correlation_pvalue

C++ Function Reference

1 Signature

double BigDataStatMeth::correlation_pvalue(double r, int n)

2 Description

Compute p-value for correlation coefficient - R equivalent implementation.

3 Parameters

r (double): Correlation coefficient [-1, 1]
n (int): Sample size (number of observations)

4 Returns

Two-tailed p-value [0, 1], or NaN if invalid input

5 Details

Implements the exact equivalent of R’s correlation test: t<-(rsqrt(n-2))/sqrt(1-r^2)p<-2(pt(abs(t),(n-2),lower.tail=FALSE))

6 Call Graph

7 Source Code

Implementation

File: inst/include/hdf5Algebra/matrixCorrelation.hpp • Lines 355-372

inline double correlation_pvalue(double r, int n) {
        if (std::isnan(r) || n < 3 || std::abs(r) >= 1.0) {
            return std::numeric_limits<double>::quiet_NaN();
        }
        
        // Calculate t-statistic exactly as in R: t <- (r*sqrt(n-2))/sqrt(1-r^2)
        double df = n - 2;
        double t_stat = (r * std::sqrt(df)) / std::sqrt(1.0 - r * r);
        
        // Calculate p-value exactly as in R: p <- 2*(pt(abs(t),(n-2), lower.tail=FALSE))
        // pt(abs(t), df, lower.tail=FALSE) = 1 - pt(abs(t), df, lower.tail=TRUE)
        double abs_t = std::abs(t_stat);
        double cdf_value = t_distribution_cdf(abs_t, df);
        double p_value = 2.0 * (1.0 - cdf_value);
        
        // Ensure p-value is in valid range [0, 1]
        return std::max(0.0, std::min(1.0, p_value));
    }

8 Usage Example

#include "BigDataStatMeth.hpp"

// Example usage
auto result = correlation_pvalue(...);

---
title: "correlation_pvalue"
subtitle: "C++ Function Reference"
---

## Signature

```cpp
double BigDataStatMeth::correlation_pvalue(double r, int n)
```

## Description

Compute p-value for correlation coefficient - R equivalent implementation.

## Parameters

- `r` (`double`): Correlation coefficient [-1, 1]
- `n` (`int`): Sample size (number of observations)

## Returns

Two-tailed p-value [0, 1], or NaN if invalid input

## Details

Implements the exact equivalent of R's correlation test: t<-(r*sqrt(n-2))/sqrt(1-r^2)p<-2*(pt(abs(t),(n-2),lower.tail=FALSE))

## Call Graph

::: {.diagram-section}
<object type="image/svg+xml" data="images/namespace_big_data_stat_meth_af47e358be69a1901acebfba04c05f5e3_cgraph.svg" class="class-diagram">
  <img src="images/namespace_big_data_stat_meth_af47e358be69a1901acebfba04c05f5e3_cgraph.svg" alt="Function dependencies"/>
</object>
:::

## Source Code

::: {.callout-note collapse="true"}
### Implementation

**File:** `inst/include/hdf5Algebra/matrixCorrelation.hpp` • **Lines 355-372**

```cpp
inline double correlation_pvalue(double r, int n) {
        if (std::isnan(r) || n < 3 || std::abs(r) >= 1.0) {
            return std::numeric_limits<double>::quiet_NaN();
        }
        
        // Calculate t-statistic exactly as in R: t <- (r*sqrt(n-2))/sqrt(1-r^2)
        double df = n - 2;
        double t_stat = (r * std::sqrt(df)) / std::sqrt(1.0 - r * r);
        
        // Calculate p-value exactly as in R: p <- 2*(pt(abs(t),(n-2), lower.tail=FALSE))
        // pt(abs(t), df, lower.tail=FALSE) = 1 - pt(abs(t), df, lower.tail=TRUE)
        double abs_t = std::abs(t_stat);
        double cdf_value = t_distribution_cdf(abs_t, df);
        double p_value = 2.0 * (1.0 - cdf_value);
        
        // Ensure p-value is in valid range [0, 1]
        return std::max(0.0, std::min(1.0, p_value));
    }
```
:::

## Usage Example

```cpp
#include "BigDataStatMeth.hpp"

// Example usage
auto result = correlation_pvalue(...);
```