tell someone how much you appreciate them being a part of your life. There are many templates available that you can use, and it is always a good idea to print off a number of cards before you get started, just to make sure that you are using the right template for what you are doing.

Financial Ratios Analysis and Comparison Paper - 1478 Words

Financial Ratios Analysis and Comparison Paper Dianne Davis MHA 612 Professor Johnson June 7, 2014 Abstract It is important for healthcare organizations to understand their present performance and weak areas in order to generate more effective operational strategies. Financial ratio analysis is an effective tool to determine hospital’s performance on several indicators such as ability to pay debt, capability to generate revenue, and sales performance etc. The objective of this paper is to describe role of different financial ratios in understanding organizational performance and in developing new strategy. The paper also presents comparative ratio analysis of local healthcare organization and industry†¦show more content†¦According to the authors, ratio analysis is very effective way to measure financial performance of hospitals (Burkhardt Wheeler, 2013). The authors mentioned about two major types of ratios important in healthcare industry i.e. return on investment and operating profit. Generally financial ratios can be divided in four major categories: liquidity ratios; assets turnover ratios; debt ratios; and profitability ratios. These financial ratios cover all major dimensions of business performance; hence a manager should include these ratios in his report (Cleverley et al., 2011). Liquidity Ratios: These ratios help company in determining its capability to pay short-term debts. Liquidity ratios inform about, how quickly a firm can obtain cash by liquidating its current assets in order to pay its liabilities. General liquidity ratios are: current ratio and quick ratio. Current ration can be obtain by dividing company’s current assets by its’ current liabilities. Generally a current ratio of two is considered as good (Cleverley et al., 2011). Quick ratio also known as acid test determines company’s liabilities that need to be fulfilled on urgent basis. Quick ratio can be obtained by dividing quick assets by current liabilities. Quick ratio is considered as stricter because it excludes inventories from current assets. Generally a quick ratio of 1:1 is considered as good for the company. Higher quickShow MoreRelatedEvaluating The Performance Of A Company1124 Words   |  5 Pagesand review of financial information and statements. Financial statement an alysis is a method of reviewing and analyzing a company’s or organizations financial statements such as their balance sheets, income statements, and statement of cash flows. Financial statement analysis helps companies gain an understanding of the financial position of the company, results of their operation, and cash flow of their company, which is also the main purpose of financial statements. In this paper, I will discussRead MoreRatio and Financial Ratio Analyisis1712 Words   |  7 PagesRatio and Financial Statements Analysis Kimberly Y. Gruber University of Maryland University College Dr. Sunando Sengupta 07/25/2013 Turnitin Score: 23% Executive Summary The purpose of this paper is to examine ratio and financial statement analysis. Such analysis is a useful tool for managers and stakeholders to evaluate a company’s financial health in order to identify opportunities for growth and areas of weakness so as to institute corrective measures.   Financial statements are usedRead MoreFinancial Statements: Industry Comparison1557 Words   |  7 PagesFinancial Statements: Industry Comparison University of Phoenix BSA 500: Business Systems I Instructor: May 28, 2007 Financial Statements: Industry Comparison More often managers are exposed to financial data and the need exists to develop knowledge and understanding of financial accounting concepts and principals. 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See Some Triboluminescence Examples

You may be familiar with the Wint-O-Green Lifesaverâ„ ¢ spark in the dark, but if you dont have Lifesavers handy, there are other ways you can see triboluminescence. Triboluminescence results from the fracture of (usually) asymmetrical materials. The break separates electrical charges, which recombine and ionize the air. The ionization of nitrogen in the air produces ultraviolet light, but you cant see that. You can observe triboluminescence when another material is present that absorbs that ultraviolet light and re-releases it in the visible range (fluoresces). Here are some examples: Cracking Wint-O-Green LifesaversCrush a wintergreen-flavored Lifesaver candy with your teeth or a hammer. You get triboluminescence whenever you smash sugar, but there usually isnt enough light for you to see it. The methyl salicylate in the wintergreen oil is fluorescent and converts the ultraviolet light into blue light. If you cant find this flavor of Lifesavers, you can use sugar with wintergreen oil or clove oil.Unwapping a Band-Aidâ„ ¢Some Band-Aid wrappers will emit a blue-green glow when they are unwrapped quickly. While you can unwrap the bandage in the dark, youll probably want to turn the lights back on before applying to a wound!Cutting a DiamondThis is not something most of us are likely to do, but some diamonds will fluoresce blue or red when being rubbed or, more usually, cut.Unrolling Friction TapeFriction tape is that cloth tape that has a rubber adhesive such that it is sticky on both sides. It can be used as an electrical insulator, but youll usually see it in t he context of sports, to wrap hockey sticks, tennis rackets, baseball bats, etc. If you unroll friction tape in the dark youll observe a glowing line as the tape is pulled away from the roll.Opening Sealed EnvelopesThe adhesive used to seal some envelopes will fluoresce blue as the contact is broken.Remove Ice from the FreezerThis is an example of fractoluminescence, which is sometimes considers synonymous with triboluminescence. Fractoluminescence is light produced by fracturing a crystal. The fracture separates charge. If enough charge is separated, an electrical discharge may occur across the gap. If you remove ice from a freezer in a dark room, you may see flashes of white light accompanying the crackling sounds of ice undergoing rapid thermal expansion.

