...percentage goes in the numerator and which goes in the denominator? Does it matter? What do we mean by something being statistically significant at the 5% level? What is a 95% confidence interval? Those questions, and much more, are what this book is all about. In his fine article regarding nominal and ordinal bivariate statistics, Buchanan (1974) provided several criteria for a good statistic, and concluded: “The percentage is the most useful statistic ever invented…” (p. 629). I agree, and thus my choice for the title of this book. In the ten chapters that follow, I hope to convince you of the defensibility of that claim. The first chapter is on basic concepts (what a percentage is, how it differs from a fraction and a proportion, what sorts of percentage calculations are useful in statistics, etc.) If you’re pretty sure you already understand such things, you might want to skip that chapter (but be prepared to return to it if you get stuck later on!). In the second chapter I talk about the interpretation of percentages, differences between percentages, and ratios of percentages, including some common mis-interpretations and pitfalls in the use of percentages. Chapter 3...
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...Screening of Diseases Answer these questions: What would be the impact on this test's sensitivity if you moved the cutoff for a positive result from A to B? What about specificity? What would happen to sensitivity and specificity if you moved the cutoff from A to C? Where would you put the cutoff for this test? What is the relationship between sensitivity and specificity for any given test? With the expanding knowledge concerning diseases and the further development of technology in diagnostics, screening has become a method in improving the state of public health through its potential for disease prevention. However, people may have misconceptions about this process because they were inadequately informed. This attempts to provide an understanding about the many aspects of screening. It is concerned with how screening is defined, its limitations and advantages, the issues involved and conditions where it is acceptable and not acceptable. Without screening, diagnosis of disease only occurs after symptoms develop. However, disease frequently begins long before symptoms occur, and even in the absence of symptoms there may be a point at which the disease could be detected by a screening test. According to the reading and establishing a relationship with this case, talking about sensitivity is the percentage of the results that will be positive when HIV is present. On the same way talking about specificity is the percentage of the results that will be negative...
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...see whether the data support her belief. • What is the null hypothesis for this test? H0: the reject rate in the packing line for bottles of equine glucosamine is equal to or greater than 32 units per 1,000. Numerically, we write: H0: u => 32 units/1,000 • In the context of this scenario, what would be the consequences of making a Type I error? A Type I error occurs when we reject H0, when it is true. In this case, a Type I would result from concluding that the reject rate in the packing line is not equal to or greater than 32 units per 1,000, when in reality it is actually equal to or greater than 32 units per 1,000. The consequences, would be that the VP of operations would implement the new process, when in reality it would not reduce the rate. Customers may feel deceived and could impact on revenue. • In the context of this scenario, what would be the consequences of making a Type II error? A Type II error occurs when we do not reject H0 when it is false. In this case, a Type II error would result from concluding that the reject rate in the packing line is equal to or greater than 32 units per 1,000. The consequences of the Type II error would be that the VP of operations would not implement the new process, when in fact it improves the process. The company would not be advertising an improvement in process. Scenario 2 Playbill Magazine had reported that the mean annual household income of its readers is $119,155. The most recent random sample of 80 households...
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...According to the book, a gold standard is a diagnostic test that is assumed to be able to determine the true disease of the patient. The gold standard is said to have known validity and reliability, and is used as a benchmark in which other diagnostic tests (screening test) are compared to. In the study, hearing loss is observed in one hundred and seventeen patients with a history of hearing loss, undergoing pure tone audiometry (PTA) for the first time. The patients in the study were divided into two groups, one of which reported increased TV volume and the other reported no increase in volume. The screening test in the article is the diagnostic utility of using television volume as a marker for hearing loss. This screening test is compared to the gold standard for hearing loss which is known as a pure tone audiogram (PTA). Each patient’s PTA was used as a reference standard. The results of the experiment indicated that if the patient reported viewing television with an increased volume, then there was a 68 per cent chance of the patient have a hearing loss of 25 dB or more. Although the study concluded that self-reported television volume can be a useful screening tool in patients presenting with hearing impairment, it is not very specific and should not be used to replace the current gold standard to measure hearing loss. Increased television volume had a sensitivity of 81 per cent and a specificity of 52 per cent as a predictor of hearing loss. A hypothetical ideal gold standard...
