rs_stats/
std_err.rs

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use crate::std_dev;

/// std_err is the standard error, represnting the standard deviation of its distribution
#[inline]
pub fn std_err<T: num::ToPrimitive>(t: &[T]) -> Option<f64> {
    std_dev(t).map(|std| std / (t.len() as f64).sqrt())
}

#[cfg(test)]
mod tests {
    use super::*;

    const EPSILON: f64 = 1e-9;

    #[test]
    fn test_std_err_integers() {
        // Dataset: [1, 2, 3, 4, 5]
        // Standard deviation of [1, 2, 3, 4, 5] is 1.414213562 (approx)
        // Standard error should be std_dev / sqrt(n) = 1.414213562 / sqrt(5) = 0.632455532 (approx)
        let data = vec![1, 2, 3, 4, 5];
        let result = std_err(&data);
        let expected = 0.632455532; // Calculated value of the standard error
        assert!(
            (result.unwrap() - expected).abs() < EPSILON,
            "Standard error should be approximately 0.632455532"
        );
    }

    #[test]
    fn test_std_err_floats() {
        // Dataset: [1.0, 2.0, 3.0, 4.0, 5.0]
        // Standard deviation of [1.0, 2.0, 3.0, 4.0, 5.0] is the same as for integers
        let data = vec![1.0, 2.0, 3.0, 4.0, 5.0];
        let result = std_err(&data);
        let expected = 0.632455532;
        assert!(
            (result.unwrap() - expected).abs() < EPSILON,
            "Standard error for floats should be approximately 0.632455532"
        );
    }

    #[test]
    fn test_std_err_single_element() {
        // Dataset with only one element: [5]
        // Standard deviation is 0, and thus standard error should also be 0
        let data = vec![5];
        let result = std_err(&data);
        let expected = 0.0;
        assert_eq!(
            result,
            Some(expected),
            "Standard error for a single element should be 0.0"
        );
    }

    #[test]
    fn test_std_err_empty() {
        // Empty dataset: []
        // There should be no standard error, result should be None
        let data: Vec<i32> = vec![];
        let result = std_err(&data);
        assert_eq!(
            result, None,
            "Standard error for an empty dataset should be None"
        );
    }
}