Analysis Of Martin Luther Small Catechism - 1256 Words

The Small Catechism was written in 1529 by Martin Luther. He wrote it after he visited with common people and saw a severe lack of instruction by both the head of the households and pastors on how to lead a good Christian life (Deuteronomy 6:5-9). He was so upset he noted; â€Å"the wretchedness I beheld† and said â€Å"many pastors were quite incompetent and unfitted for teaching† (Preface to Small Catechism) (LC: Live Session). The Small Catechism is a handbook to Christian Doctrine and Christian Living. It includes the 10 Commandments and how to follow them, the Lord’s Prayer, introduction to Christian Life, Baptism, Lord’s Supper and how the Holy Spirit brings the Lord to u (LC: Table of Duties). Luther’s Small Catechism is written in a†¦show more content†¦Charles V was resistant to the reforms wanted by Lutherans and wanted to condemn Martin Luther for heresy. The confession was written as a script for the princes about reform. Ho wever, so many other princess read the confession and signed and it became a confession of the Lutheran beliefs (LC: Charles V) (Romans 11:6). John Fredrick - Elector of Saxony knew how to use the political system of the greek empire and help lead this reform movement (LC:John Fredrick). The Augsburg Confession is the basis of the foundations of our belief and clarifies our instructions given to us in God’s holy Bible. It is the center of the Book of Concord because it looks back to the creeds and forward describing our confessions of living a good Christian life (LC: The Augsburg Confession). The Apology to the Augsburg Confession was written in 1531 by Philip Melanchthon. He wrote it because the Roman Catholics did not give the princes a chance to reply to the Augsburg Confessions. We can see clearly in Melanchthon’s writing his method of centering message in Jesus Christ (LC: Apology of Augsburg). â€Å"After the Roman theologians had condemned many of the teaching of the Augsburg Confession, Melanchthon authored this lengthy defense (Book of Concord, page 15). This was the Lutherans strongest defense of justification by faith (Article 4) (Genesis 15:6; Romans 4 1:5). The Apology also stresses that absolution and forgiveness is valid from any Christian, pastor,Show MoreRelatedGreat Innovators Essay1414 Words   |  6 Pagesone’s he invented were being used all over Europe to spread the ideas of many other happy people. Luther Martin Luther was conceived into the religion of Roman Catholicism in the minute town of Eisleben, near modern day Berlin in Germany. His father was a miner that worked through all the jobs he needed to get done to make enough money and to ensure proper education for his son. Martin Luther seized a Master of Arts degree from the University of Erfurt when he was only a mere twenty one yearsRead MoreRastafarian79520 Words   |  319 Pagesreligion include: 1. Rastafarianism has been around for only about seventy years. Yet in that time it has gained inexplicable fame around the world, boasting converts from all races and nationalities. 2. Adherents of the faith appear to be relatively small in number. One study suggests that less than one percent of Jamaicans describe themselves as Rastafarians. Yet the average non-Jamaican assumes that Rastafarianism is the national religion of Jamaica. 3. Rastas believe that Selassie is the returned

Statistics Business Transformation Business Techniques

Question: 1. Statisticians divide variables into different classes (or types). Describe the classes of variables and give examples of each. Briefly describe (for each class of variables) the methods used to compare 2 independent groups of cases. Describe the assumptions and/or limitations of each technique. 2. What do you understand by the following statistical and epidemiological terms? You may find it helpful to use examples to illustrate your explanations. a)Boxplot (box and whisker plot) [20 marks] b)Addition law of probability [15marks] c)Retrospective study [15marks] d)R-squared (r2)[15marks] e)Cluster sampling[15marks] f)Standard error of a mean[20 marks] 3.This question is concerned with statistical measures to assess the reliability and accuracy of tests (for example, for diagnosing caries based on radiographs). a) What method(s) would you use to measure the extent to which 2 observers agree whether teeth are carious or not (reliability)? b) What method(s) would you use to measure the extent to which an observer agrees with a gold standard test (accuracy)? c) When might you use a ROC curve? d) Show the principles behind ROC curves by presenting a small example. 