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First line treatment with omeprazole provides an effective and superior alternative strategy in the management of dyspepsia compared to antacid/alginate liquid: a multicentre study in general practice arthritis in back mattress buy arcoxia visa. Antisecretory therapy in 1017 patients with ulcerlike or refluxlike dyspepsia in general practice arthritis light relief purchase arcoxia cheap. The management of acid-related dyspepsia in general practice: a comparison of an omeprazole versus an antacid-alginate/ranitidine management strategy arthritis medication enbrel generic 120 mg arcoxia amex. Cost effectiveness of treatment for gastro-oesophageal reflux disease in clinical practice: a clinical database analysis arthritis diets work cheap arcoxia online master card. A cost-effectiveness analysis of prescribing strategies in the management of gastroesophageal reflux disease. The second Canadian gastroesophageal reflux disease consensus: moving forward to new concepts. Modelling different approaches to the management of upper gastrointestinal disease. The clinical and economic impact of competing management strategies for gastro-oesophageal reflux disease. Testing for Helicobacter pylori in dyspeptic patients suspected of peptic ulcer disease in primary care: cross sectional study. A prospective study of the management of the young Helicobacter pylori negative dyspeptic patient: can gastroscopies be saved in clinical practiceff For what conditions is there evidence-based justification for treatment of Helicobacter pylori infectionff Helicobacter pylori consensus: Report of the 1997 Asia Pacific Consensus Conference on the management of Helicobacter pylori infection (Singapore; August 30-31, 1997. American Gastroenterological Association medical position statement: evaluation of dyspepsia. Review article: nonsteroidal antiinflammatory drug-associated gastrointestinal complications: guidelines for prevention and treatment. Recommendations for the appropriate use of anti-inflammatory drugs in the era of the coxibs: defining the role of gastroprotective agents. Stomach pain: evidence-based methods in the diagnosis and treatment of dyspepsia: summary and conclusions. Lack of effect of treating Helicobacter pylori infection in patients with nonulcer dyspepsia. Absence of benefit of eradicating Helicobacter pylori in patients with nonulcer dyspepsia. Symptomatic benefit from eradicating Helicobacter pylori infection in patients with nonulcer dyspepsia. Randomised double blind controlled study of recurrence of gastric ulcer after treatment for eradication of Helicobacter pylori infection. Cure with omeprazole plus amoxicillin versus long-term ranitidine therapy in Helicobacter pylori-associated peptic ulcer bleeding. Antimicrobial therapy for Helicobacter pylori infection versus long-term maintenance antisecretion treatment in the prevention of recurrent hemorrhage from peptic ulcer: prospective nonrandomized trial on 125 patients. Eradication of Helicobacter pylori reduces the rate of duodenal ulcer rebleeding: a long-term follow-up study. Omeprazole-amoxycillin therapy for eradication of Helicobacter pylori in duodenal ulcer bleeding: preliminary results of a pilot study. Duodenal ulcer healing after 7-day treatment: a pilot study with lansoprazole, amoxicillin and clarithromycin. Efficacy of 1 week omeprazole or lansoprazole-amoxycillin-clarithromycin therapy for Helicobacter pylori infection in the Japanese population. Catalano F, Branciforte G, Catanzaro R, Bentivegna C, Cipolla R, Nuciforo G, et al. Comparative treatment of Helicobacter pylori-positive duodenal ulcer using pantoprazole at low and high doses versus omeprazole in triple therapy. Short-term triple therapy with lansoprazole 30 mg or 60 mg, amoxycillin and clarithromycin to eradicate Helicobacter pylori. Eradication of Helicobacter pylori using 30 mg or 60 mg lansoprazole combined with amoxicillin and metronidazole: one and two weeks of a new triple therapy. One week triple therapy with low dose rabeprazole in eradicating Helicobacter pylori; a preliminary report [abstract]. Influence of clarithromycin dosage on pantoprazole combined triple therapy for eradication of Helicobacter pylori. Randomised controlled trial of short term treatment to eradicate Helicobacter pylori in patients with duodenal ulcer. The combination of omeprazole, amoxicillin and clarithromycin eradicates Helicobacter pylori in 95% of cases: 7-day equals 10-day therapy [abstract]. The efficacy of two dosage regimens of omeprazole, amoxicillin and metronidazole for cure of Helicobacter pylori infection: the Hera Study. Pantoprazole plus clarithromycin and metronidazole versus pantoprazole plus clarithromycin and amoxicillin for therapy of H. Triple therapy (omeprazole + amoxicillin + clarithromycin) for Helicobacter pylori eradication in patients with peptic ulcer: no difference between six or twelve days. A prospective, controlled randomised trial of 