DOCSLIB.ORG

Thirteen Statistics Every Biostatistician Should Know Annmaria De Mars, the Julia Group, Santa Monica, CA

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Thirteen Statistics Every Biostatistician Should Know Annmaria De Mars, the Julia Group, Santa Monica, CA Paper 3561-2019 Thirteen Statistics Every Biostatistician Should Know AnnMaria De Mars, The Julia Group, Santa Monica, CA ABSTRACT No one knows all of SAS® or all of statistics. There will always be some technique that you don’t know. However, there are a few techniques that anyone in biostatistics should know. Make your life easier by learning to calculate those with SAS. In this session you will learn how to compute and interpret 12 of these techniques, including several statistics that are frequently confused. The following statistics are covered: prevalence, incidence, sensitivity, specificity, attributable fraction, population attributable fraction, risk difference, relative risk, odds ratio, Fisher’s exact test, number needed to treat, and McNemar’s test. The 13th, extra bonus tool, is SAS statistical graphics. With these 13 tools in their tool chest, even non-statisticians or statisticians who are not specialists will be able to answer many common questions in biostatistics. You’re in luck because each of these can be computed with a few statements in SAS. INTRODUCTION No one can know all of SAS or all of statistics, no, not even that annoying guy down the hall. Especially not that annoying guy down the hall. However, certain statistics are so commonly used that every biostatistician should know them. All of these can be computed easily with SAS. Biostatistics, broadly defined, is the application of statistics to topics in biology. However, most people when discussing biostatistics are really focused on biomedical topics, and not, say, the average lifespan of a particular species of ant-decapitating fly. There are five ways (at least) statistics can be applied to the study of disease: 1. How common is it? This is a question of prevalence (how likely you are to have it) and incidence (how likely you are to get it). If you think those two are the same, you should take a course in epidemiology, or just finish reading this paper. 2. What causes it? What are the factors that increase (or decrease) your risk of contracting a disease? 3. What pattern(s) does it follow? What is the prognosis? Are you likely to die of it quickly, eventually or never? To determine if a treatment is effective for cancer of the eyelashes, we need to first have an idea of what the probability of disability or death is when one is left untreated and over how long of a period of time, that is, what is the “natural progression” of a disease 4. How effective are attempts to prevent or treat a disease? 5. Developing policies to minimize disease. This paper covers basic statistics to address the first four questions. Policy should be developed based on the application of answers to those questions. While there is obviously a lot to be learned in the field of biostatistics, and a wide range of SAS procedures that can be applied, there are a basket of techniques that ought to be in everyone’s hand, computable with SAS. These are prevalence, incidence, sensitivity, specificity, attributable 1 fraction, population attributable fraction, risk difference, relative risk, odds ratio, Fisher’s exact test, number needed to treat, and McNemar’s test. That’s only 12. What’s the extra? Graphs. I admit, I cheated by including a whole category, but you’ll find that ROC curves, survival curves, maps and odds ratio plots are invaluable in explaining results to a non- technical audience. PREVALENCE AND INCIDENCE – TWO DIFFERENT ANSWERS TO THE SAME (MORE OR LESS) QUESTION Policy makers have very good reasons for wanting to know how common a condition or disease is. It allows them to plan and budget for treatment facilities, supplies of medication, rehabilitation personnel. There are two broad answers to the question, “How common is condition X?” and, interestingly, both of these use the exact same SAS procedures. HOW TO COMPUTE PREVALENCE USING SAS Prevalence rate is the proportion of persons with a condition divided by the number in the population. It’s often given as per thousand, or per 100,000, depending on how common the condition is. In brief, prevalence is how likely a person is to have condition X. Assuming that your data are already cleaned and you have a variable with a binary coding for “has disease”, “doesn’t have disease”, (pretty big assumptions) you can simply do a PROC FREQ. PROC FREQ DATA = yourdatasetname ; TABLES variable ; In the example below, from the California Health Interview Survey, approximately 11% of the respondents had been told they had Diabetes, giving a prevalence of 110 per 1,000. Diabetes- ever Cumulative Cumulative AB22 Frequency Percent Frequency Percent 1 4701 10.95 4701 10.95 2 38234 89.05 42935 100.00 Table 