pitfalls of statistics

The habit of presenting sample sizes as ranges (eg, n=5 to 12 in each group) is not useful from a statistical perspective. And the average number of spectators per match in the Bundesliga is higher than any other top league in Europe. Researchers investigated the effects of a multidimensional lifestyle intervention on aerobic fitness and adiposity in predominantly migrant preschool children. Hassloch in Rhineland-Palatinate is regarded as the quintessential average community in Germany. Pitfalls of Ranking; Home > Crime Info & Support > Crime Information Center > Crime Statistics > Pitfalls of Ranking. The goal is to ensure that bias (systematic errors introduced in the conduct, analysis, or interpretation of study results) and confounding (distortions of effect caused by other factors) are minimized to produce valid estimates of effect. I told her not to worry because "Statistically, it's more likely that a person will die on the way to the hospital than during Outcomes observed under each of the 4 conditions could be represented by means (for continuous variables) or proportions (for binary variables) and typically would be compared statistically with ANOVA or a chi‐square test, respectively. As a statistician, which figures and facts would you use to best describe the people in Germany? Investigators can also minimize variability by carefully planning how many treatments, experimental conditions, or factors can be measured in an individual unit (eg, animal). A single figure, such as the number of people employed by the big banks, is often not enough to understand how an entire industry is performing. If we measure the weight 12 times in 1 day, we have 12 measurements per mouse but still only 5 mice; therefore, we would still have n=5 but with 12 repeated measures rather than an n value of 5×12=60. One of the greatest pitfalls of statistics is that the average person does not understand them AT ALL!!! We wish to compare organ blood flow recovery at 7 days after arterial occlusion in 2 different strains of mice. These are conditions or circumstances which affect the external validity of statistical results. Professor at the University of Ontario Institute of Technology, where he teaches business statistics, forecasting and risk management. A type I error is also known as a false‐positive result and occurs when the null hypothesis is rejected, leading the investigator to conclude that there is an effect when there is actually none. This design provides information on the effect of diet, the effect of genotype, and the combination of the 2. Another alternative is to transform the data (by log or square root) to yield a normal distribution and then to perform analyses on the transformed data. This is an open access article under the terms of the. Foremost, only those statistical comparisons that are of scientific interest should be conducted. A critically important first step in any data analysis is a careful description of the data. Investigators should always perform sample size computations, particularly for experiments in which mortality is the outcome of interest, to ensure that sufficient numbers of experimental units are considered to produce meaningful results. Unauthorized The basic assumptions for ANOVA are independence (ie, independent experimental units and not repeated assessments of the same unit), normally distributed outcomes, and homogeneity of variances across comparison groups. Here are 15 places with outstanding characteristics. Philip Sedgwick reader in medical statistics and medical education. It presents some examples of statistical pitfalls in empirical research practice, which increase the probability of false positive results and … Multiple comparison procedures are techniques that allow for more comparisons but that control the overall type I error rate for the set of all comparisons. The sample size, which affects the appropriate statistical approach used for formal testing, is the number (ie, n value) of independent observations under 1 experimental condition. Connor There is often confusion about when to present the standard deviation or the standard error. In every study, it is important to recognize limitations. A single measurement is taken for each mouse. -- Arthur Benjamin, Professor of Mathematics, Harvey Mudd College, Author of Data can be summarized as shown in Figure 5, in which means and standard error bars are shown for each time point and compared statistically using repeated‐measures ANOVA (again, assuming that normalized blood flow is approximately normally distributed). Let’s define a 5km x 5km area and map the location of each individual inside the study area. For instance, on average each German person has less than two legs, exactly 1.99999. Professor Krämer, our topic is “Germany in general”. However, only 13,710 deaths have been recorded as COVID-19-related over the same period, which explains only 54% of the observed excess mortality. In the absence of statistical interaction, one is free to test for the main effects of each factor. The Bonferroni adjustment is another popular approach with which the