3-,7and 10-day rabeprazole based triple therapy for H. Triple therapy for Helicobacter pylori eradication: a comparison of pantoprazole once versus twice daily. Omeprazole once or twice daily with clarithromycin and metronidazole for Helicobacter pylori. Efficacy and optimum dose of omeprazole in a new 1week triple therapy regimen to eradicate Helicobacter pylori. Kurzzeit-TripelTherapie mit Pantoprazol, Clarithromycin und Metronidazol zur Heilung der Helicobacter-pyloriInfektion [Short-term triple therapy with pantoprazole, clarithromycin and metronidazole for the healing of Helicobacter pylori infection]. Tratamiento con omeprazol, claritromicina y amoxicilina durante 6 dias en pacientes con ulcera doudenal infectados por Helicobacter pylori [Treatment with omeprazole, clarithromycin and amoxicillin over 6 days in patients with Helicobacter pylori-infected duodenal ulcer]. Low dose, short-term triple therapy for cure of Helicobacter pylori infection and healing of peptic ulcers. One-week triple therapy with lansoprazole, clarithromycin, and metronidazole to cure Helicobacter pylori infection in peptic ulcer disease in Korea. Seven-day triple therapy with lansoprazole, clarithromycin, and metronidazole for the cure of Helicobacter pylori infection: a short report. The efficacy and safety of oneweek triple therapy with lansoprazole, clarithromycin, and metronidazole for the treatment of Helicobacter pylori infection in Japanese patients. Triple therapy omeprazole (O) + amoxicillin (A) + clarithromycin (C) for Helicobacter pylori (Hp) infection. Pantoprazole plus amoxycillin and metronidazole: a safe, cost-effective therapy of H. Short-term triple therapy of pantoprazole, clarithromycin and metronidazole for cure of H. Low dose triple therapy is effective for eradicating Helicobacter pylori in Asian patients despite a high rate of metronidazole resistance [abstract]. Kurzzeit-tripel-therapie mit pantoprazol, clarithromycin und metronidazol zur eradikation von Helicobacter pylori [Short-term triple therapy with pantoprazole, clarithromycin and metronidazole in eradication of Helicobacter pylori]. One-week triple therapy with omeprazole, amoxycillin and either clarithromycin or metronidazole for cure of Helicobacter pylori infection. One-week low-dose triple therapy for the eradication of Helicobacter pylori infection. Is short-term triple therapy with lansoprazole, clarithromycin, and metronidazole a definitive answer for Helicobacter pylori eradicationff Ranitidine bismuth citrate therapy regimens for treatment of Helicobacter pylori infection: a review. Review article: one-week clarithromycin triple therapy regimens for eradication of Helicobacter pylori. Review article: treatments that impact favourably upon the eradication of Helicobacter pylori and ulcer recurrence.
Primary autoimmune neutronot be required because most children will spontaneously penia is caused by autoantibodies directed against neutrophils arthritis in neck and back treatment buy arcoxia 60 mg, 148-150 and in general spontaneously resolves arthritis swelling purchase arcoxia australia. Treatment is usually provided to those children at greatest risk for bleeding complications and those with chronic autoimmune neutropenia rarely have signiffcant infections and refractory disease arthritis fingers popping buy generic arcoxia 120 mg line. Commonly used therapeutic modalities can mount a neutrophil response to bacterial infections rheumatoid arthritis diet recipes benefits 60mg arcoxia with mastercard. Clinical response (increased neutrophil 152-155 counts) have been described in several small series of patients its use. Treatment modalities low-dose (5 mg/kg every 3 weeks) therapy in a randomized, include corticosteroids, cyclophosphamide, cyclosporine, and double-blind, placebo-controlled trial in 20 patients with 210 more recently rituximab. However, international guidelines recommend initial arising in children <16 years of age. Adverse events have with systemic corticosteroids and additional immunosuppressive been rare and relatively minor. Overall benefft has been reported, therapeutic agents, such as azathioprine or mycophenolate but well-controlled trials are lacking, and a follow-up study 198 mofetil, as corticosteroid-sparing agents. Others suggest that early institution of corticoste244 lymphadenopathy and hepatomegaly) indicative of a systemic inroids in a hospital setting may be beneffcial. Macrophage activation syndrome is a severe, lifeimproving outcomes if gastrointestinal hemorrhage is present. Disorders associated with vasculitis and vasculitSystemic vasculitides involving medium and large ides. Treatment primarily con189 232 marrow suppression, and lupus-induced multiorgan disease. However, improvements in the Rodnan skin score, a key outcome in clinical trials, was reported in patients who received additional 234,235 doses. Only a few case reports recommended because other therapies are more cost-effective. In milder disease, treatment includes