I am new here, reading a lot what null hypothesis is but not quite get clear picture. Could someone give me a simple explanatation or example please.
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$\begingroup$ It might make more sense to try to figure out what particular parts of what you're reading are remaining unclear and focus attention on those. If you've read a lot you'll likely have read explanations people would give here also (in what you're reading almost everyone is attempting to give you simple explanations already), so identifying your specific concerns would improve people's ability to give helpful answers rather than more of the same explanations. $\endgroup$– Glen_bCommented Mar 15 at 2:25
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3 Answers
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Imagine someone proposes a research question, like 'electric car sales are increasing'. Now they must test it with a hypothesis test.
The null hypothesis can be thought of as the hypothesis of no change. For example, 'electric car sales are the same as last year'
The alternative hypothesis usually links to the research question. For example, 'electric car sales have increased since last year'
Now, we need evidence (data) to reject the null hypothesis, which would allow us to conclude that electric car sales are not the same as last year. If we did not have strong enough evidence to reject the null hypothesis, we can't say that it's necessarily true, we just conclude that we 'fail to reject the null hypothesis'.
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The null hypothesis is the hypothesis you want to reject. Usually, but not always, it is "no change" or "no relationship" or something similar.
In statistical hypothesis inference testing, you test the null by gathering data and running a test (which kind depends on what data you have and what you are trying to show) and then seeing if the results are unlikely if the null is true. How unlikely they have to be is up to you, but common levels are 5% and 1%.
We then either reject the null (yippee!) or fail to reject (we don't accept it). This is similar to a criminal trial (at least in the US and many other places) where we can find the defendant "guilty" or "not guilty" but not "innocent". The prosecution has to prove its case.
In statistics, the researchers are the prosecution and they have to prove their case.
In my opinion, nulls other than the usual are not used enough and unconventional levels of doubt to reject are also not used enough. But that's an aside.
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1$\begingroup$ IMO null hypotheses can be useful, but often I find that a null effect is already out of the question and rather it is a matter of deciding which of a set of alternative hypotheses are the best reflection of the data generating process. Outside of NHST, for me, it often becomes a matter of comparing models whether they are null or not. $\endgroup$– GalenCommented Mar 14 at 15:21
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Consider the frequentist approach: you repeat an experiment N times, you record a value of interest and with those N measures you create a distribution. This distribution tells how frequent each value you may later observd is. In a general setting this distribution is already available (say, the t-distribution), so for the purpose of this explanation we might call it "the theoretical distribution".
Now you come in with the value you observed on your data, and you compare it to the theoretical distribution. Where it lands? If it lands on the extremes than you might conclude that your value does not come from that theoretical distribution.
The null hypothesis is the hypothesis you assume to be true when generating the theoretical distribution we mentioned above. So when your value "fits in" the theoretical distribution, you cannot reject your assumptions - that is, the null hypothesis. If your value is very extreme then you conclude that probably your value does not come from that distribution and you have yo reject your initial hypothesis/assumptions.
Probably is not a very precise explanation but I think the intuition is there.