significance criterion (usually α=0.05) is set at α/k, in which k represents the number of comparisons of interest. Because many basic science experiments are exploratory and not confirmatory, investigators may want to conduct more statistical tests without the penalty of strict control for multiple testing. use prohibited. The outcome of interest is again normalized blood flow (a continuous outcome), and the comparison of interest is the trajectory (pattern over time) of mean normalized blood flow between strains. This site uses cookies. Comparisons between experimental conditions in terms of survival are often performed with the log‐rank test. In such cases, we recommend that investigators consider a range of possible values from which to choose the sample size most likely to ensure the threshold of at least 80% power. Pitfalls of Ranking. By convention, an independent experiment infers that the researcher has independently set up identical experiments each time rather than just measuring the outcome multiple times. The units could be animals, organs, cells, or experimental mixtures (eg, enzyme assays, decay curves). aMean and SD if there are no extreme or outlying values. Readers are going to be most interested in studies that uncover interesting, and new non-zero relationships. One of the major pitfalls with relying heavily on statistical significance is that it leads to publication bias. pitfalls in the interpretation of statistics Although determining an appropriate sample size for basic science research might be more challenging than for clinical research, it is still important for planning, analysis, and ethical considerations. Failure to satisfy these assumed characteristics can lead to incorrect inferences and is a common oversight in basic science studies. Jetzt einloggen Kostenlos registrieren ★ PREMIUM-INHALT. Similar tests can be conducted for TG mice (significant differences [P<0.05] are noted between treated TG1 mice and TG1 treated with Ad‐LacZ and between treated TG2 mice and TG2 treated with Ad‐LacZ). 7272 Greenville Ave. If the latter condition is not satisfied, an alternative exact test (eg, Fisher's exact test) should be used. In some experiments, it might be useful to display the actual observed measurements under each condition. Berlin is Germany’s largest city, but it doesn’t score all the top ratings. Dallas, TX 75231 Failure to explore the data. Who wants to know the average speed of the athletes running in the 100 metre sprint at the last Olympic Games? You would like to receive regular information about Germany? Without Abstract. This clearly illustrates that the normal use of arithmetic averages results in values that simply don’t occur in real life. When three friends drink an average of five beers in an evening, it makes a big difference whether they all drink the same amount, or one of them drinks 15 beers and the others none. But in per capita beer consumption they have been overtaken by the Czech Republic and Austria. Data can be summarized as shown in Figure 7 and are displayed as means and standard error bars for each time point and compared statistically using repeated‐measures ANOVA (again, assuming that cell protein levels are approximately normally distributed). In developing competing treatments or experimental conditions, the various conditions should be identical in every way except for the experimental condition under study. Concurrent control groups are preferred over historical controls, and littermates make the best controls for genetically altered mice. Arteriosclerosis, Thrombosis, and Vascular Biology (ATVB), Journal of the American Heart Association (JAHA), Basic, Translational, and Clinical Research, Journal of the American Heart Association. You can find the answers here. Having published a paperback in collaboration with the BBC (The Fifty-years War) Penguin is now collaborating with the Social Market Foundation in producing Public Spending. They find that until 31 March 2020, deaths in Italy increased by 39% or 25,354 compared to the average of the five previous years. In basic science studies, investigators often move immediately into comparisons among groups. Replication is also a critical element of many experiments. The outcome of interest is normalized blood flow (a continuous outcome), and the comparison of interest is mean normalized blood flow between strains. Subscribe here: Statistics professor Walter Krämer, Technical University Dortmund. Photos of fans replace real spectators in the stadium, Offsetting carbon emissions ID: ZRI-BSC-471559. We wish to compare cell protein as an index of cell growth in fibroblasts from 2 different strains of mice (wild type and TG) after fibroblasts are plated and allowed to grow for 0, 1, 3, 5, 7, and 9 hours. We can consider three broad classes of statistical pitfalls. Article excerpt. This approach can be appropriate, but with many statistical tests, investigators must recognize the possibility of a false‐positive result and, at a minimum, recognize this particular limitation. Journal editors, and peer reviewers like to publish findings that are statistically significant, and