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...“Economics of IT Security Management” 1) The article questions the loss estimate obtained from CSI/FBI security surveys since they exclude some categories of costs associated with security breaches. It suggests that cost estimate based on the loss in capital markets as a result of a breach in security may be a proxy to estimate true cost of security breaches. a. What do you think about the quality of this cost estimate? Can you think of better ways to capture true cost of security breaches? Although I can see the benefit to utilizing capital market losses as a basis for estimating the true costs of a security breach because it attempts to capture the intangible costs of a breach, there is a great deal of uncertainty in the market and market share may go up or down as much based on the public perception of company’s ability to handle the situation as the damage done by the event itself. Additionally, the marketplace is often affected, in the long term by a multitude of indirect factors that skew the data; the price of fuel, socio-economic instability or new laws/regulations in parts of the world where they have warehouses or production facilities, natural disasters etc. Furthermore capital market changes only capture the effects of those security breaches that are publicly reported. Privately held companies are not subject to many of the laws and regulations that compel larger businesses to self-report and even when companies are required by law, to report security...
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...Notes for Statistics 3011 University of Minnesota Fall 2012 Section 010 Instructor: Shanshan Ding Notes accompany the Third Edition of Statistics: The Art and Science of Learning From Data by Alan Agresti and Christine Franklin Contents CHAPTER 9: HYPOTHESIS TESTS 9.1 Elements of a Hypothesis Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2 Normal Hypothesis Test for Population Proportion p . . . . . . . . . . . . . . . . . . 9.3 The t-Test: Hypothesis Testing for Population Mean µ . . . . . . . . . . . . . . . . . 9.4 Possible Errors in Hypothesis Testing . . . . . . . . . . . . . . . . . . . . . . . . . . 9.5 Limitations and Common Misinterpretations of Hypothesis Testing . . . . . . . . . . 1 1 6 10 15 17 Stat 3011 Chapter 9 CHAPTER 9: HYPOTHESIS TESTS Motivating Example A diet pill company advertises that at least 75% of its customers lose 10 pounds or more within 2 weeks. You suspect the company of falsely advertising the benefits of taking their pills. Suppose you take a sample of 100 product users and find that only 5% have lost at least 10 pounds. Is this enough to prove your claim? What about if 72% had lost at least 10 pounds? Goal: 9.1 Elements of a Hypothesis Test 1. Assumptions 2. Hypotheses Each hypothesis test has two hypotheses about the population: Null Hypothesis (H0 ): Alternative Hypothesis (Ha ): 1 Stat 3011 Chapter 9 Diet Pill Example: Let p = true proportion of diet pill customers that lose at least...
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...Type I error (or, error of the first kind) and Type II error (or, error of the second kind) are precise technical terms used in statistics to describe particular flaws in a testing process, where a truenull hypothesis was incorrectly rejected (Type I error) or where one fails to reject a false null hypothesis (Type II error). The terms are also used in a more general way by social scientists and others to refer to flaws in reasoning. This article is specifically devoted to the statistical meanings of those terms and the technical issues of the statistical errors that those terms describe. Statistical test theory In statistical test theory the notion of statistical error is an integral part of hypothesis testing. The test requires an unambiguous statement of a null hypothesis, which usually corresponds to a default "state of nature", for example "this person is healthy", "this accused is not guilty" or "this product is not broken". An alternative hypothesis is the negation of null hypothesis, for example, "this person is not healthy", "this accused is guilty" or "this product is broken". The result of the test may be negative, relative to null hypothesis (not healthy, guilty, broken) or positive (healthy, not guilty, not broken). If the result of the test corresponds with reality, then a correct decision has been made. However, if the result of the test does not correspond with reality, then an error has occurred. Due to the statistical nature of a test, the result is never...
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...250 words will be hard. Stevenson (2012) tells us that a Type II error is “concluding a process is in control when it is not” (p. 429). To categorize the decisions made on that fateful day would be to say a ‘series of errors occurred’. When reading, Deepwater: Report to the President, one can easily tell that numerous mistakes lead to the events, and that BP was aware of several maintenance issues. “A September 2009 BP safety audit had produced a 30-page list of 390 items requiring 3,545 man-hours of work” (OilSpillCommission, 2011, p.6). It is apparent to this researcher that several ‘signs’ were missed when the crews were performing the negative-pressure test. They ran the test approximately three times on the main drill pipe, all of which failed; then they ran the test on the kill line, it passed, but the main drill pipe was still holding pressure, which actually means a failure (OilSpillCommission, 2011, p.107). In reading further, this was ‘put off’ as a bladder effect, when in reality; it was mounting signs of a ‘kick’. If one continues to read the Commission’s report, it is evident that numerous errors and misses directly influenced the events of April 20, 2010. The Commission goes on to say, “What nobody appears to have noticed during those six minutes (perhaps as a result of all of the activity) was that drill-pipe pressure was increasing again (OilSpillCommission, 2011, p. 112). Clearly, this disaster was a Type II error, as the processes and people were definitely not...
