Improve this question. Jeromy Anglim Pulkit Sinha Pulkit Sinha 1 1 gold badge 4 4 silver badges 6 6 bronze badges. We need to know the conditions under which this "proof" is to occur. Add a comment. Active Oldest Votes. Improve this answer. This is a nice example of the importance of being clear about one's standard of "proof. But maybe Bayesian methods are better I added a link to an online version of Streiner's article; I hope you don't mind feel free to remove.
S says, "wait--you need power H's pt is actually just as subversive of empirical proofs rejecting the null as of proofs of the null. H says induction can't support causal inference. Ok; but there's no alternative for empirical study!
A simple rendering of the math is that the null and its alternatives are assumed to yield disjoint sets of outcomes; e. Of course "prove" here implicitly includes "conditional on the model," which itself is never established with the same rigor as, say, a mathematical theorem; it implicitly includes "conditional on the accuracy of the observations;" and it implicitly includes that the hypotheses can be unambiguously interpreted.
That is, just as you can't say "there is no effect of the variable" you are unable to say that "the effect size of the variable is 1. Statistics always have confidence intervals. The fact that the accepted answer is claiming otherwise is absolutely tragic. What hypothesis testing provides as an answer is: assuming my hypothesis is true , are the data that I sampled consistent with it? And by no means the other way around.
It does not take much reasoning to understand that you cannot deduce from that whether the hypothesis is true or not. From a decision theory perspective the answer is clearly yes if 1 there is no uncertainty in the decision making process, for then it is a mathematical exercise to work out what the correct decision is. Henry Henry Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password.
Post as a guest Name. Email Required, but never shown. Featured on Meta. Now live: A fully responsive profile. Linked 2. A pre-eminent mathematician, he had laid the foundation for the theory of infinite numbers in the s.
But it was not just rejection by Kronecker that pushed Cantor to depression; it was his inability to prove a particular mathematical conjecture he formulated in , and was convinced was true, called the Continuum Hypothesis.
But if he blamed himself, he did so needlessly. Poor Cantor had chosen quite the mast to lash himself to. How is it possible, though, for something to be provably neither provable nor disprovable?
An exact answer would take many pages of definitions, lemmas, and proofs. But we can get a feeling for what this peculiar truth condition involves rather more quickly. Consider a collection of goats in a small forest. If there are six goats and six trees, and each goat is tethered to a different tree, then each goat and tree are uniquely paired. If, however, there are six goats and eight trees, we will not be able to set up such a correspondence: no matter how hard we try, there will be two trees that are goat-free.
Correspondences can be used to compare the sizes of much larger collections than six goats—including infinite collections. The rule is that, if a correspondence exists between two collections, then they have the same size. If not, then one must be bigger. At first glance, this seems to indicate that the collection of natural numbers is larger than the collection of multiples of five. But in fact they are equal in size: every natural number can be paired uniquely with a multiple of five such that no number in either collection remains unpaired.
A hypothesis also includes an explanation of why the guess may be correct, according to National Science Teachers Association. A hypothesis is a suggested solution for an unexplained occurrence that does not fit into current accepted scientific theory.
The basic idea of a hypothesis is that there is no pre-determined outcome. For a hypothesis to be termed a scientific hypothesis, it has to be something that can be supported or refuted through carefully crafted experimentation or observation. This is called falsifiability and testability, an idea that was advanced in the midth century a British philosopher named Karl Popper, according to the Encyclopedia Britannica.
A key function in this step in the scientific method is deriving predictions from the hypotheses about the results of future experiments, and then performing those experiments to see whether they support the predictions. This statement gives a possibility if and explains what may happen because of the possibility then.
The statement could also include "may. Notice that all of the statements, above, are testable. The primary trait of a hypothesis is that something can be tested and that those tests can be replicated, according to Midwestern State University. An example of untestable statement is, "All people fall in love at least once. Also, it would be impossible to poll every human about their love life.
An untestable statement can be reworded to make it testable, though. For example, the previous statement could be changed to, "If love is an important emotion, some may believe that everyone should fall in love at least once.
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