4.What is a 95% Confidence Interval for the mean of a variable? Explain how you would calculate it and state the assumptions behind the method you describe. Explain the relationship between a 95% Confidence Interval for the mean and a one-sample t-test. Explain briefly the principles behind, and the use and limitations of threeof the following. Suggest situations where they might be used when analysing dental data. [equal marks for each sub-section] a)Oneway analysis of variance (ANOVA) b)Survival analysis c)Log transformation d)Paired samples t-test 6 A researcher claims the mean DMFT of males aged 14 to 16 in a particular British region is 6. a) How you would set up a study to assess this? b) What are the appropriate hypotheses? c) How would you summarize the observations? d) What statistical test you would apply? e) How would you interpret the results of such a test? f) How would the size of your sample tend to affect the results? Answer: 1: Observations on a particular trait or character that are distinguishable or countable are called variables. A variable can be any number or measurement or characteristics whose value can vary over a certain range. Income of a person in a month is an example of a variable. Income of a person can take any values starting from 0. Age of students in class, the color of a flower, the number of books in a library is other examples of variables. Variables are classified into two types. By counting, the variables are categorized in to Qualitative and quantitative variables. Variables that can be counted are called quantitative variables. Age of students, the number of books in a library is examples of quantitative variables. On the other hand, the variables like the color of a flower, the first letter in the number plate of a car cannot be counted. These variables are referred to as qualitative variables. A quantitative variable can be classified into two types-discrete and continuous variables. Variables that can take values only a discrete set of points are referred to as discrete variables. While, on the other hand, if a variable takes values on a continuous scale then it is known as continuous variables. Number of books in a library, the number of people in a household is examples of discrete variables as these variables take distinct values. Height, weight, age are examples of continuous variables. Qualitative variables are also referred to as categorical variables as they describe a particular characteristic of a data point like to which category the data point belongs. Categorical variables can be of two types: Nominal variable: The categorical variables that cannot be arranged in an increasing or decreasing order are called nominal variables. Nominal variables can only be classified into a particular group. Type of business, eye color of a person is examples of nominal variables. Ordinal variables: The categorical variables that can be arranged in an increasing or decrease order are termed as ordinal variables. Grades that are given in an examination, any attitude towards a decision (disagree, agree, moderate, strongly agree) are examples of the ordinal variable. Two independent groups of variables can be compared using a different test. If the variables are quantitative, then t-test can be performed to test the whether the two groups are independent. If the variables are qualitative, then a two sample proportion test can be performed. The t-test can be used for the test of equivalence of two means of two independent samples. The hypothesis is given by H0: 1= 2 against H1: The means are unequal. The statistic for the test is: If the calculated t value greater than tabulated t value then the given hypothesis is rejected. The rejection of hypothesis implies that the two means are equal. If the variables are quantitative, then test for proportion can be performed. The hypothesis to be tested is p1=p2 against H1: proportions are unequal. The test statistic is given by Z= /s.d S.d=sqrt((p(1-p)(1/n1+1/n2)) Where p1 is the estimated proportion of the first sample and p2 denotes the estimated proportion of the second sample. "n1" and "n2" are the sizes of the two samples. The test statistic is rejected if the calculated p-value is less than the level of significance . The limitation of t-test is that the underlying distribution of the sample is assumed to be normal. If the distribution is not a normal distribution, then a robust statistic like median has to be used. Then the median test can be performed. In the median test, the hypothesis to be tested is H0:me1=me2 against H1: me1me2. In the proportion test, the sample variance is the pooled variance of the two samples. Pooled variance can be assumed if the variance of each group is more or less same. If the two groups greatly differ by variance, then pooled variance cannot be used. In that case, test for proportion is invalid. 