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For example, when would a hypothesis test bed used?

Ljones
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  • Whatever you do in statistics depends on your aim, i.e., what you want to find out. "If I know that the proportion of people who play basketball increased from 3.1% to 4.5% over 4 years" - couldn't that be enough to know? What more would you want to know for which you'd need a hypothesis test? – Christian Hennig May 23 '21 at 09:13
  • Hi, why did you shorten and alter the question? I think it should be rolled back to the previous (more detailed and informative) version, unless you have a strong reason for the change. – Arya McCarthy Jun 12 '21 at 23:48
  • Yeah changed for a reason :) – Ljones Jun 14 '21 at 02:27

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That's a fair question and the answer relates to the difference between taking a population census and taking a sample. It depends of how the statistics of 3.1% and 4.5% were obtained. Do you have complete data or were the proportions estimated from a sample of your target population?

If you have complete data, i.e., if you know the total number of people who play basketball in your target population, then there is indeed no purpose in a hypothesis test. You already know the truth.

If the proportions were instead estimated by polling a random collection of people, say by telephone or by a questionaire, then a hypothesis test would be needed in order to confirm that the increase from 3.1% to 4.5% is statistically significant and likely to be representative of the whole population. The null hypothesis in this case would be that the proportion has not changed. As well as conducting a hypothesis test, it would also be useful to attach a "margin of error" to each of the proportions, as is often done for political polls.

Gordon Smyth
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