surprising. Cat indicates catalase; SOD, superoxide dismutase; TG, transgenic; WT, wild type. And with more than 7 million members and more than 26,000 clubs, the German Football Federation (DFB) is the world’s largest individual sport association. The analysis of clinical samples, population samples, and controlled trials is typically subjected to rigorous statistical review. Discover here why, and what is so special about it. In the case of averages it’s always important to keep the deviations in mind. Such an approach not only fails to examine longitudinal effects contained in the data but also results in decreased statistical power compared with a repeated‐measures analysis. Determining what statistical technique or test to do when: (1) mean and standard deviation if no extreme or outlying values are present; (2) independence of observations, normality or large samples, and homogeneity of variances; (3) independence of pairs, normality or large samples, and homogeneity of variances; (4) repeated measures in independent observations, normality or large samples, and homogeneity of variances; (5) independence of observations and expected count >5 in each cell; (6) repeated measures in independent observations. Mean percentage of apoptosis can be compared among strains treated with control (Ad‐LacZ) using t tests comparing 2 groups or ANOVA comparing >2 groups, assuming that the percentage of apoptosis is approximately normally distributed (significant differences [P<0.05] are noted against wild type treated with Ad‐LacZ). By continuing to browse this site you are agreeing to our use of cookies. Not all journals publishing basic science articles use statistical consultation, although it is becoming increasingly common.1 In addition, most statistical reviewers are more comfortable with clinical study design than with basic science research. The effectiveness of a home based intervention on children’s body mass index (BMI) at age 2 years was investigated. If it is of interest to compare all pairs of experimental conditions, then the Tukey or Duncan test may be best, depending on the number of desired comparisons and the sample sizes. 1-800-AHA-USA-1 This makes sense from a business standpoint. In basic science research, investigators often have small sample sizes, and some of their statistical comparisons may fail to reach statistical significance. In the above example, wild‐type and genetically altered littermates could be randomized in sufficient numbers to competing diets and observed for blood pressure, left ventricular mass, and serum biomarkers. Read preview. Statistical power is the probability that a test will detect a real difference in conversion rate between offers. Or from where the most expats come? It is difficult to overestimate the value of plotting data. Investigators must be aware of assumptions and design studies to minimize such departures. And the Sauerkraut cliché is completely misleading. Basic science studies are complex because they often span several scientific disciplines. This can be done with graphic displays or assessment of distributional properties of the outcome within the current study or reported elsewhere (note that the assumption of normality relates to normality of the outcome in the population and not in the current study sample alone). Percentage of apoptosis by strain. Continuous variables such as age, weight, and systolic blood pressure are generally summarized with means and standard deviations. L.R. 352 . Several options exist for investigators to informatively display data in graphical format. These issues and their implications are discussed next. With large samples, randomization ensures that any unintentional bias and confounding are equally present in control and experimental groups. The unit of analysis is the isolate, and we have repeated measurements of cell protein at baseline (time 0) and then at 1, 3, 5, 7, and 9 hours. Basic science experiments often have many statistical comparisons of interest. A single basic science manuscript, for example, can span several scientific disciplines and involve biochemistry, cell culture, model animal systems, and even selected clinical samples. In contrast, not very many readers … Pairwise comparisons (2 at a time) are perhaps the most popular, but general contrasts (eg, comparing the mean of groups 1 and 2 with the mean of groups 3 and 4) are also possible with these procedures. Investigators should evaluate the various procedures available and choose the one that best fits the goals of their study. Most common statistical methods assume that each unit of analysis is an independent measurement. Oct-Dec 2015;6(4):222-4. doi: 10.4103/2229-3485.167092. The 9 Pitfalls of Data Science is the modern version of the classic book, How to Lie with Statistics. †P<0.05 between treated TG1 mice and TG1 treated with Ad‐LacZ. A typical “reasonable” value is ≥80% power. Local Info The procedures differ in terms of how they control the overall type I error rate; some are more suitable than others in specific research scenarios.7, 8 If the goal is to compare each of several experimental conditions with