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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  1. new T_Test1(x: VectorD, μ0: Double)

    x

    the sample's vector of data

    μ0

    the "known" population mean

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  14. 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.

  15. 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

  16. def se(n: Int): Double

    Compute the standard error for mean difference.

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  18. def t(se: Double): Double

    Compute the Student's t statistic.

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