1. Output from PROC FREQ for Prevalence of Diabetes HOW TO COMPUTE INCIDENCE USING SAS INCIDENCE RATE is the rate at which new cases are occurring. Incidence is computed by dividing the number of new cases that occur in a specified period by the number of people in the population at risk. The population at risk in the next example was defined as all infants born in 2014. If you are interested in birth statistics, the National Center for Health Statistics is highly recommended as a source. This example is from a public use data set of all 40,002 births in U.S. territories in the year 2014. (Winning trivial pursuit fact: The United States has 16 territories.) Both incidence and prevalence estimates assume an accurate definition of cases, which requires understanding the data and the diagnosis. This data set required a very slight amount of coding because the Down syndrome variable at birth is coded as C for Confirmed, 2 N for No and P for Pending (Center for Disease Control, 2014). “Pending” means that the medical personnel suspect Down syndrome but they are waiting for the results of a chromosomal analysis. “Confirmed” means the analysis has confirmed a diagnosis of Down syndrome. Based on the presumption that most experienced medical personnel recognize Down syndrome, these two categories were combined, using IF/THEN and ELSE statements. LIBNAME out “C:\Users\me\mydir\” ; DATA incidence ; SET out.birth2014 ; IF ca_down in (“C”,”P”) THEN down = “Y” ; ELSE down = “N” ; Again, a PROC FREQ is used. The difference between incidence and prevalence is not in the computation but in the selection of the population and definition of the numerator. Because Down syndrome is present at birth and never acquired afterward, the new cases are going to be those children born in the year 2014 who have a diagnosis of Down syndrome and the denominator will be all births during the year. PROC FREQ DATA = out.birth2014 ; TABLES down ; Results are shown in Table 2 below. Down Syndrome Cumulative Cumulative Down Frequency Percent Frequency Percent N 39963 99.90 39963 99.90 Y 39 0.10 40002 100.00 Table 2. Output from PROC FREQ for Incidence of Down syndrome The incidence rate is .10 or 1 per 1,000. Since this estimate falls perfectly in line with the World Health Organization (2016) estimate of between 1 in 1,000 to 1,100 live births, it appears that the case definition was appropriate. SENSITIVITY AND SPECIFICITY – TWO ANSWERS TO A SECOND QUESTION: DO YOU HAVE A DISEASE? Both sensitivity and specificity address the same question – how accurate is a test for disease – but from opposite perspectives. Sensitivity is defined as the proportion of those who have the disease that are correctly identified as positive. Specificity is the proportion of those who do not have the disease who are correctly identified as negative. Specificity and sensitivity can be computed simultaneously, as shown in the example below using a hypothetical Disease Test. The results are in and the following table has been obtained: Disease No Disease Test Positive 240 40 Test Negative 60 160 Table 3 Results from Hypothetical Screening Test 3 COMPUTING SENSITIVITY AND SPECIFICITY USING SAS Step 1 (optional): Reading the data into SAS. If you already have the data in a SAS data set, this step is unnecessary. The example below demonstrates several SAS statements in reading data into a SAS dataset when only aggregate results are available. The ATTRIB statement sets the length of the result variable to be 10, rather than accepting the SAS default of 8 characters. The INPUT statement uses list input, with a $ signifying character variables. DATALINES; a statement on a line by itself, precedes the data. (Trivial pursuit fact #2: CARDS; will also work, dating back to the days when this statement was followed by cards with the data punched on them.) A semi-colon on a line by itself denotes the end of the data. DATA diseasetest; ATTRIB result LENGTH= $10; INPUT result $ disease $ weight; DATALINES; positive present 240 positive absent 40 negative present 60 negative absent 160 ; Step 2: PROC FREQ PROC FREQ DATA= diseasetest ORDER=FREQ ; TABLES result* disease; WEIGHT weight; Yes, another PROC FREQ. The ORDER = FREQ option is not required but it makes the data more readable, in my opinion, because with these data the first cell will now be those who had a positive result and did, in fact, have the disease and this is the format in which sensitivity and specificity data are typically presented. The total for column 1 is the numerator for the formula for sensitivity, which is: Sensitivity = (Number tested positive)/ (Total with disease). TABLES variable1*variable2 will produce a cross-tabulation with variable1 as the row variable and variable2 as the column variable. Weight weightvariable will weight each record by the value of the weight variable. The variable was named ‘weight’ in the example above but any valid SAS name is acceptable.