a control, the Dunnett test is best. The unit of analysis is the entity from which measurements of “n” are taken. Figure 8 walks investigators through a series of questions that lead to appropriate statistical techniques and tests based on the nature of the outcome variable, the number of comparison groups, the structure of those groups, and whether or not certain assumptions are met. William Goodman. A simple example is a single measurement (eg, weight) performed on 5 mice under the same condition (eg, before dietary manipulation), for n=5. © 2016 The Authors. Common pitfalls in statistical analysis: Odds versus risk Perspect Clin Res. An appropriate analytic technique is a repeated‐measures ANOVA with 1 between factor (ie, genotype) and 1 within factor (ie, time). This latter observation would escape detection if performed in separate experiments, and the factorial design has the advantage of involving fewer mice than would be required for the 2 separate experiments. Walter Krämer is Professor for Statistics in Dortmund and knows which facts best describe Germans, and which don’t. When hypothesis testing is to be performed, a sample size that results in reasonable power (ie, the probability of detecting an effect or difference if one exists) should be used. If the statistical interaction is significant, then the interaction should be reported and formal tests for main effects should be omitted (because there are different associations depending on the second factor, as discussed in detail by Kleinbaum et al6). Basic science studies often involve several outcome variables from the same sample (eg, group of mice), making sample size decisions challenging. Sample sizes are often quite small and are not likely to support formal statistical testing of the underlying hypothesis. The aim of the intervention was to improve the health and wellbeing of parents and children. Standard deviations describe variability in a measure among experimental units (eg, among participants in a clinical sample), whereas standard errors represent variability in estimates (eg, means or proportions estimated for each comparison group). This may not be the most efficient approach and introduces additional bias and confounding by performing serial sets of experiments that are separated in time. 1-800-242-8721 One of the most popular is based on Tukey fences, which represent lower and upper limits defined by the upper and lower quartiles and the interquartile range, specifically, values below Q1−1.5 (Q3−Q1) or above Q3+1.5 (Q3−Q1).4 Extreme values should always be examined carefully for errors and corrected if needed but never removed. Germans move home far less often than people in other countries, such as in the USA. Indeed, statistics is perhaps more open to misuse than any other subject, particularly by the nonspecialist. Crime Statistics. The outcome of interest is percentage of apoptosis (a continuous outcome), and the comparison of interest is percentage of apoptosis among strains. Table 2 outlines some common statistical procedures used for different kinds of outcomes (eg, continuous, categorical) to make comparisons among competing experimental conditions with varying assumptions and alternatives. The third class of problems concerns interpretation of results, or how statistical results are applied (or misapplied) to real world … Unfortunately, these different concepts are sometimes used interchangeably. The data are means and standard errors taken over n=6 isolates for each type of mouse and condition. If the outcome being compared among groups is continuous, then means and standard errors should be presented for each group. Bitte loggen Sie sich ein, um Zugang zu diesem Inhalt zu erhalten. In this review, we focused on common sources of confusion and errors in the analysis and interpretation of basic science studies. When does the calculation of averages reach its limits as a method for describing complex issues? Common Statistical Pitfalls in Setting Up an Analysis 1. It is based on the notion that a more reliable AI-solution will be one that maximizes the time-scale separation between slow and fast processes. 8. Pitfalls of statistical hypothesis testing: type I and type. In basic science research, studies are often designed with limited consideration of appropriate sample size. Mean and standard error of systolic blood pressure (SBP) by type. Investigators can limit type I error by making conservative estimates such that sample sizes support even more stringent significance criteria (eg, 1%). This fact is understandable, given that the results of clinical investigation will often be used to inform patient care or clinical decision making. And sometimes averages are totally uninteresting. The American Heart Association is qualified 501(c)(3) tax-exempt It is common to find basic science studies that neglect this distinction, often to the detriment of the investigation because a repeated‐measures design is a very good way to account for innate biological variability between experimental units and often is more likely to detect treatment differences than analysis of independent events. It might