Creating a P-value in PHP

Question

I need to calculate a P-value (for significance checking) out of the Z value, mean(0), standarddeviation(1), normal distrubution being cummulative.

Is there a function in PHP that could do that?

This is my current code:

$P_value = (1/sqrt(2*pi()))*exp(-0.5*pow($this->ZValue,2));

ZValue = -4,688072309 which is confirmed the right value.

Expected value: 1,37895E-06

Value: 6.9681241978373E-6

Probably something wrong in the formula, but can't spot the fault.

Edit:

If anyone is interested, here is the code that does work:

function CalculateP_Value(){
    $this->CalculateZ();

    $this->PValue = (1/sqrt(2*pi()))*exp(-0.5*pow($this->ZValue,2));
}

function SetConstant(){
    $this->CalculateZ();

    $this->A1 = 0.319381530;
    $this->A2 = -0.356563782;
    $this->A3 = 1.781477937;
    $this->A4 = -1.8221255978;
    $this->A5 = 1.330274429;
    if($this->ZValue>0){
        $this->K = 1.0/(1.0+0.2316419*$this->ZValue);
    }
    else{
        $this->ZValue*=-1;
        $this->K = 1.0/(1.0+0.2316419*$this->ZValue);
    }
}

function CalculateCumulative(){
    $this-> SetConstant();
    $this-> CalculateP_Value();

    $this->Cumulative = $this->GetCalculateCumulative($this->ZValue);

}

function GetCalculateCumulative($z) {
    if($z >= 0) {
        $val = 1.0 - $this->PValue*($this->A1*$this->K + $this->A2*pow($this->K,2) + $this->A3*pow($this->K,3) + $this->A4*pow($this->K,4) + $this->A5*pow($this->K,5));
        return $val;
    }
    else {
        $val = 1.0 - $this->GetCalculateCumulative(-1 * $z);
        return $val;
    }
}

Answer 1

I looked into it some more and it seems like it's not that easy to calculate p-value from z-score. This gives a formula, which seems to be a series calculation. Your formula looks like a good enough approximation to it, but it's weird that it gives a larger value than expected. If anything, it should be smaller than expected.

As for a solution, I think it's best you just use a conversion table since you're dealing with a standard distribution and a set significance level (or a few).