addressing the unorgan-speciffc autoimmune diseases derlying hyperthyroidism, and symptomatic care. Additionally, Bendorsed by the International Consensus Report and the cell depletion with rituximab is emerging as an alternative, American Society of Hematology 2011 evidence-based especially in severe disease, because it efffciently decreases 158,159 guidelines. Multispecialty management, including endocriand are therefore without randomized studies. Current guidelines recommend a corticosteroid as the discussed, data are limited to open-label or retrospective studies ffrst-line treatment, with the addition of an immunosuppressive and case reports. For the most part, the efffcacy of immunoglobagent in corticosteroid-resistant cases or for corticosteroidulin therapy in patients with organ-speciffc autoimmune disease sparing effects. Newer biologics are also being considered, 259,260 or various forms of autoimmune vasculitides is limited, and depending on the type of autoimmune uveitis. Importantly, new biologic therapies have emerged autoimmune posterior uveitis that frequently requires immunorecently as better alternatives or even as primary therapies for suppressive therapy. Autoimmune hepatitis is responsiveness, airffow limitation, respiratory symptoms, and typically treated with a corticosteroid and azathioprine or another disease chronicity. Atopy is the strongest identiffable predisposing immunosuppressive agent, such as rituximab, in refractory disfactor for developing asthma. Patients who showed normalization of liver enzymes, undetectable with these symptoms are occasionally found to have antibody 267-274 circulating immune complexes, and improvement in periportal deffciency. Insome patients withimmuneabnormalities and mononuclear cell inffltrates after treatment. This, in turn, may decrease 274,275 variety of other available second-line immunosuppressive agents the symptoms and morbidity of asthma. Inffammatory bowel deffciency and not of asthma, although the benefft of this comorbid diseases are chronic inffammatory disorders involving the tissues diagnosis can be substantive. Multiple open-label trials have examined the effects of late mofetil or omalizumab have failed. However, small showed no signiffcant effect of immunoglobulin therapy numbers of patients have severe resistant disease despite 283,284 in asthma, while the third reported a signiffcant receiving second-line therapies. In addition, these patients can corticosteroid-sparing effect in a subgroup that required relatively develop unacceptable adverse events from therapy. A similar trend was seen in the allergic inffammahigh doses of systemic corticosteroids may be of interest. Urticaria Dosing in each patient varied from 300 mg/kg to 2 g/kg, and Chronic urticaria is a disorder that is often difffcult to treat, duration ranged from 6 to 39 months. Time to response seen although advances in the understanding of the underlying was 3-6 months. Signiffcant decreases in serum IgE and mechanisms have provided new insights and therapeutic ratioeosinophils were seen at the 3-month time point, and the 304 nale. An autoimmune process is implicated in about one third of decrease in serum IgE persisted after discontinuation. Slight improvement in skin disease was observed in 6 trial; one third of the enrolled patients experienced remission, patients; no improvement, in 2 patients; and worsening, in 1 another third experienced some benefft, and the rest did not patient. The cause of provided confficting results, and the majority of successful reports illness remains unknown but several clinical, laboratory, and were case series. Long-term beneffts following discontinuation of may be associated with even better outcomes, but these data 314 treatment are confficting, and additional randomized, placebohave been challenged. All patients should be given a single 315 controlled studies with longer follow-up are needed. Another meta-analysis of data from >3400 patients for which no speciffc chemotherapy exists. Age, duration of illness, immunoglobulin products with high concentrations of speciffc neutrophil and platelet counts, elevated aspartate aminotransantibodies to pathogens such as those causing tetanus, ferase and C-reactive protein, and hyponatremia have been pro322-325 rabies, and diphtheria have been made available in the United posed to predict resistance to treatment. A larger-scale study in 3493 infants receiving not responding to initial dosing within 48-72 hours (ie, when antibiotics for the treatment of sepsis did not show differences in neutrophil counts, C-reactive protein, and N-terminal of the mortality or major disability at 2 years between patients who prohormone brain natriuretic peptide, which are independent 343 received immunoglobulins and those who received placebo. Immunoprophylaxis with 5 332 coccal disease in newborns, streptococcal toxic shock/invasive monthly doses of palivizumab is an effective intervention that 333-337 338 streptococcal