be that the effect of diet and genotype is additive, or there may be a statistical interaction (a different effect of diet on blood pressure depending on genotype). If there is potential for other factors to influence associations, investigators should try to control these factors by design (eg, stratification) or be sure to measure them so that they might be controlled statistically using multivariable models, if the sample size allows for such models to be estimated. Ideally, investigators performing measurements should be blinded to treatment assignments and experimental conditions. Investigators must carefully evaluate assumptions of popular statistical tests to ensure that the tests used best match the data being analyzed. *P<0.05. Investigators might observe mice for 12 weeks, during which time some die and others do not; for those that do not, the investigators record 12 weeks as the last time these mice were observed alive. Data simply have to be cleaned and the best way to see if data are, in fact, clean is to look at them. Statistics professor Walter Krämer, Technical University Dortmund. There are also specific statistical tests of normality (eg, Kolmogorov‐Smirnov, Shapiro‐Wilk), but investigators should be aware that these tests are generally designed for large sample sizes.5 If one cannot assume normality, the most conservative strategy is to use a nonparametric test designed for nonnormal data. Figure 2. The Pitfalls of Statistics . A type II error is described as a false‐negative result and occurs when the test fails to detect an effect that actually exists. The authors write with authority, experience, and humor and makes for a very enjoyable and informative reading experience." Customer Service These designs allow investigators to test for effects of each experimental condition alone (main effects) and to test whether there is a statistical interaction (difference in the effect of 1 factor as a function of another) on the outcome of interest. II errors. Figure 8. A common pitfall in basic science research is the treatment of repeated measurements of a unit of analysis as independent when, in fact, they are correlated, thus artificially increasing the sample size. Composites are familiar in cardiovascular trials, yet almost unknown in sepsis. We aim to provide a non-technical and easily accessible resource for statistical practitioners who wish to spot and avoid misinterpretations and misuses of statistical significance tests. The misleading average, the graph 240. Cell protein over time by strain. Let’s assume, for sake of argument, that individuals are laid out in a perfect grid pattern. In this instance, an efficient approach is to perform sample size computations for each outcome, and the largest practical sample size could be used for the entire experiment. Statistical results are not always beyond doubt: “Statistics deals only with measurable aspects of things and therefore, can seldom give the complete solution to problem. By Sherman, Alfred. Because of the random, or as statisticians like to call it, “stochastic,” nature of conversion events, a test might not … Clinical data, regardless of publication venue, are often subject to rather uniform principles of review. Stratification is a means to combat bias and confounding. Replication provides additional information to estimate desired effects and, perhaps more important, to quantify uncertainty in observed estimates (as outlined). Exceptions are their love of cars, their love of their homeland and their enthusiasm for football. National Center We need to be alert to potential pitfalls. Pitfall 3: Ignoring the effects of statistical power. Several statistical comparisons are of interest. For this reason, most major journals publishing clinical research include statistical reviews as a standard component of manuscript evaluation for publication. Blood flow over time by strain. If a Kaplan–Meier curve is displayed in a figure, it is important to include the number of units at risk over time along with estimates of variability (eg, confidence limits along with estimates of survival probabilities over time). In designing even basic science experiments, investigators must pay careful attention to control groups (conditions), randomization, blinding, and replication. Do you know from which countries the most students in Germany come? Dot plot of percentage of apoptosis by type. Development of heart failure (%) by type. Things become even more vague when using cell culture or assay mixtures, and researchers are not always consistent. Several approaches can be used to determine whether a variable is subject to extreme or outlying values. Contact Us. We wish to compare apoptosis in cell isolates in 3 different strains of mice (wild type and 2 strains of transgenic [TG] mice) treated with control (Ad‐LacZ) versus adenoviruses expressing catalase or superoxide dismutase. In addition, investigators should specify the details of the design of the experiment to justify the choice of statistical test used. Many statistical pitfalls lie in wait for the un-wary.

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