2: Box Plot: Box plot or box and whiskers plot is a way to represent statistical data graphically. A box plot is also termed as box and whiskers plot. The lines that extend vertically from two sides of the box are called the whiskers. A box plot is a nonparametric representation. It does not assume any underlying distribution. The Box in the box plot is the space between first and the third quartile. Outliers can be easily detected with the help of box plot. The box plot gives an idea about the spread or dispersion of the dataset. Any box and whiskers plot depicts the following statistical measures: Median: The median is the midpoint of the data and is represented in the box plot by the line inside the box. From the position of the median in the box plot, one can determine whether the distribution is skew or symmetric. Sometimes an additional line for the arithmetic mean is also given inside the box. If the mean and median line coincides, then the distribution is symmetric. Otherwise, it is skewed. Quartile: 75 percent of the observation falls below the first quartile, and 25 percent of the observations fall below the first quartile. Range: It is the difference between the minimum and maximum observation in a dataset. Interquartile range: Interquartile range is the length of the box.50% of the observations are expected to lie within the range. Outlier: Any outlier if present is detected in the outside the interquartile range. The outliers lie between the points 1.5 IQR and 3 IQR. Addition law of probability: Two events A and B are considered. The events are mutually exclusive if the probability of their intersection equals zero. Two events are collectively exhaustive if the union of the two events makes up the entire sample space. P( Addition law of probability states that A1, A2,,, An be n events The events possesses the above two properties that are the events are events collectively exhaustive and mutually exclusive. Then the probability of the union of the events is equal to the sum of their probabilities. Retrospective study: A retrospective study refers to the longitudinal study design of two cohorts. In this kind of study, one cohort is exposed to particular disease and another cohort is not exposed to the disease. The two cohorts are compared to identify the factors in their history that can be associated with the disease. The data are collected from past values. The study is mainly conducted to determine the risk associated with the disease and to estimate the number of causalities from the disease. The risk ratio or Odd ratio of the two groups is calculated which gives the relative risk of the disease in the particular cohort. The Risk ratio is given by the following formula: DISEASE PRESENT DISEASE ABSENT Group1 A b a+b Group 2 C d c+d a+c b+d n Then risk ratio is given by Odds ratio is given by: OR=ad/bc If the value of Risk ratio is greater than one, then, the cohort has a less chance of developing the disease.If the value of risk ratio is greater than one, then the cohort has a higher chance of developing the disease. Same interpretation also applies for the Odds ratio. The advantages of Retrospective study is that it is less costly, less time consuming and could easily be conducted and gives a better comparison of disease between the cohorts. For example, if one wants to compare the oral health status of two groups, an idea about the oral health status of the new generation can be obtained from the oral health status of the mothers. R-squared: R-squared values are calculated to determine how good a fitted model is. The R-squared value is the ratio of the residual and total sum of the squared values. The greater the value of R squared statistic in the case of a regression model; the better is the fitted model. R-squared=RSS/TSS. A good model is expected to have the minimum error. The sum of errors is equal to zero. To make a comparison, squared sum of errors has to be considered. The smaller the value of RSS or residual sum of the square the better is the model. So more the value of R squared, the better is the model. R-squared value does not consider the number of parameters involved in a model. For a model to be good, the model should be parsimonious. For this, another measure of R-squared is developed which is called adjusted R-squared. The adjusted R-squared measure is given by the following formula: R-squared (adjusted)= 1- (RSS/n-k)/(TSS/n-1) .K is the number of parameters. So higher the value of adjusted R-squared the better is the fitted model regarding both parsimony (minimum no of parameters) as well minimum errors. Cluster Sampling: Sampling is the procedure in which only a drawn sample from the population is considered for the purpose of statistical computation. Cluster sampling is an efficient sampling procedure where the total population is at first divided into some clusters and then the sample is collected from this clusters. The clusters are made as homogeneous as possible. Cluster sampling can be one stage or two stages. For example, for obtaining sample of household expenditure from a city, at first, the city can be divided into several blocks according to locality and then sample could be collected from each of the blocks. These blocks form the cluster. Standard error of a mean: The average sample value is an unbiased estimate of the average value of a population. The deviation of the mean of sample from the population mean value is the error. The standard deviation of the mean of sample value is called the standard error of the mean. 3: Inter-rater reliability is used to measure the extent to which two observers agree whether the teeth are carious or not. Inter-rater reliability is used in case of subjective judgment. If the rating scale is continuous, then Pearson's product moment correlation is used. If the rating scale is ordinal, then Spearman's product