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...One of the important features of medicine is diagnostic testing. The companies that produce diagnostic tests are multi-billion dollar companies. Not only is the effectiveness of their tests important for their botXXXXX XXXXXne, but it’s also important for the health and well-being of those who rely on the tests for their health. One such test important diagnostic test is the test for colorectal cancer known as the fecal occult blood test. When analyzing the effectiveness of such tests, we consider the sensitivity and the specificity of the test. In this case, the sensitivity of the test is the proportion of results that correctly identify people with colorectal cancer. In symbolic terms, P(testing positive | have colorectal cancer). The specificity is the proportion of tests that correctly identify those people who do not have colorectal cancer. Symbolically, it is P( testing negative | do not have colorectal cancer). In reality, we are very interested in the probability having the disease given that you tested positive. That is, we are interested in the false alarm rate. This is important from a treatment perspective, but also from a business perspective. For example, a test that identified everyone who took it has having colorectal cancer would have perfect sensitivity, but it would have a very high false alarm rate. Similarly, a test that identifies everyone has being healthy (i.e., does not have colorectal cancer) would have perfect specificity, but it would fail to diagnose...
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...Week 4 Individual Assignment Erwin O. Raymer III PSY/315 Jan. 13th 2014 Jennifer Lapin Week 4 Individual Assignment The five steps of hypothesis testing consist of the following. Restate the question as a research hypothesis and a null hypothesis. This is where an individual would make a research hypothesis, which is basically a prediction intended to be tested in a research study. This prediction is usually based on the researcher’s theory. A null hypothesis is the opposite of the research hypothesis. If the null hypothesis is found to be true then it is not possible for the research hypothesis to be relevant. Same goes for if the research hypothesis is true then the null hypothesis is unable to be relevant as well. Determine the characteristics of the comparison distribution. In the hypothesis testing process you want to find out the probability that you could have a sample score as extreme as what you got if your sample was from a population with a distribution of the sort you would have if the null hypothesis were true. That is in the hypothesis testing process, you compare the actual samples score to this comparison distribution. Determine the cut off sample score on the comparison distribution at which the null hypothesis should be rejected. (Critical value) Ideally, before conducting a study, researchers set a target against which they will compare their results. How extreme a sample score they would need to decide against...
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...e DRAFT Reflection: I believe I have tried to cover every aspect of the topic even though it gets fairly technical and I may have missed out on some salient points. I Also think that I may need to have a stronger conclusion to justify the use of this new technologies NEW TECHNOLOGIES THAT MAY IMPROVE BREAST CANCER DETECTION. Amy was just seven months shy of her 45th birthday when the doctor delivered the deadly news. She had just been diagnosed with breast cancer and unfortunately for her the cancer had spread and the doctor could not offer any consoling news. She was given two years max to live. Amy was devastated, and as predicted she passed on just two months shy of her 47th birthday. Surprisingly, Amy had always done her breast exams and mammograms at the recommended intervals. Unfortunately cases similar to Amy’s are on the rise and have brewed lots of controversies on breast cancer screening using mammography-the gold standard. Clinicians are querying the effectiveness of Mammograms as a gold standard. There is increasing awareness of subpopulations of women for whom mammography has reduced sensitivity. Mammography screening is not very effective in women between the ages of 20 and 40, and only moderately effective in women aged 40 to 49.It is estimated through mathematical modeling that regular screening of a woman between ages 40 and 49 will decrease her risk of breast cancer death by about 15%. In comparison, clinical trials show that screening reduces risk of death...