Load more

Recommended publications
  • Projections of Education Statistics to 2022 Forty-First Edition
    Projections of Education Statistics to 2022 Forty-first Edition 20192019 20212021 20182018 20202020 20222022 NCES 2014-051 U.S. DEPARTMENT OF EDUCATION Projections of Education Statistics to 2022 Forty-first Edition FEBRUARY 2014 William J. Hussar National Center for Education Statistics Tabitha M. Bailey IHS Global Insight NCES 2014-051 U.S. DEPARTMENT OF EDUCATION U.S. Department of Education Arne Duncan Secretary Institute of Education Sciences John Q. Easton Director National Center for Education Statistics John Q. Easton Acting Commissioner The National Center for Education Statistics (NCES) is the primary federal entity for collecting, analyzing, and reporting data related to education in the United States and other nations. It fulfills a congressional mandate to collect, collate, analyze, and report full and complete statistics on the condition of education in the United States; conduct and publish reports and specialized analyses of the meaning and significance of such statistics; assist state and local education agencies in improving their statistical systems; and review and report on education activities in foreign countries. NCES activities are designed to address high-priority education data needs; provide consistent, reliable, complete, and accurate indicators of education status and trends; and report timely, useful, and high-quality data to the U.S. Department of Education, the Congress, the states, other education policymakers, practitioners, data users, and the general public. Unless specifically noted, all information contained herein is in the public domain. We strive to make our products available in a variety of formats and in language that is appropriate to a variety of audiences. You, as our customer, are the best judge of our success in communicating information effectively.
    [Show full text]
  • Use of Statistical Tables
    TUTORIAL | SCOPE USE OF STATISTICAL TABLES Lucy Radford, Jenny V Freeman and Stephen J Walters introduce three important statistical distributions: the standard Normal, t and Chi-squared distributions PREVIOUS TUTORIALS HAVE LOOKED at hypothesis testing1 and basic statistical tests.2–4 As part of the process of statistical hypothesis testing, a test statistic is calculated and compared to a hypothesised critical value and this is used to obtain a P- value. This P-value is then used to decide whether the study results are statistically significant or not. It will explain how statistical tables are used to link test statistics to P-values. This tutorial introduces tables for three important statistical distributions (the TABLE 1. Extract from two-tailed standard Normal, t and Chi-squared standard Normal table. Values distributions) and explains how to use tabulated are P-values corresponding them with the help of some simple to particular cut-offs and are for z examples. values calculated to two decimal places. STANDARD NORMAL DISTRIBUTION TABLE 1 The Normal distribution is widely used in statistics and has been discussed in z 0.00 0.01 0.02 0.03 0.050.04 0.05 0.06 0.07 0.08 0.09 detail previously.5 As the mean of a Normally distributed variable can take 0.00 1.0000 0.9920 0.9840 0.9761 0.9681 0.9601 0.9522 0.9442 0.9362 0.9283 any value (−∞ to ∞) and the standard 0.10 0.9203 0.9124 0.9045 0.8966 0.8887 0.8808 0.8729 0.8650 0.8572 0.8493 deviation any positive value (0 to ∞), 0.20 0.8415 0.8337 0.8259 0.8181 0.8103 0.8206 0.7949 0.7872 0.7795 0.7718 there are an infinite number of possible 0.30 0.7642 0.7566 0.7490 0.7414 0.7339 0.7263 0.7188 0.7114 0.7039 0.6965 Normal distributions.