moment is calculated. For the case of a categorical variable, Cohen's Kappa is used. The formula for Cohen's Kappa is: Where O is the observed agreement, and E is the expected value of the agreement. N is the total sample size. The failure rate is used to measure the extent to which an observer agrees with the gold standard test. The failure rate is given by f(t)/R(t) where f(t) is time to failure of an event and R(t)=1-F(t).F(t) is the cumulative distribution function of t. C.ROC curve is drawn to discriminate between the presence or absence of a disease.ROC curve is drawn by plotting FPR against the TPR. The FPR is equal to (1- specificity), and true positive rate is calculated by sensitivity. Sensitivity refers to the proportion of population with the disease tests positive. Specificity relates to the part of population without the disease testing negative. The area inside the curve of ROC helps to determine the level of discrimination between the individuals with test positive and individual with test negative. The underlying principles of the ROC curve are: The threshold value for drawing the ROC curve influences the specificity and sensitivity values. The threshold value should be so chosen that distribution of test results for presence or absence of disease should not overlap. In most of the cases, the two distributions overlap. But in most of the cases, the two distributions overlap. So the diseased people are misclassified as normal people. Lowering the threshold value will increase specificity while higher threshold value decreases specificity. 4: The mean of a variable that is to be calculated is the sample mean. The population mean is different from the sample mean. In a practical situation, a confidence interval with confidence coefficient 95 for any statistic gives the probability that the value of the mean lies within the interval with confidence limit 95%. That means if the sample is repeated as many times as possible, the probability that the mean value lies within the interval is 0.95.if the distribution of test statistic is standard normal, then the confidence interval is given by the following formula: Ucl=xbar +s/sqrt(n)*z Lcl= xbar-s/sqrt(n)*z Again if the test statistic follows a t distribution, then the upper and the lower control limits are given by: Ucl=xbar +s/sqrt(n)*t Lcl= xbar-s/sqrt(n)*t The t statistic is generally used in case of confidence interval if the standard deviation value is to be calculated from the sample. If the population standard deviation value is given then, one can use z test to determine the value. 5: The following methods are used for analysis of dental data: One way ANOVA: One way ANOVA or variance analysis is carried out to test whether the means of several groups are equal or not in the case of fixed effect model and equality of variance of several groups in case of random effects model. In one way ANOVA, there is only one factor affecting the values of the variable. The one-way ANOVA model is given by: Where yij represents j the observation in the ith cell. is the common mean effect and i is the effect due to the ith group and eij is the error assumed to follow N(0,^2) distribution. The random effect model is given by Yij=+ai +eij , where eij is the random effect due to the ith group. An example where ANOVA test can be conducted in dental study: One wants to measure the performance of five brands of toothpaste that heals tooth sensitivity. Certain volunteers are selected and each of them is given a brand of toothpaste to use. After the completion of one tube, the patients were asked to give a score about how their sensitivity problem is. The mean score from each volunteer is collected, and the mean scores are tested with the help of ANOVA, and the toothpaste that performs best can be found out. ANOVA test has certain assumptions: The error is distributed as normal with zero mean and uniform variance ^2 across all groups. The observations are supposed to be independent. If the above assumptions are violated, then ANOVA test cannot be carried out. Besides, ANOVA can tell only if all the means are equal. If the means are unequal, then one has to perform t-test to compare two means. Survival Analysis: Survival analysis determines the time to failure (or survival) of an event. Survival analysis is particularly useful in case of censored data. For example, if one wants to find the time required f or recovering from a disease then survival analysis can be used. Survival Analysis can be used to study a particular impact of certain dental surgery on the patients. For this analysis, one can study the time to the occurrence of the event(death) of the patient along with other factors. The study can be done with the help of Kaplan-Meir estimator. If there are several factors affecting the time, then a regression model such as Cox model of proportional hazard functions can be used. This analysis aims to study the time to occurrence of an event. It gives the chance or probability of survival from a particular disease. Survival analysis also takes into account the effect of other covariates over time to survival. But