syndromes, postoperative sepsis, traumahas been reported to reduce hospitalization by 39-82% among 339 340 351 associated sepsis, and neonatal sepsis. Category Ib evidence exists to support the retrospective study, in 9 of 14 patients with refractory C. Those probably beneffcial in the treatment of neonatal sepsis (Ia), but not studies were of relatively small sample size and used different in prophylaxis of infection. It is thought to result from 369,370,373,374 371 were common and treatment failures did occur, immunologic destruction of myelin or Schwann cells within the but the latter approach was associated with long-term eradication peripheral nervous system. None of the treatments signiffcantly reduced mortients with autonomic instability. Nonetheless, a randomized, placebo-controlled 414 remain unclear, although genetic factors may play a role. A retrospective chart review of data from 53 patients 416-418 conduction block or Medical Research Council scores. Limited but moderateto high-quality evnow the recommended therapy for this neurologic disease. A similar response and lack of serious and other centralnervous system syndromes) that is associated with adverse events have been reported in additional case reports and autoantibodies against the astrocyte water channel called aqua443-445 461 uncontrolled trials. It may thus be used as an alternative prine, mycophenolate mofetil, or rituximab, based on retrospective treatment in patients who fail to respond or do not tolerate other and prospective open-label studies only. When larger doses were tried (1 g/kg/d for Intractable childhood epilepsy 2 days at 4-week intervals), 65% (of 25 patients) had no There is some evidence that an aberrant immune response is 449 exacerbations in 6 months versus 35% of the control group. However, event suggesting demyelinating disease signiffcantly lowered the there are 2 randomized placebo-controlled trials that have been 450 prevalence of a second attack and reduced disease activity. However, further randomized, double-blind studies are 4 days, then once each in weeks 2, 3, and 6, 6 month 6) reduced 452 needed to conffrm these ffndings. A multicenter, randomized, double-blind, placeboimmunomodulatory treatment in resistant cases. Another study reported increased plasma anti– 475,483 there are contraindications of steroid use. It was also b-amyloid antibody concentrations associated with decreased reported to improve acute disseminated encephalomyelitis b-amyloid peptide levels in the cerebrospinal ffuid following 484 following pertussis in an infant. These changes at the molecular level were 496-499 case series that included 6 patients with steroid-dependent accompanied by improved cognitive function. Case reports and series extend to preg510 512 513 conditions nant, adolescent, and infant patients. A consensus statement 517 ness in a number of disorders of the peripheral and central from the American Academy of Dermatology on the use of nervous systems. The blistering skin diseases group as adjuvant therapy in combination with an immunosuppressive of autoimmune disorders includes pemphigus vulgaris, bullous agent.
The controls were identifed in the National Health System records and were matched to cases on age (within 1 year) and registration with the same family pediatrician arthritis medication nz discount 60 mg arcoxia amex. The pediatricians certifed that all controls were free of diabetes and none were diagnosed with diabetes during the study period arthritis med for dogs purchase genuine arcoxia on line. Trained physicians collected immunization information from the parents of diabetic cases and controls using a questionnaire at the frst diabetologic examination or pediatric examination arthritis pain treatment for dogs discount arcoxia 90mg mastercard, respectively arthritis back nerve pain order discount arcoxia on-line. The participants were identifed in the Danish Civil Registration System, and linked to information on type 1 diabetes diagnosis in the Danish National Hospital Register and vaccination data from the National Board of Health. The children were followed from birth and removed from the study at the frst occurrence of an outcome of interest. The study outcomes included diagnosis of type 1 diabetes, loss to follow-up or emigration, reaching 12 years of age, and death. Vaccination status was considered a time-varying variable and was classifed according to the number of doses administered (zero, one, two, or three doses of each vaccine. A total of 739,694 children were included in the study, of whom 16,421 were prematurely removed from the analysis because of loss to follow-up, emigration, or death. The fve studies had relatively large sample sizes and were representative of European and U. See Table 4-12 for a summary of the studies that contributed to the weight of epidemiologic evidence. Mechanistic Evidence the committee identifed fve publications reporting type 1 diabetes developing after the administration of vaccines