class T_Test1 extends AnyRef
The T_Test1 class is used to test whether a data sample 'x' comes from a
population with "known" mean 'μ0', by comparing the sample mean 'μ' with 'μ0',
using a (Two-Sided/Two-Tailed) One-Sample t-test.
Assumes the sample is drawn from a Normal distribution.
The error in the test is measured by the conditional probability 'p' that
a "difference is detected" when there "actually is none".
p = P(different | μ = μ0)
The power of the test is the ability to detect actual differences. '1 - power' is measured by the conditional probability 'p2' that a "difference is not detected" when there "actually is one".
p2 = P(! different | μ ≠ μ0)
These are called Type I (measured by p) and Type II (measured by p2) errors.
- See also
en.wikipedia.org/wiki/Type_I_and_type_II_errors ----------------------------------------------------------------------------- H0: μ = μ0 Null Hypothesis H1: μ ≠ μ0 Alternative Hypothesis (Two-Sided) -----------------------------------------------------------------------------
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- new T_Test1(x: VectorD, μ0: Double)
- x
the sample's vector of data
- μ0
the "known" population mean
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- def p(t: Double, df: Int): Double
Compute the probability of a Type I Error using the Student's t distribution.
Compute the probability of a Type I Error using the Student's t distribution.
- t
the value of the Student's t statistic
- df
the effective degrees of freedom
- See also
scalation.random.CDF.studentTCDF Mistake probability: in rejecting the null hypothesis.
- def p2(t: Double, df: Int, α: Double = 0.05): Double
Compute the probability of a Type II Error using the Student's t distribution.
Compute the probability of a Type II Error using the Student's t distribution. Mistake probability: in not rejecting the null hypothesis.
- t
the value of the Student's t statistic
- df
the effective degrees of freedom
- α
the desired sigificance level
- See also
statweb.stanford.edu/~susan/courses/s141/hopower.pdf
- def se(n: Int): Double
Compute the standard error for mean difference.
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- def t(se: Double): Double
Compute the Student's t statistic.
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