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In subsequent examples, the Null hypothesis is always stated explicitly, e.g. as "data comes from the standard normal distribution", "the coin is fair", etc. There is no example when a property of the distribution is stated and the null hypothesis would be defined as non-existence or a logical
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Would it be better to stick with the Null hypothesis only, state that the test can reject it or not reject it and leave the logic implications to the reader? Or perhaps add a clear example where we can infer acceptance of "our hypothesis" based on rejection of the null hypothesis?
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I propose the sentence say "As stated above, T is a test statistic." This matches a sentence earlier in the article, this sentence is present: "The p-value is a function of the chosen test statistic and is therefore a random variable."
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As a reader, if I read "usually" that suggests an exception. But there is no counter-example. A p-value is ALWAYS derived from a a test statistic. Therefore, Knowledge should drop "usually" in this sentence.
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However, all three examples are from the USA. There should be more balance, preferably with an international source (ISO standard, or IMS, or IMU, or ISI?), or at least from some other countries/regions.
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negation of the property. Furthermore, "data comes not from N(0,1)" makes little sense as "our statistical hypothesis" because it is too unspecific.
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This is especially confusing in the beginning when the reader does not know what is going to be tested.
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Recommended
Standards for Statistical Symbols and Notation. COPSS Committee on Symbols and Notation
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As our statistical hypothesis will, by definition, state some property of the distribution, the
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has already been assigned to another variable. Italics should always be used for the "
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is the default hypothesis under which that property does not exist.
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What is the best way to use here? I have seen all of these.
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Unnecessary hedging: "Usually, T is a test statistic."
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