containing measles and mumps alone or in combination. The publications did not provide evidence beyond temporality, some too long or too short based on the possible mechanisms involved (Ehrengut and Zastrow, 1989; Fescharek et al. Long latencies between vaccine administration and development of symptoms make it impossible to rule out other possible causes. Two publications studied antibodies to mumps in patients developing type 1 diabetes or autoantibodies associated with the development of type 1 diabetes in patients after mumps infection or vaccination. The authors isolated autoantibodies from patients after mumps infection or vaccination but reported that the patients did not develop type 1 diabetes. Adverse Effects of Vaccines: Evidence and Causality 208 Copyright National Academy of Sciences. Adverse Effects of Vaccines: Evidence and Causality 209 Copyright National Academy of Sciences. Adverse Effects of Vaccines: Evidence and Causality 210 Copyright National Academy of Sciences. Several publications have reported cases of type 1 diabetes developing after mumps infection (Litman and Baum, 2010. Epidemiologic studies report a 3to 4-year lag time between mumps infection and type 1 diabetes (Litman and Baum, 2010), which would be consistent with a slow loss of islet cells not clinically apparent for several years; however, it would also be consistent with numerous other triggers. In addition, a decrease in the frequency of type 1 diabetes has not been associated with a decrease in the frequency of mumps infection after implementation of mumps vaccines (Litman and Baum, 2010. Owing to the uncertainty the committee did not consider mumps infection when determining the weight of mechanistic evidence. The symptoms described in the publications referenced above are consistent with those leading to a diagnosis of type 1 diabetes. Hepatitis was not reported as a symptom after vaccination and the liver was not enlarged, but a liver biopsy showed paramyxovirus-like intranuclear flaments suggesting the presence of measles virus or mumps virus or both. Weight of Mechanistic Evidence On rare occasions, infection with wild-type measles, mumps, and rubella viruses has been associated with hepatitis (Gershon, 2010a,b; Litman and Baum, 2010. The committee considers the effects of natural infection one type of mechanistic evidence. The symptoms described above are consistent with those leading to a diagnosis of hepatitis. Mechanistic Evidence the committee identifed 11 publications reporting hearing loss after the administration of vaccines containing measles, mumps, and rubella alone or in combination. Two publications described multiple cases, some did not provide a time frame between vaccination and development of hearing loss while others did not provide evidence beyond temporality, some too long or too short based on the possible mechanisms involved (Asatryan et al. Long latencies between vaccine administration and development of symptoms make it impossible to rule out other possible causes. Described below are eight publications reporting clinical, diagnostic, or experimental evidence that contributed to the weight of mechanistic evidence. In most of the cases, fever develops between days 5 and 12 after vaccination, a time frame consistent with studies researching fevers after immunization. The committee included some cases in which fever developed outside this time frame when in association with other symptoms suggestive of involvement of the ear, such as tinnitus and gait disturbance. Four years after vaccination laboratory evaluation detected complete failure of the caloric labyrinth on the left with good excitability on the right. Of the remaining 44 reports the authors summarized the 14 cases providing the most detailed clinical information. The following cases provided clinical evidence in addition to a temporal relationship between vaccination and the development of hearing loss that contributed to the weight of mechanistic evidence. Case 1 (number 6 in the report) describes a 1-year-old girl presenting with a fever within 1 month, and possibly as early as 1 week, after administration of measles, mumps, and rubella and Haemophilus infuenzae type B (HiB) vaccines. The patient was diagnosed with bilateral hearing loss 3 years after vaccination. Ataxia and bilateral hearing loss were reported 1 month and 4 months after vaccination, respectively. Brodsky and Stanievich (1985) describe a 3-year-old presenting with fever, ataxia, irritability, headache, nausea, vomiting, and nystagmus 10 days after administration of a measles, mumps, and rubella vaccine at 15 months of age. A diagnosis of persistent otitis media led to the insertion of tympanostomy tubes at 2. No change in hearing was noted after the insertion of the tubes, and the patient was subsequently diagnosed as having bilateral hearing loss. The patients father had sensorineural hearing loss in the left ear thought to be caused by a mumps infection in childhood. Louis encephalitis