survival analysis has certain limitations. The limitations of Survival regression is same as that of ordinary regression problems. The statistical data and real life data are different. So the estimates from survival analysis are valid up to certain extent and may not be true for every case. The error in survival models is assumed to be normally distributed. Another important feature in survival analysis is censored observations. If the number of edited cases is too many, then survival analysis can lead to faulty results. C.Log transformation: Log transformation is used in the following cases: 1.To make the data skewed: Log transformation is mainly used to make a skewed data more less skewed. Taking logarithm of the values, one can compare the geometric mean of the values instead of arithmetic mean. For example, if the brain weight of a person is plotted with body weight then the distribution is skewed as the body weight is very large as compared to brain weight. Plotting the log-transformed variables, the distribution becomes less skewed. 2.Log transformation is used if the dependent variable is discrete or binary and the response variables are continuous. By taking logarithm of variable, the response variable can be converted into a discrete variable. This often happens if the response variable is dependent on some categorical variable. To standardize the data: Sometimes data do not follow normal distribution. Taking a log transformation of the values will make the data follow normal distribution. Log transformation has certain limitations. It is not applicable to confounded data. Data point has to be independent. Otherwise, change is not useful. D.T-test: This is a test of paired sample observations which is used to test the dependence of the arithmetic mean value of two variables. Paired sample t-test can only be done if the sample size of two samples is equal. In paired sample t test the difference of each observation is calculated. Let di denote dit. The mean of the observation is tested to be equal to zero or not. The hypothesis of interest is to test H0: The mean value of the paired observation is equal to zero against H1: not H0.and the test statistic is (dbar/sd) where dbar is the mean of di and sd is the standard deviation of di values. The statistic for performing the test is said to follow a t distribution. In this case, the d.f will be equal to n-1 where n is the sample size. The limitations of paired t-test are that it is applicable when the groups have same sample size. If the sample size varies then, another t-test has to be performed. It is also applicable to datasets that have standard normal distribution. If underlying distribution is nonnormal, then nonparametric tests could be performed. 6: The DMF index is a method used in dentistry for testing dental caries. The dmft of males between 12 to 14 years of age is six as claimed by a certain researcher. So to support this claim a test has to be conducted. A sample has to be drawn from the population of males between the age group 12 to 14 years. Then the mean value of dmft obtained from the sample has to be tested. The hypothesis that has to be tested in this case is whether the mean or median of the population is equal to 4 or not. H0: = 6 against h1: six where represents the mean of the distribution. Or, h0: me=6 against h1: me6. The distribution of the population of males can be assumed to be normally distributed. In that case, one can test whether the mean value is equal to 6 or not. The mean value of the population can be estimated by sample mean. Then the problem is to test whether the sample mean value is less than a particular value. If the population does not follow standard normal distribution, then a nonparametric test for median of the observation can be done. If the population distribution is assumed to be normal, then a test for the sample mean could be performed. Then the problem is to test h0: =6 against h1: 6. If the value of s.d of population is known, then z-test can be performed. If the population value of standard deviation has to be estimated from sample value, a t-test has to be performed. The statistic for the z test is given by: Z=( - )/ where is the sample mean. The test statistic for t distribution is: T=( - )/s where s is the s.d of sample. Interpreting test results: A test is rejected if probability value of the test is less than level of significance. H0 is rejected if z-value is greater than z/2 at level of significance . Z/2 is the tabulated of value of upper alpha point from the standard normal distribution table. In case of t test the null hypothesis is rejected at level of significance if tt value determined from sample is greater than tabulated t value at the level of significance /2 at degrees of freedom n-1. The size of the sample is important in case of performing a test. The accuracy of a test depends on the sample size. The value of sample size is given by the following formula: N = (1.96*sigma^2)/e^2 .here sigma denotes value of standard deviation. E denotes the correction limit within which the value of the mean that is to be estimated.