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</html>";s:4:"text";s:9530:"Morris Kline, "Mathematics - The Loss of Certainty", Oxford University Press, 1980). @whuber I'm tough enough to stand a few down-votes regardless. As experiments became harder to control, experimental errors needed to be formally described and accounted for to calibrate the preponderance of experimental evidence against the proposed mathematical model. The majority of limit theorems can be loosely connected to Murphy's law, i.e. Thus it is important to understand what statistics is, not only from an application point of view but also from an interpretation point of view. Consider hypothesis testing with p-values. I don't know what to make of the statement, "the $p$-value, which is a concept that arose to make sense of data, but it's not a logical consequence of more basic principles", I'm not even sure if it can really even be right or wrong. It is the interpretation done by the business and/or the translation of the results to the business by the statistician that isn't math. It's gambling. I advise you to give it a try and you will be surprised about the mathematical beauty of it. It certainly includes an element of philosophy, but I don't think it is the only branch of mathematics where that is the case (see e.g. I'd say statistics is a branch of mathematics in the same way that logic is a branch of mathematics. The one central theme in these applied sciences the formulation of a process as a model relating some predictor to a response. the subjectivity is made explicit here too), it's just often chosen based on convention, whereas there's usually more thought put into choosing (informative) Bayesian priors. If we're going to reject the null, then we want this probability to be small, to approach zero. But just like those other disciplines, statistics is not math; math is just a tool used to solve statistical problems. Our test statistic was developed such that it conformed to a particular distribution, probably student's t. Under the null hypothesis, the percentile of our observed test statistic is the p-value. Statistics depends on math, like a lot of other disciplines (physics, engineering, chemistry, computer science). In the end, the statistical analysis should be able to tell us something concrete about the sample that we are studying. This of course is not the case for physics. A number of errors are possible in the interpretation of statistical results and a careful analysis needs to be made to prevent these errors. Statistics uses math, but it is not math. What is the significance? In other words, the p-value gives the probability that we would get a value as far from the expectation of the distribution (or farther) as the observed test statistic. How can I deal with claims of technical difficulties for an online exam? @David: The "at least as extreme" makes a great difference - the probability of the observed value under the null is not in general the p-value, even for discrete test statistics where it makes sense. :) I think you were respectful at all times, so don't worry about that. The techniques of statistics are applied to a multitude of other areas of knowledge. I've already delved much deeper in the p-value example than I was intending to. This is a sensitive topic for many--for example, many college math departments are still trying to treat statisticians as mathematicians, to the detriment of both--and so it's likely to elicit some strong reactions. Statistics is also used in associated tasks such as designing experiments and surveys and planning the collection and analysis of data from these. So we reject the null hypothesis in favor of an alternative hypothesis. With respect to (3), consider the following list of disciplines: All of these disciplines could easily be classified as “applied statistics”. However, these two usages usually occur in distinct contexts and though there is a scope for confusion, a careful study of the usage context should clear matters up. Statistics PhDs do not have to "contribute to the body of mathematical concepts." (ii) The calculations almost always involve numbers, but what makes it, I feel obligated to give a short answer, as I am former pure mathematician (PhD and 3.5 years of postdoc in some kind algebra), and now an applied statistician... well, the kind of stats you learn for applied stats, like "when do I use a $t$-test" or what not, for a mathematician, looks like a recipe book, not like maths. This allows us to make educated guesses, but that's really all that statistics is: the art of making very well informed guesses. The signficance level is a fairly arbitrary rule-of-thumb cutoff: setting it to $0.01$ is equivalent to saying, "it's acceptable if 1 in 100 repetitions of this experiment suggest that we reject the null, even if the null is in fact true.". Forward domain to a specific port and IP while using the forwarded domain in the URL. For instance, no mathematical theorem can tell what distribution or prior you can use for your data/model. No problem, save it as a course and come back to it later. When such practices are intentional, they can be hard to detect.   certain; and as far as they are certain, they do not refer to reality. The ideas of presenting data and drawing relevant inferences are central to the successful use of statistical theory. In our specific example, we found that the probability of observing the data we gathered if the null hypothesis were true was just $0.1\%$, so we rejected the null. But what is this p-value really? I think the key difference between "chemistry", "engineering", and "balancing my checkbook" is that those fields just use existing mathematical concepts. site design / logo © 2020 Stack Exchange Inc; user contributions licensed under cc by-sa. There's certainly a degree of subjectivity in frequentist hypothesis testing, but it's the same kind of subjectivity that gets invoked when interpreting a Bayes Factor. It is only once we hand the results to someone for interpretation does statistics exit mathematics. What is the benefit of having FIPS hardware-level encryption on a drive when you can use Veracrypt instead? Let's say we are testing some hypothesis with significance $\alpha = 0.01$, and after gathering data we find a p-value of $0.001$. It only takes a minute to sign up. We've found these tools to be extremely effective over the last 100 years, but the people of the future may wonder in horror at the fragility of our methods. Statistical tools often make simplifying assumptions to reduce the messy real world data to something that fits into the problem domain of a solved mathematical abstraction. Statistics is the study of numerical information, called data. You can use it freely (with some kind of link), and we're also okay with people reprinting in publications like books, blogs, newsletters, course-material, papers, wikipedia and presentations (with clear attribution). Maybe its because I'm a plebe and haven't taken any advanced mathematical courses, but I don't see why statistics isn't mathematics. "What is statistics?" We can keep calculating up to the limit, just as we can keep making a sample size larger, but neither give increased insight past a certain threshold. Didn't the Bernoulli's interest in probability stem from gambling rather than physics? Hi Paul, as you say, stats is full of nice theorems and proofs (+1), there is even an axiomatic theory of probability, developed by Kolmogorov, as I explain in my answer. Assumptions/approximations are useful for lots of math. Is information conserved in quantum mechanics (after wave function collapse)? Category with zero morphisms implies zero object? ;o). I know it's tangential to the point you were making, but if. Statistics is a collection of mathematical techniques that help to analyze and present data. It is the science of discovering complex but necessary consequences from simple axioms. formal languages) to be a variety of mathematics, so yes, I suppose I probably would. Is there any *mathematical* basis for the Bayesian vs frequentist debate? Statistics can also imply a second meaning, which is the computed quantity with the help of statistical methods. Isn't there still an important distinction, though, between Probability Theory (Maths) & its application to problems of inference (Statistics)? leading professional societies say statistics is, The p-value gives us the probability that we observe the data at hand given that the null is true, here at the bottom of page 1 and next pages, If a random variable is a function, then how do we define a function of a random variable, stats.stackexchange.com/questions/230415/…, “Question closed” notifications experiment results and graduation, MAINTENANCE WARNING: Possible downtime early morning Dec 2/4/9 UTC (8:30PM…. @whuber That is very interesting. But math did not give us our conclusion. *: The notable exception is this answer that effectively states the boundaries are artificial due to various social reasons. I would view the study of any system for manipulating symbols according to a set of rules (e.g. The properties of a triangle that I learned about in grade school I believe are considered true math, even though they don't hold true in non-Elucidean geometry. There is a lot of overlap. Given that it's all numbers, mostly taught by maths departments and you get maths credits for it, I wonder whether people just mean it half-jokingly when they say it, like saying it's a minor part of maths, or just applied maths. ";s:7:"keyword";s:18:"is statistics math";s:5:"links";s:4147:"<a href="http://digiprint.coding.al/site/page.php?tag=41e064-fever-tree-elderflower-tonic-water">Fever Tree Elderflower Tonic Water</a>,
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