virus, western equine and eastern equine encephalomyelitis viruses, systemic lupus, and syphilis. Watson (1990) described a 14-month-old girl presenting with a generalized pink blotchy rash starting on the neck 12 days after administration of a measles vaccine. Two weeks later the mother noticed the patient would not respond to commands leading to the realization that the patient was unable to hear. Two publications provided experimental evidence for an association between the development of hearing loss and vaccination against measles or mumps. The authors were studying the association of silent mumps infection with idiopathic sudden sensorineural hearing loss. The authors used a hamster-adapted neurotropic strain of measles to inoculate the perilymphatic compartment of the ipsilateral cochlea in Syrian gold hamsters. Four to fve days after virus inoculation the temporal bones were removed and subjected to indirect immunofuorescence using antimeasles virus antisera. Positive immunofuorescence was observed in the infammatory cell infltrates in the cochlear ducts and the lining of the perilymphatic structure. Weight of Mechanistic Evidence Wild-type mumps virus infection has been associated with transient high-frequency-range deafness in 4. Permanent unilateral deafness has been reported to occur in 1 in 20,000 cases of mumps virus infection (Litman and Baum, 2010. Similarly, infection with wild-type measles virus has been associated with bilateral sensorineural hearing loss in 5–10 percent of measles cases (McKenna, 1997. The committee considers the effects of natural infection one type of mechanistic evidence. In addition, the eight publications described above presented clinical Copyright National Academy of Sciences. The publications presented a symptomology of fever, rash, and nystagmus consistent with direct infection of the measles or mumps viruses leading to hearing loss. The diagnosis of hearing loss after vaccination ranged from 6 days to 4 years after vaccination.
The number 62 on the fourth line from the top tells us that there are 62 observations on that line and all the ones below what does rheumatoid arthritis in fingers look like purchase arcoxia 90 mg. The parentheses mark the line containing the middle observation if the total number of observations is odd or the two middle observations if the total number of observations is even arthritis in back and shoulders cheap arcoxia on line. The line contains only 65 leaves arthritis quick relief buy arcoxia from india, so the + indicates that there are ffve more leaves arthritis in fingers cure order arcoxia 120mg without prescription, the number 9, that are not shown. This is accomplished by making the distance between lines shorter, that is, by decreasing the widths of the class intervals. For the present example, we may use class interval widths of 5, so that the distance between lines is 5. For example, they may be symmetric (the left half is at least approximately a mirror image of the right half), skewed to the left (the frequencies tend to increase as the measurements increase in size), skewed to the right (the frequencies tend to decrease as the measurements increase in size), or U-shaped (the frequencies are high at each end of the distribution and small in the center. One of the demographic variables the researchers collected for all subjects was the Body Mass Index (calculated by dividing weight in kg by the square of the patients height in cm. The goal of the study was to compare selenium levels in the region-raised beef to selenium levels in cooked venison, squirrel, and beef from other regions of the United States. The data below are the selenium levels calculated on a dry weight basis in mg>100 g for a sample of 53 regionraised cattle. Describe these data relative to symmetry and skewness as discussed in Exercise 2. Describe the two sets of data with respect to symmetry and skewness as discussed in Exercise 2. From information provided by urine specimens from the 216 subjects, the investigators computed the ratio of unchanged S-mephenytoin to R-mephenytoin (S/R ratio. The following table shows the heights in centimeters of the 109 subjects of whom 97 were males. What we need in many instances is the ability to summarize the data by means of a single number called a descriptive measure. Descriptive measures may be computed from the data of a sample or the data of a population. A descriptive measure computed from the data of a population is called a parameter. In this chapter, however, we limit discussion to measures of central tendency and measures of dispersion. We consider measures of central tendency in this section and measures of dispersion in the following one. In each of the measures of central tendency, of which we discuss three, we have a single value that is considered to be typical of the set of data as a whole. Measures of central tendency convey information regarding the average value of a set of values. The three most commonly used measures of