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Starnes, UPDATED The Practice of Statistics, 6e, Chapter 9
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Terms in this set (11)
significance test
Formal procedure for using observed data to decide between two competing claims (the null hypothesis and the alternative hypothesis). The claims are usually statements about parameters.
null hypothesis H₀
Claim we weigh evidence against in a significance test. Often the null hypothesis is a statement of "no difference."
alternative hypothesis Hₐ
The claim that we are trying to find evidence for in a significance test.
one-sided alternative hypothesis
An alternative hypothesis is one-sided if it states that a parameter is greater than the null value or if it states that the parameter is less than the null value.
two-sided alternative hypothesis
The alternative hypothesis is two-sided if it states that the parameter is different from the null value (it could be either smaller or larger).
P-value
The probability of getting evidence for the alternative hypothesis Hₐ as strong as or stronger than the observed evidence when the null hypothesis H₀ is true. The smaller the P-value, the stronger the evidence against H₀ and in favor of Hₐ provided by the data.
significance level
Fixed value α that we use as a boundary for deciding whether an observed result is too unlikely to happen by chance alone when the null hypothesis is true. The significance level gives the probability of a Type I error.
Type I error
An error that occurs if we reject H₀ when H₀ is true. That is, the data give convincing evidence that Hₐ is true when it really isn't.
Type II error
An error that occurs if we fail to reject H₀ when Hₐ is true. That is, the data do not give convincing evidence that Hₐ is true when it really is.
standardized test statistic
Value that measures how far a sample statistic is from what we would expect if the null hypothesis H₀ were true, in standard deviation units.
power
The probability that a test will find convincing evidence for Hₐ when a specific alternative value of the parameter is true. The power of a test against any alternative is 1 minus the probability of a Type II error for that alternative; that is, power = 1 − P(Type II error).
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