Question

目前，我正在研究awk脚本，对测量数据进行一些统计分析。我使用线性回归来获得参数估计，标准误差等，并且还想计算零假设检验（t检验）的p值。

到目前为止，这是我的脚本，知道如何计算p值吗？

BEGIN {
    ybar = 0.0
    xbar = 0.0
    n = 0
    a0 = 0.0
    b0 = 0.0
    qtinf0975 = 1.960 # 5% n = inf
}

{ # y_i is in $1, x_i has to be counted
    n = n + 1
    yi[n] = $1*1.0
    xi[n] = n*1.0
}

END {
    for ( i = 1; i <= n ; i++ ) {
        ybar = ybar + yi[i]
        xbar = xbar + xi[i]
    }
    ybar = ybar/(n*1.0)
    xbar = xbar/(n*1.0)

    bhat = 0.0
    ssqx = 0.0
    for ( i = 1; i <= n; i++ ) {
        bhat = bhat + (yi[i] - ybar)*(xi[i] - xbar)
        ssqx = ssqx + (xi[i] - xbar)*(xi[i] - xbar)
    }
    bhat = bhat/ssqx
    ahat = ybar - bhat*xbar

    print "n: ", n
    print "alpha-hat: ", ahat
    print "beta-hat: ", bhat

    sigmahat2 = 0.0
    for ( i = 1; i <= n; i++ ) {
        ri[i] = yi[i] - (ahat + bhat*xi[i])
        sigmahat2 = sigmahat2 + ri[i]*ri[i]
    }
    sigmahat2 = sigmahat2 / ( n*1.0 - 2.0 )

    print "sigma-hat square: ", sigmahat2

    seb = sqrt(sigmahat2/ssqx)

    print "se(b): ", seb

    sigmahat = sqrt((seb*seb)*ssqx)
    print "sigma-hat: ", sigma
    sea = sqrt(sigmahat*sigmahat * ( 1 /(n*1.0) + xbar*xbar/ssqx))

    print "se(a): ", sea


    # Tests

    print "q(inf)(97.5%): ", qtinf0975

    Tb = (bhat - b0) / seb
    if ( qtinf0975 > Tb )
        print "T(b) plausible: ", Tb, " < ", qtinf0975
    else
        print "T(b) NOT plausible: ", Tb, " > ", qtinf0975

    print "confidence(b): [", bhat - seb * qtinf0975,", ", bhat + seb * qtinf0975 ,"]"

    Ta = (ahat - a0) / sea
    if ( qtinf0975 > Ta )
        print "T(a) plausible: ", Ta, " < ", qtinf0975
    else
        print "T(a) NOT plausible: ", Ta, " > ", qtinf0975

    print "confidence(a): [", ahat - seb * qtinf0975,", ", ahat + seb * qtinf0975 ,"]"
}

Answer 1

你可能试图在方差相等的假设下进行配对t检验。我建议你看看优秀的MathWorld网站上的corresponding entry。

Answer 2

好的，我发现了一个javascript实现并将其移植到awk这是用于计算p值的函数：

function statcom ( mq, mi, mj, mb )
{
    zz = 1
    mz = zz
    mk = mi
    while ( mk <= mj ) {
        zz = zz * mq * mk / ( mk - mb)
        mz = mz + zz
        mk = mk + 2
    }
    return mz
}

function studpval ( mt , mn )
{
    PI = 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679 # thank you wikipedia
    if ( mt < 0 )
        mt = -mt
    mw = mt / sqrt(mn)
    th = atan2(mw, 1)
    if ( mn == 1 )
        return 1.0 - th / (PI/2.0)
    sth = sin(th)
    cth = cos(th)
    if ( mn % 2 == 1 )
        return 1.0 - (th+sth*cth*statcom(cth*cth, 2, mn-3, -1))/(PI/2.0)
    else
        return 1.0 - sth * statcom(cth*cth, 1, mn-3, -1)
}

我已将它们整合为：

    pvalb = studpval(Tb, n)
    if ( pvalb > 0.05 )
        print "p-value(b) plausible: ", pvalb, " > 0.05"
    else
        print "p-value(b) NOT plausible: ", pvalb, " < 0.05"

    pvala = studpval(Ta, n)
    if ( pvala > 0.05 )
        print "p-value(a) plausible: ", pvala, " > 0.05"
    else
        print "p-value(a) NOT plausible: ", pvala, " < 0.05"

如何计算假设检验中的p值（线性回归）

2 个答案: