Think about what a low alpha test means when the results are found to be significant and what a higher alpha test means when the results are found to be significant. Explain when a lower alpha should be used and when it\’s okay to use a higher alpha.
Researchers routinely choose an alpha level of 0.05 for testing their hypotheses. What are some experiments for which you might want a lower alpha level (e.g., 0.01)? What are some situations in which you might accept a higher level
Researchers routinely choose an alpha level of 0.05 for testing their hypotheses. What are some experiments for which you might want a lower alpha level (e.g., 0.01)? What are some situations in which you might accept a higher level (e.g., 0.1)?\n \nFollow this guideline for credit please…\nThink about what a low alpha test means when the results are found to be significant and what a higher alpha test means when the results are found to be significant. Explain when a lower alpha should be used and when it\’s okay to use a higher alpha. You should not necessarily need to use resources to find examples.\n\n Scientific method: Statistical errors\nP values, the \’gold standard\’ of statistical validity, are not as reliable as many scientists assume.\n\nRegina Nuzzo\n12 February 2014\nArticle tools\n \nFor a brief moment in 2010, Matt Motyl was on the brink of scientific glory: he had discovered that extremists quite literally see the world in black and white.\n\nThe results were “plain as day”, recalls Motyl, a psychology PhD student at the University of Virginia in Charlottesville. Data from a study of nearly 2,000 people seemed to show that political moderates saw shades of grey more accurately than did either left-wing or right-wing extremists. “The hypothesis was sexy,” he says, “and the data provided clear support.” The P value, a common index for the strength of evidence, was 0.01 — usually interpreted as \’very significant\’. Publication in a high-impact journal seemed within Motyl\’s grasp.\n\nBut then reality intervened. Sensitive to controversies over reproducibility, Motyl and his adviser, Brian Nosek, decided to replicate the study. With extra data, the P value came out as 0.59 — not even close to the conventional level of significance, 0.05. The effect had disappeared, and with it, Motyl\’s dreams of youthful fame1.\n\nIt turned out that the problem was not in the data or in Motyl\’s analyses. It lay in the surprisingly slippery nature of the P value, which is neither as reliable nor as objective as most scientists assume. “P values are not doing their job, because they can\’t,” says Stephen Ziliak, an economist at Roosevelt University in Chicago, Illinois, and a frequent critic of the way statistics are used.\n\nFor many scientists, this is especially worrying in light of the reproducibility concerns. In 2005, epidemiologist John Ioannidis of Stanford University in California suggested that most published findings are false2; since then, a string of high-profile replication problems has forced scientists to rethink how they evaluate results.\n\nAt the same time, statisticians are looking for better ways of thinking about data, to help scientists to avoid missing important information or acting on false alarms. “Change your statistical philosophy and all of a sudden different things become important,” says Steven Goodman, a physician and statistician at Stanford. “Then \’laws\’ handed down from God are no longer handed down from God. They\’re actually handed down to us by ourselves, through the methodology we adopt.”\n\nOut of context\nP values have always had critics. In their almost nine decades of existence, they have been likened to mosquitoes (annoying and impossible to swat away), the emperor\’s new clothes (fraught with obvious problems that everyone ignores) and the tool of a “sterile intellectual rake” who ravishes science but leaves it with no progeny3. One researcher suggested rechristening the methodology “statistical hypothesis inference testing”3, presumably for the acronym it would yield.\n\nThe irony is that when UK statistician Ronald Fisher introduced the P value in the 1920s, he did not mean it to be a definitive test. He intended it simply as an informal way to judge whether evidence was significant in the old-fashioned sense: worthy of a second look. The idea was to run an experiment, then see if the results were consistent with what random chance might produce. Researchers would first set up a \’null hypothesis\’ that they wanted to disprove, such as there being no correlation or no difference between two groups. Next, they would play the devil\’s advocate and, assuming that this null hypothesis was in fact true, calculate the chances of getting results at least as extreme as what was actually observed. This probability was the P value. The smaller it was, suggested Fisher, the greater the likelihood that the straw-man null hypothesis was false.\n\nFor all the P value\’s apparent precision, Fisher intended it to be just one part of a fluid, non-numerical process that blended data and background knowledge to lead to scientific conclusions. But it soon got swept into a movement to make evidence-based decision-making as rigorous and objective as possible. This movement was spearheaded in the late 1920s by Fisher\’s bitter rivals, Polish mathematician Jerzy Neyman and UK statistician Egon Pearson, who introduced an alternative framework for data analysis that included statistical power, false positives, false negatives and many other concepts now familiar from introductory statistics classes. They pointedly left out the P value.\n\nBut while the rivals feuded — Neyman called some of Fisher\’s work mathematically “worse than useless”; Fisher called Neyman\’s approach “childish” and “horrifying [for] intellectual freedom in the west” — other researchers lost patience and began to write statistics manuals for working scientists. And because many of the authors were non-statisticians without a thorough understanding of either approach, they created a hybrid system that crammed Fisher\’s easy-to-calculate P value into Neyman and Pearson\’s reassuringly rigorous rule-based system. This is when a P value of 0.05 became enshrined as \’statistically significant\’, for example. “The P value was never meant to be used the way it\’s used today,” says Goodman.\n\nWhat does it all mean?\nOne result is an abundance of confusion about what the P value means4. Consider Motyl\’s study about political extremists. Most scientists would look at his original P value of 0.01 and say that there was just a 1% chance of his result being a false alarm. But they would be wrong. The P value cannot say this: all it can do is summarize the data assuming a specific null hypothesis. It cannot work backwards and make statements about the underlying reality. That requires another piece of information: the odds that a real effect was there in the first place. To ignore this would be like waking up with a headache and concluding that you have a rare brain tumour — possible, but so unlikely that it requires a lot more evidence to supersede an everyday explanation such as an allergic reaction. The more implausible the hypothesis — telepathy, aliens, homeopathy — the greater the chance that an exciting finding is a false alarm, no matter what the P value is.\n\n\nNature special: Challenges in irreproducible research\nThese are sticky concepts, but some statisticians have tried to provide general rule-of-thumb conversions (see \’Probable cause\’). According to one widely used calculation5, a P value of 0.01 corresponds to a false-alarm probability of at least 11%, depending on the underlying probability that there is a true effect; a P value of 0.05 raises that chance to at least 29%. So Motyl\’s finding had a greater than one in ten chance of being a false alarm. Likewise, the probability of replicating his original result was not 99%, as most would assume, but something closer to 73% — or only 50%, if he wanted another \’very significant\’ result6, 7. In other words, his inability to replicate the result was about as surprising as if he had called heads on a coin toss and it had come up tails.\n\nCritics also bemoan the way that P values can encourage muddled thinking. A prime example is their tendency to deflect attention from the actual size of an effect. Last year, for example, a study of more than 19,000 people showed8 that those who meet their spouses online are less likely to divorce (p < 0.002) and more likely to have high marital satisfaction (p < 0.0
01) than those who meet offline (see Nature https://doi.org/rcg; 2013). That might have sounded impressive, but the effects were actually tiny: meeting online nudged the divorce rate from 7.67% down to 5.96%, and barely budged happiness from 5.48 to 5.64 on a 7-point scale. To pounce on tiny P values and ignore the larger question is to fall prey to the “seductive certainty of significance”, says Geoff Cumming, an emeritus psychologist at La Trobe University in Melbourne, Australia. But significance is no indicator of practical relevance, he says: “We should be asking, \’How much of an effect is there?\’, not \’Is there an effect?\’”\n\nPerhaps the worst fallacy is the kind of self-deception for which psychologist Uri Simonsohn of the University of Pennsylvania and his colleagues have popularized the term P-hacking; it is also known as data-dredging, snooping, fishing, significance-chasing and double-dipping. “P-hacking,” says Simonsohn, “is trying multiple things until you get the desired result” — even unconsciously. It may be the first statistical term to rate a definition in the online Urban Dictionary, where the usage examples are telling: “That finding seems to have been obtained through p-hacking, the authors dropped one of the conditions so that the overall p-value would be less than .05”, and “She is a p-hacker, she always monitors data while it is being collected.”\n\n“The P value was never meant to be used the way it\’s used today.”\nSuch practices have the effect of turning discoveries from exploratory studies — which should be treated with scepticism — into what look like sound confirmations but vanish on replication. Simonsohn\’s simulations have shown9 that changes in a few data-analysis decisions can increase the false-positive rate in a single study to 60%. P-hacking is especially likely, he says, in today\’s environment of studies that chase small effects hidden in noisy data. It is tough to pin down how widespread the problem is, but Simonsohn has the sense that it is serious. In an analysis10, he found evidence that many published psychology papers report P values that cluster suspiciously around 0.05, just as would be expected if researchers fished for significant P values until they found one.
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