    [Show full text]
  • On the Meaning and Use of Kurtosis
    Psychological Methods Copyright 1997 by the American Psychological Association, Inc. 1997, Vol. 2, No. 3,292-307 1082-989X/97/$3.00 On the Meaning and Use of Kurtosis Lawrence T. DeCarlo Fordham University For symmetric unimodal distributions, positive kurtosis indicates heavy tails and peakedness relative to the normal distribution, whereas negative kurtosis indicates light tails and flatness. Many textbooks, however, describe or illustrate kurtosis incompletely or incorrectly. In this article, kurtosis is illustrated with well-known distributions, and aspects of its interpretation and misinterpretation are discussed. The role of kurtosis in testing univariate and multivariate normality; as a measure of departures from normality; in issues of robustness, outliers, and bimodality; in generalized tests and estimators, as well as limitations of and alternatives to the kurtosis measure [32, are discussed. It is typically noted in introductory statistics standard deviation. The normal distribution has a kur- courses that distributions can be characterized in tosis of 3, and 132 - 3 is often used so that the refer- terms of central tendency, variability, and shape. With ence normal distribution has a kurtosis of zero (132 - respect to shape, virtually every textbook defines and 3 is sometimes denoted as Y2)- A sample counterpart illustrates skewness. On the other hand, another as- to 132 can be obtained by replacing the population pect of shape, which is kurtosis, is either not discussed moments with the sample moments, which gives or, worse yet, is often described or illustrated incor- rectly. Kurtosis is also frequently not reported in re- ~(X i -- S)4/n search articles, in spite of the fact that virtually every b2 (•(X i - ~')2/n)2' statistical package provides a measure of kurtosis.
    [Show full text]
  • The Probability Lifesaver: Order Statistics and the Median Theorem
    The Probability Lifesaver: Order Statistics and the Median Theorem Steven J. Miller December 30, 2015 Contents 1 Order Statistics and the Median Theorem 3 1.1 Definition of the Median 5 1.2 Order Statistics 10 1.3 Examples of Order Statistics 15 1.4 TheSampleDistributionoftheMedian 17 1.5 TechnicalboundsforproofofMedianTheorem 20 1.6 TheMedianofNormalRandomVariables 22 2 • Greetings again! In this supplemental chapter we develop the theory of order statistics in order to prove The Median Theorem. This is a beautiful result in its own, but also extremely important as a substitute for the Central Limit Theorem, and allows us to say non- trivial things when the CLT is unavailable. Chapter 1 Order Statistics and the Median Theorem The Central Limit Theorem is one of the gems of probability. It’s easy to use and its hypotheses are satisfied in a wealth of problems. Many courses build towards a proof of this beautiful and powerful result, as it truly is ‘central’ to the entire subject. Not to detract from the majesty of this wonderful result, however, what happens in those instances where it’s unavailable? For example, one of the key assumptions that must be met is that our random variables need to have finite higher moments, or at the very least a finite variance. What if we were to consider sums of Cauchy random variables? Is there anything we can say? This is not just a question of theoretical interest, of mathematicians generalizing for the sake of generalization. The following example from economics highlights why this chapter is more than just of theoretical interest.