central tendency are the mean, the median, and the mode. Arithmetic Mean the most familiar measure of central tendency is the arithmetic mean. It is the descriptive measure most people have in mind when they speak of the “average. Since we are not covering these other means in this book, we shall refer to the arithmetic mean simply as the mean. The mean is obtained by adding all the values in a population or sample and dividing by the number of values that are added. Let us begin by designating the random variable of interest by the capital letter X. To distinguish one value from another, we attach a subscript to the x and let the subscript refer to the ffrst, the second, the third value, and so on. We may now write the general formula for a ffnite population mean as follows: N a xi i=1 m = (2. When from the context it is obvious which values are to be added, the symbols above and below g will be omitted. The Sample Mean When we compute the mean for a sample of values, the procedure just outlined is followed with some modiffcations in notation. We use x to designate the sample mean and n to indicate the number of values in the sample. Since each and every value in a set of data enters into the computation of the mean, it is affected by each value. Extreme values, therefore, have an inffuence on the mean and, in some cases, can so distort it that it becomes undesirable as a measure of central tendency. As an example of how extreme values may affect the mean, consider the following situation. Suppose the ffve physicians who practice in an area are surveyed to determine their charges for a certain procedure. The mean charge for the ffve physicians is found to be $118, a value that is not very representative of the set of data as a whole. Median the median of a ffnite set of values is that value which divides the set into two equal parts such that the number of values equal to or greater than the median is equal to the number of values equal to or less than the median. If the number of values is odd, the median will be the middle value when all values have been arranged in order of magnitude. In this case the median is taken to be the mean of these two middle values, when all values have been arranged in the order of their magnitudes. In other words, the median observation of a data set is the 1n + 12>2th one when the observation have been ordered. If, for example, we have 11 observations, the median is the 111 + 12>2 = 6th ordered observation. Solution: the values are already ordered so we need only to ffnd the two middle values. Solution: Arraying the 10 ages in order of magnitude from smallest to largest gives 38, 43, 50, 57, 57, 59, 61, 64, 65, 66. If all the values are different there is no mode; on the other hand, a set of values may have more than one mode. I For an example of a set of values that has more than one mode, let us consider a laboratory with 10 employees whose ages are 20, 21, 20, 20, 34, 22, 24, 27, 27, and 27. The sample consisting of the values 10, 21, 33, 53, and 54 has no mode since all the values are different. For example, suppose the patients seen in a mental health clinic during a given year received one of the following diagnoses: mental retardation, organic brain syndrome, psychosis, neurosis, and personality disorder. The diagnosis occurring most frequently in the group of patients would be called the modal diagnosis. An attractive property of a data distribution occurs when the mean, median, and mode are all equal. The well-known “bell-shaped curve” is a graphical representation of a distribution for which the mean, median, and mode are all equal. Much statistical inference is based on this distribution, the most common of which is the normal distribution. Another common distribution of this type is the t-distribution, which is introduced in Section 6. Skewness Data distributions may be classiffed on the basis of whether they are symmetric or asymmetric. If a distribution is symmetric, the left half of its graph (histogram or frequency polygon) will be a mirror image of its right half. When the left half and right half of the graph of a distribution are not mirror images of each other, the distribution is asymmetric. If a distribution is not symmetric because its graph extends further to the right than to the left, that is, if it has a long tail to the right, we say that the distribution is skewed to the right or is positively skewed. If a distribution is not symmetric because its graph extends further to the left than to the right, that is, if it has a long tail to the left, we say that the distribution is skewed to the left or is negatively skewed. A distribution will be skewed to the right, or positively skewed, if its mean is greater than its mode. A distribution will be skewed to the left, or negatively skewed, if its mean is less than its mode. Skewness can be expressed as follows: n n 3 3 2n a 1xi x2 2n a 1xi x2 i=1 i=1 Skewness = n 3>2 = (2.
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