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...CANCER CONTROL PROJECT ABSTRACT A. PROJECT TITLE: Self-sampling for HPV infection among low-income Hispanic women. B. SPECIFIC AIMS: Although cervical cancer is preventable through regular screening 1 with Pap smear and liquid-based cytology,2 only 72% of women in the Texas-Mexico border and 82% of women in the US undergo such regular screening.3 Hispanic women in this region have one of the highest cervical cancer mortality rates in the nation.4 Previous studies have identified barriers to screening in this minority population such as lack of access to healthcare, fear of pain during the gynecological exam and embarrassment.5 Persistent infection with oncogenic Human Papillomavirus (HPV) types is necessary for developing cervical cancer.6 Thus, HPV testing of women 30 – 65 years of age has been added to the cervical cancer screening guidelines in addition to Pap/cytology (co-testing).2 Self-sampling is a novel approach to detect HPV infection, it allows women to collect their own cervical specimen with a brush in the clinic or in their own homes.7 It has high sensitivity (74%) and specificity (88%) compared to physician collected samples.8-13 Women that deem it acceptable cite reasons such as privacy, costs, and lack of need for an office visit.13-21 However, Pap/cytology has been preferred over self-sampling among some groups because of low confidence in self-sampling accuracy and uncertainty over performing it correctly.13,17,20,22,23 Self-sampling has been least likely...
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...compare how data is associated with the subject matters being discussed. In this paper, I will discuss how three different magazine articles use statistics to improve and expound on their theories, the methodology used, and if their use of statistics made the article more or less convincing. The statistical methods that will discuss statistics in the news include correlation, predication, confidence, and errors. Correlation “exists between two variables when higher values of one variable consistently go with higher values of another variable or when higher values of one variable consistently go with lower values of another variable. (Bennet, Briggs & Triola 2014)” It is only used with quantifiable data where the numbers are meaningful (height, weight, age, etc), therefore, it can’t be used for categorical data (gender, favorite foods, jobs, etc). Predication is defined by Britannica.com as the attribution of characteristics to a subject to produce something meaningful. This combines verbal elements and those that exist in name only (Britannica 2015). Confidence in statistics is defined as “a group of continuous or discrete adjacent values used to estimate a statistical parameter as a means of variance” (Merriam-Webster 2015). Statistical errors means that when null hypothesis is proven incorrect, then the alternative hypothesis is accepted (Rogers 2015). Errors are broken into two types, based on the null hypothesis where the assumption is that the treatment didn’t do anything...
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...the “Pizzazz.” Thirty (n=30) random selected Pizzazzes are driven for a month and the mileage is carefully measured in each. The mean mileage for the sample is 28.6 miles per gallon (mpg) and the sample standard deviation is 2.2 mpg. Estimate a 95% confidence interval for the mean mpg in the entire population of Pizzazzes (you might need to round your answer a little bit to agree with mine). (a) (b) (c) (d) (e) (23.42, 33.84) (27.81, 29.39) (26.82, 30.47) (27.23, 30.03) None of the above 2. Determine the test statistic for testing the null hypothesis that the population mean is 27 mpg ( H0 : µ = 27 Ha : µ ≠ 27 ) (a) (b) (c) (d) (e) (f) t = 3.98 t = -3.98 t = 4.6 t = -4.6 t = 1.96 None of the above 3. A Type II error is made when a. b. c. d. e. the null hypothesis is accepted when it is false. the null hypothesis is rejected when it is true. the alternate hypothesis is accepted when it is false. the null hypothesis is accepted when it is true. the alternate hypothesis is accepted when it is true. 4. A recent USA TODAY/CNN/Gallup Poll showed that most American people support Bush’s efforts in the Middle East peace process. The poll of 2000 adults was conducted and 1243 people said they supported Bush’s efforts. a) Find a 95% confidence interval for p, the fraction of Americans who support Bush’s efforts phat = 1243/2000 =62.15% then use the CI formula for a proportion b) Perform the hypothesis test Ho : p = 0.6 versus Ha :...
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...be appropriately large--meaning that you have a higher chance of rejecting the hypothesis that the drug is safe when it fact actually is. Although it shouldn't be too large since you don't want to send to waste a good product. This would give less room for type II error, which would mean you would accept the null hypothesis when if fact it is false. They don't want to say a drug is safe and effective when it actually isn't. Part B Type I error means that you reject the null hypothesis when it is true. Therefore for Set 1, you reject that the drug is safe when it actually is. And for Set 2 you reject that a drug is effective when it actually is. For each of these sets, a type I error would be of concern because you'd actually waste a good profitable product due to bad statistics. Part C Type II error means that you accept the null hypothesis when it is false. For set 1 you would accept that the drug is safe when it actually isn't. For Set 2 you would accept that a drug is effective when it actually isn't For set 1, accepting safety for a drug that could be dangerous, can lead to injury death and subsequently law suits. That's unethical and costly. A type 2 error could ruin the company's reputation. For Set 2, accepting efficacy when it isn't not good for business, because doctor's would quickly stop prescribing your drug or if it is an over the counter, people would stop buying it. It would be a big waste of money, but...
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