    [Show full text]
  • Testing Hypotheses
    Chapter 7 Testing Hypotheses Chapter Learning Objectives Understanding the assumptions of statistical hypothesis testing Defining and applying the components in hypothesis testing: the research and null hypotheses, sampling distribution, and test statistic Understanding what it means to reject or fail to reject a null hypothesis Applying hypothesis testing to two sample cases, with means or proportions n the past, the increase in the price of gasoline could be attributed to major national or global event, such as the Lebanon and Israeli war or Hurricane Katrina. However, in 2005, the price for a Igallon of regular gasoline reached $3.00 and remained high for a long time afterward. The impact of unpredictable fuel prices is still felt across the nation, but the burden is greater among distinct social economic groups and geographic areas. Lower-income Americans spend eight times more of their disposable income on gasoline than wealthier Americans do.1 For example, in Wilcox, Alabama, individuals spend 12.72% of their income to fuel one vehicle, while in Hunterdon Co., New Jersey, people spend 1.52%. Nationally, Americans spend 3.8% of their income fueling one vehicle. The first state to reach the $3.00-per-gallon milestone was California in 2005. California’s drivers were especially hit hard by the rising price of gas, due in part to their reliance on automobiles, especially for work commuters. Analysts predicted that gas prices would continue to rise nationally. Declines in consumer spending and confidence in the economy have been attributed in part to the high (and rising) cost of gasoline. In 2010, gasoline prices have remained higher for states along the West Coast, particularly in Alaska and California.
    [Show full text]
  • Tests of Hypotheses Using Statistics
    Tests of Hypotheses Using Statistics Adam Massey¤and Steven J. Millery Mathematics Department Brown University Providence, RI 02912 Abstract We present the various methods of hypothesis testing that one typically encounters in a mathematical statistics course. The focus will be on conditions for using each test, the hypothesis tested by each test, and the appropriate (and inappropriate) ways of using each test. We conclude by summarizing the di®erent tests (what conditions must be met to use them, what the test statistic is, and what the critical region is). Contents 1 Types of Hypotheses and Test Statistics 2 1.1 Introduction . 2 1.2 Types of Hypotheses . 3 1.3 Types of Statistics . 3 2 z-Tests and t-Tests 5 2.1 Testing Means I: Large Sample Size or Known Variance . 5 2.2 Testing Means II: Small Sample Size and Unknown Variance . 9 3 Testing the Variance 12 4 Testing Proportions 13 4.1 Testing Proportions I: One Proportion . 13 4.2 Testing Proportions II: K Proportions . 15 4.3 Testing r £ c Contingency Tables . 17 4.4 Incomplete r £ c Contingency Tables Tables . 18 5 Normal Regression Analysis 19 6 Non-parametric Tests 21 6.1 Tests of Signs . 21 6.2 Tests of Ranked Signs . 22 6.3 Tests Based on Runs . 23 ¤E-mail: [email protected] yE-mail: [email protected] 1 7 Summary 26 7.1 z-tests . 26 7.2 t-tests . 27 7.3 Tests comparing means . 27 7.4 Variance Test . 28 7.5 Proportions . 28 7.6 Contingency Tables .
    [Show full text]
  • Understanding Statistical Hypothesis Testing: the Logic of Statistical Inference
    Review Understanding Statistical Hypothesis Testing: The Logic of Statistical Inference Frank Emmert-Streib 1,2,* and Matthias Dehmer 3,4,5 1 Predictive Society and Data Analytics Lab, Faculty of Information Technology and Communication Sciences, Tampere University, 33100 Tampere, Finland 2 Institute of Biosciences and Medical Technology, Tampere University, 33520 Tampere, Finland 3 Institute for Intelligent Production, Faculty for Management, University of Applied Sciences Upper Austria, Steyr Campus, 4040 Steyr, Austria 4 Department of Mechatronics and Biomedical Computer Science, University for Health Sciences, Medical Informatics and Technology (UMIT), 6060 Hall, Tyrol, Austria 5 College of Computer and Control Engineering, Nankai University, Tianjin 300000, China * Correspondence: [email protected]; Tel.: +358-50-301-5353 Received: 27 July 2019; Accepted: 9 August 2019; Published: 12 August 2019 Abstract: Statistical hypothesis testing is among the most misunderstood quantitative analysis methods from data science. Despite its seeming simplicity, it has complex interdependencies between its procedural components. In this paper, we discuss the underlying logic behind statistical hypothesis testing, the formal meaning of its components and their connections. Our presentation is applicable to all statistical hypothesis tests as generic backbone and, hence, useful across all application domains in data science and artificial intelligence. Keywords: hypothesis testing; machine learning; statistics; data science; statistical inference 1. Introduction We are living in an era that is characterized by the availability of big data. In order to emphasize the importance of this, data have been called the ‘oil of the 21st Century’ [1]. However, for dealing with the challenges posed by such data, advanced analysis methods are needed.
    [Show full text]
  • History of Health Statistics
    certain gambling problems [e.g. Pacioli (1494), Car- Health Statistics, History dano (1539), and Forestani (1603)] which were first of solved definitively by Pierre de Fermat (1601–1665) and Blaise Pascal (1623–1662). These efforts gave rise to the mathematical basis of probability theory, The field of statistics in the twentieth century statistical distribution functions (see Sampling Dis- (see Statistics, Overview) encompasses four major tributions), and statistical inference. areas; (i) the theory of probability and mathematical The analysis of uncertainty and errors of mea- statistics; (ii) the analysis of uncertainty and errors surement had its foundations in the field of astron- of measurement (see Measurement Error in omy which, from antiquity until the eighteenth cen- Epidemiologic Studies); (iii) design of experiments tury, was the dominant area for use of numerical (see Experimental Design) and sample surveys; information based on the most precise measure- and (iv) the collection, summarization, display, ments that the technologies of the times permit- and interpretation of observational data (see ted. The fallibility of their observations was evident Observational Study). These four areas are clearly to early astronomers, who took the “best” obser- interrelated and have evolved interactively over the vation when several were taken, the “best” being centuries. The first two areas are well covered assessed by such criteria as the quality of obser- in many histories of mathematical statistics while vational conditions, the fame of the observer, etc. the third area, being essentially a twentieth- But, gradually an appreciation for averaging observa- century development, has not yet been adequately tions developed and various techniques for fitting the summarized.
    [Show full text]
  • An Introduction to Regression Analysis Alan O
    University of Chicago Law School Chicago Unbound Coase-Sandor Working Paper Series in Law and Coase-Sandor Institute for Law and Economics Economics 1993 An Introduction to Regression Analysis Alan O. Sykes Follow this and additional works at: https://chicagounbound.uchicago.edu/law_and_economics Part of the Law Commons Recommended Citation Alan O. Sykes, "An Introduction to Regression Analysis" (Coase-Sandor Institute for Law & Economics Working Paper No. 20, 1993). This Working Paper is brought to you for free and open access by the Coase-Sandor Institute for Law and Economics at Chicago Unbound. It has been accepted for inclusion in Coase-Sandor Working Paper Series in Law and Economics by an authorized administrator of Chicago Unbound. For more information, please contact [email protected]. The Inaugural Coase Lecture An Introduction to Regression Analysis Alan O. Sykes* Regression analysis is a statistical tool for the investigation of re- lationships between variables. Usually, the investigator seeks to ascertain the causal effect of one variable upon another—the effect of a price increase upon demand, for example, or the effect of changes in the money supply upon the inflation rate. To explore such issues, the investigator assembles data on the underlying variables of interest and employs regression to estimate the quantitative effect of the causal variables upon the variable that they influence. The investigator also typically assesses the “statistical significance” of the estimated relationships, that is, the degree of confidence that the true relationship is close to the estimated relationship. Regression techniques have long been central to the field of eco- nomic statistics (“econometrics”).
