Statistics¶

These functions compute statistical summaries and hypothesis tests.

mean¶

mean(list)

Computes the arithmetic mean of a list of numbers.

Parameters:

• list - A list of numbers

Returns: The mean value.

let avg = mean([10, 20, 30]);
// avg = 20.0

median¶

median(list)

Computes the median (middle value) of a list of numbers.

Parameters:

• list - A list of numbers

Returns: The median value.

let mid = median([1, 3, 5, 7, 9]);
// mid = 5.0

variance¶

variance(list)

Computes the sample variance of a list of numbers (using ddof=1).

Parameters:

• list - A list of numbers

Returns: The sample variance.

let v = variance([2, 4, 6, 8]);

standard_deviation¶

standard_deviation(list)

Computes the sample standard deviation of a list of numbers.

Parameters:

• list - A list of numbers

Returns: The sample standard deviation.

let sd = standard_deviation([2, 4, 6, 8]);

percentile¶

percentile(list, p)

Computes the p-th percentile of a list of numbers.

Parameters:

• list - A list of numbers
• p - Percentile value between 0 and 100

Returns: The value at the specified percentile.

let p95 = percentile(scores, 95);
let p50 = percentile(scores, 50);  // equivalent to median

confidence_interval¶

confidence_interval(list, confidence_level)

Computes a confidence interval for the mean of a list of numbers.

Parameters:

• list - A list of numbers
• confidence_level - Confidence level between 0 and 1 (default: 0.95)

Returns: A record with three fields:

• "lower" - Lower bound of the interval
• "upper" - Upper bound of the interval
• "mean" - The sample mean

let ci = confidence_interval(scores, 0.95);
// ci = {"lower": 0.72, "upper": 0.88, "mean": 0.80}

paired_t_test¶

paired_t_test(mean_diff, std, num_samples)

Computes a paired t-test statistic.

Parameters:

• mean_diff - Mean of the paired differences
• std - Standard deviation of the paired differences
• num_samples - Number of paired samples

Returns: The t-statistic.

let t_stat = paired_t_test(0.05, 0.02, 100);

t_test_p_value¶

t_test_p_value(t_statistic, num_samples)

Computes a p-value from a t-statistic.

Parameters:

• t_statistic - The t-statistic value
• num_samples - Number of samples (used to compute degrees of freedom)

Returns: The two-tailed p-value.

let p = t_test_p_value(t_stat, 100);