Overview of basic concepts in Statistics and Probability - SAMSI
Overview of basic concepts in Statistics and Probability - SAMSI
Overview of basic concepts in Statistics and Probability - SAMSI
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Hypothesis test<strong>in</strong>g<br />
<strong>Overview</strong> <strong>of</strong><br />
<strong>basic</strong> <strong>concepts</strong><br />
<strong>in</strong> <strong>Statistics</strong><br />
<strong>and</strong><br />
<strong>Probability</strong><br />
Avanti<br />
Athreya<br />
Prelim<strong>in</strong>aries<br />
Important<br />
distributions,<br />
scal<strong>in</strong>g laws,<br />
<strong>and</strong> the CLT<br />
Parametric<br />
estimation <strong>and</strong><br />
hypothesis<br />
test<strong>in</strong>g<br />
A statistical hypothesis is an assertion about the value <strong>of</strong> some<br />
unknown parameter, either a characteristic <strong>of</strong> a population or a<br />
characteristic <strong>of</strong> a probability distribution.<br />
The null hypothesis H 0 is the claim that is <strong>in</strong>itially assumed to<br />
be true (sometimes called the prior belief).<br />
The alternative hypothesis H a is a claim that is different from<br />
the null.<br />
Example: the average height <strong>of</strong> American women is µ = 65<br />
<strong>in</strong>ches; H 0 = 65, compared to an alternative hypothesis µ ≠ 65.<br />
Question: What does the sample data tell us about the likely<br />
truth <strong>of</strong> H 0 ?
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