    [Show full text]
  • 1 - to Overcoming the Reluctance of Epidemiologists to Explicitly Tackle the Measurement Error Problem
    Statistics → Applications → Epidemiology Does adjustment for measurement error induce positive bias if there is no true association? Igor Burstyn, Ph.D. Community and Occupational Medicine Program, Department of Medicine, Faculty of Medicine and Dentistry, the University of Alberta, Edmonton, Alberta, Canada; Tel: 780-492-3240; Fax: 780-492-9677; E-mail: [email protected] Abstract This article is a response to an off-the-record discussion that I had at an international meeting of epidemiologists. It centered on a concern, perhaps widely spread, that measurement error adjustment methods can induce positive bias in results of epidemiological studies when there is no true association. I trace the possible history of this supposition and test it in a simulation study of both continuous and binary health outcomes under a classical multiplicative measurement error model. A Bayesian measurement adjustment method is used. The main conclusion is that adjustment for the presumed measurement error does not ‘induce’ positive associations, especially if the focus of the interpretation of the result is taken away from the point estimate. This is in line with properties of earlier measurement error adjustment methods introduced to epidemiologists in the 1990’s. An heuristic argument is provided to support the generalizability of this observation in the Bayesian framework. I find that when there is no true association, positive bias can only be induced by indefensible manipulation of the priors, such that they dominate the data. The misconception about bias induced by measurement error adjustment should be more clearly explained during the training of epidemiologists to ensure the appropriate (and wider) use of measurement error correction procedures.
    [Show full text]
  • Vital Statistics Rapid Release, Number 015 (July 2021)
    Vital Statistics Rapid Release Report No. 015 July 2021 Provisional Life Expectancy Estimates for 2020 Elizabeth Arias, Ph.D., Betzaida Tejada-Vera, M.S., Farida Ahmad, M.P.H., and Kenneth D. Kochanek, M.A. Introduction not produced due to the impact of race of births for the same period based on and ethnicity misclassification on death birth records received and processed The National Center for Health certificates for these populations on the by NCHS as of April 7, 2021; and, July Statistics (NCHS) collects and precision of life expectancy estimates 1, 2020, monthly postcensal population disseminates the nation’s official vital (2). There are two types of life tables: the estimates based on the 2010 decennial statistics through the National Vital cohort (or generation) and the period (or census. Provisional mortality rates are Statistics System (NVSS). NCHS uses current) life table. The cohort life table typically computed using death data provisional vital statistics data for presents the mortality experience of a after a 3-month lag following date of conducting public health surveillance particular birth cohort from the moment death, as completeness and timeliness and final data for producing annual of birth through consecutive ages in of provisional death data can vary national natality and mortality statistics. successive calendar years. The period by many factors, including cause of NCHS publishes annual and decennial life table does not represent the mortality death, month of the year, and age of national life tables based on final experience of an actual birth cohort but the decedent (4,5). Mortality data used vital statistics.
    [Show full text]
  • Introduction to Hypothesis Testing 3
    CHAPTER Introduction to Hypothesis 8 Testing 8.1 Inferential Statistics and Hypothesis Testing 8.2 Four Steps to LEARNING OBJECTIVES Hypothesis Testing After reading this chapter, you should be able to: 8.3 Hypothesis Testing and Sampling Distributions 8.4 Making a Decision: 1 Identify the four steps of hypothesis testing. Types of Error 8.5 Testing a Research 2 Define null hypothesis, alternative hypothesis, Hypothesis: Examples level of significance, test statistic, p value, and Using the z Test statistical significance. 8.6 Research in Focus: Directional Versus 3 Define Type I error and Type II error, and identify the Nondirectional Tests type of error that researchers control. 8.7 Measuring the Size of an Effect: Cohen’s d 4 Calculate the one-independent sample z test and 8.8 Effect Size, Power, and interpret the results. Sample Size 8.9 Additional Factors That 5 Distinguish between a one-tailed and two-tailed test, Increase Power and explain why a Type III error is possible only with 8.10 SPSS in Focus: one-tailed tests. A Preview for Chapters 9 to 18 6 Explain what effect size measures and compute a 8.11 APA in Focus: Reporting the Test Cohen’s d for the one-independent sample z test. Statistic and Effect Size 7 Define power and identify six factors that influence power. 8 Summarize the results of a one-independent sample z test in American Psychological Association (APA) format. 2 PART III: PROBABILITY AND THE FOUNDATIONS OF INFERENTIAL STATISTICS 8.1 INFERENTIAL STATISTICS AND HYPOTHESIS TESTING We use inferential statistics because it allows us to measure behavior in samples to learn more about the behavior in populations that are often too large or inaccessi­ ble.
    [Show full text]