Null hypothesis

Its purpose is to be tested and either accepted or rejected based on the evidence obtained from a statistical analysis. The null hypothesis is often used in hypothesis testing, where researchers aim to determine if there is enough evidence to support an alternative hypothesis (denoted as Ha) ... More on findtutors.co.uk

Hi! So, yours is actually a sophisticated question that masquerades as a simple one, so I'll try to answer this in a way that conveys the concept while perhaps alluding to some of its problems. At its heart, the null hypothesis is a sort of "straw man" that is defined by a researcher at the beginning of an experiment that usually represents a state of affairs that would be expected to occur if the researcher's proposal were false. Note that a null hypothesis is entirely imaginary, and it has nothing to do with the actual state of the world. It is contrived, usually to show that the actual state of the world is inconsistent with the null hypothesis. Suppose a researcher is trying to determine whether the heights of men and women are different. A suitable null hypothesis might be that the difference of the two population averages (height of men and height of women) is equal to zero. Then the researcher would conduct his or her experiment by measuring the heights of many men and women. When it comes time to draw a statistical conclusion, he or she will compute the probability that the observed data (the set of heights) could have come from the null hypothesis (i.e., a world where there is no difference). This probability is called a "p-value". Conceptually, this is similar to a "proof by contradiction," in which we assert that, if the probability is very small that the data could have originated from the null hypothesis, it must not be true. This is what is meant by "rejecting the null hypothesis". It is different from a proof by contradiction because rejecting the null proves nothing, except perhaps that the null is unlikely to be the source of the observed data. It doesn't prove that the true difference is 5 inches, or 1 inch, or anything. Because of this, rejecting the null hypothesis is in NO WAY equivalent to accepting an alternative hypothesis. Usually, in the course of an experiment, we observe a result (such as the observed height difference, perhaps it is ~5 inches) that, once we reject, replaces the hypothesized value of 0 under the null. However, we DON'T know anything about the probability that our observed value is "correct", which is why we never say that we have "accepted" an alternative. I actually hesitate to discuss an "alternative" hypothesis because most researchers never state one and it doesn't matter for the purposes of null hypothesis significance testing (NHST). It is just the name given to the conclusion drawn by the researchers after they have rejected their null hypothesis. Philosophically, there is an adage that data can never be used to prove an assertion, only to disprove one. It includes an analogy about a turkey concluding that he is loved by his human family and is proven wrong upon being slaughtered on Thanksgiving. I'll include a link if I can find it. Now, think about this: The concept of rejecting a null hypothesis probably seems very reasonable as long as we are careful not to overinterpret it, and this is how NHST was performed for decades. But consider - what is the probability that the null hypothesis is true in the first place? In other words, how likely is it that the difference between mens' and womens' heights is equal to zero? I propose that the probability is exactly zero, and if you disagree then I will find a ruler small enough to prove me correct. The difference can never be equal to exactly zero (even though this is the "straw man" that our experiment refutes), so we are effectively testing against a hypothesis that can never be true. Rejecting a hypothesis we already know to be false tells us nothing important ("the data are unlikely to have come from this state that cannot be true"). And since every null hypothesis is imaginary, it is suggested that any null hypothesis can be rejected with enough statistical power (read:sample size). Often a "significant" result says more about a study's sample size than it does about the study's findings, even though the language used in papers/media suggests to readers that the findings are more "important" or "likely to be correct". This has, in part, led to a reproducibility crisis in the sciences and, for some, an undermining of subject-matter-experts' trust in the use of applied statistics. More on reddit.com

More or less, the null hypothesis is a hypothesis that states there wasn't anything important discovered in observation. If it's a two-group trial and control study, the null hypothesis is generally "the trial group is no different".

If the study is testing a medication, the null hypothesis is "it doesn't do anything".

If the study is comparing gender differences in some mental task, the null hypothesis is "there isn't a difference".

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Going to start off with some relevant definitions first Dependent variable — the thing that’s being measured, a response variable (ie. heart rate) Independent variable — the thing that’s being manipulated or set by the researchers; the variable that is hypothesized to cause a change in the dependent variable (ie. a drug treatment) Population — the group being tested. Important to note that the conclusion can only be generalized to the population of the study. If the experiment (“sample population”) only includes men of Asian descent aged 45 and over, then the conclusion cannot be assumed to extend to men of other backgrounds, women, young men, children, etc. The alternative hypothesis is the research question in the form of a true/false statement (This drug affects heart rate). The null hypothesis is the “blank.” It assumes there is no relation between the independent and dependent variables (This drug has no effect on heart rate). With no evidence, we default that the null hypothesis is true. The experiment aims to disprove the null hypothesis in favor of the alternative.* The p-value is the probability of getting the observed result under the assumption that the null hypothesis is true — that there is no relation between the variables. A small p-value means that it would be very unlikely to observe this result by random chance; therefore, it is likely that something is causing it. In a well-designed experiment, the cause can be attributed to the independent variable. *Just because a result is not significant, does not necessarily mean that the null hypothesis is definitively true, it just means we did not find evidence to say otherwise. Same goes for the alternative. Just because a result is significant, does not mean it is the end-all explanation. We just have evidence to support the conclusion. That’s not a go-ahead for all you conspiracy theorists out there to say “Gotcha!” If the results can be observed time and time again, then that’s more and more evidence to support the explanation. More on reddit.com