Implementation:Online ml River Stats SEM

Knowledge Sources	Online_ml_River
Domains	Online_Learning, Statistics
Last Updated	2026-02-08 16:00 GMT

Overview

SEM computes the running standard error of the mean using Welford's algorithm.

Description

This statistic calculates the standard error of the mean, which measures the precision of the sample mean as an estimate of the population mean. It is computed as the standard deviation divided by the square root of the sample size. The implementation extends the Var class and uses Welford's algorithm for numerical stability. The ddof parameter controls the degrees of freedom correction.

Usage

Use SEM when you need to quantify the uncertainty in the estimated mean of streaming data. Common applications include confidence interval construction, hypothesis testing, quality control, A/B testing analysis, and any scenario where you need to assess how precisely you have estimated the true mean.

Code Reference

Source Location

• Repository: Online_ml_River
• File: river/stats/sem.py

Signature

class SEM(var.Var):
    # Inherits from Var class
    # Constructor uses parent Var.__init__(ddof)
    # Overrides get() method to compute SEM
    pass

Import

from river import stats

I/O Contract

Inputs

Name	Type	Required	Description
x	numbers.Number	Yes	Value to update the statistic with
ddof	int	Yes (init)	Delta Degrees of Freedom (default: 1)

Outputs

Name	Type	Description
get()	float or None	Current standard error of the mean (None if n=0)

Usage Examples

from river import stats

# Basic standard error of mean
X = [3, 5, 4, 7, 10, 12]
sem = stats.SEM()

for x in X:
    sem.update(x)
    print(f"Value: {x}, SEM: {sem.get():.6f}")

# Output:
# Value: 3, SEM: 0.000000
# Value: 5, SEM: 1.000000
# Value: 4, SEM: 0.577350
# Value: 7, SEM: 0.853912
# Value: 10, SEM: 1.240967
# Value: 12, SEM: 1.447219

# Rolling SEM
from river import utils

X = [1, 4, 2, -4, -8, 0]
rolling_sem = utils.Rolling(stats.SEM(ddof=1), window_size=3)

for x in X:
    rolling_sem.update(x)
    print(f"Value: {x}, Rolling SEM: {rolling_sem.get():.6f}")

# Output:
# Value: 1, SEM: 0.000000
# Value: 4, SEM: 1.500000
# Value: 2, SEM: 0.881917
# Value: -4, SEM: 2.403700
# Value: -8, SEM: 2.905932
# Value: 0, SEM: 2.309401

# Use case: confidence interval estimation
mean = stats.Mean()
sem_stat = stats.SEM()

data = [23, 25, 27, 22, 26, 24, 28, 25, 23, 26]

for x in data:
    mean.update(x)
    sem_stat.update(x)

# 95% confidence interval (approximately mean ± 2*SEM)
mean_val = mean.get()
sem_val = sem_stat.get()
ci_lower = mean_val - 2 * sem_val
ci_upper = mean_val + 2 * sem_val

print(f"Mean: {mean_val:.2f}")
print(f"SEM: {sem_val:.2f}")
print(f"95% CI: [{ci_lower:.2f}, {ci_upper:.2f}]")

# Comparing two groups
group_a_sem = stats.SEM()
group_b_sem = stats.SEM()

for x in [10, 12, 11, 13, 9]:
    group_a_sem.update(x)

for x in [15, 17, 16, 18, 14]:
    group_b_sem.update(x)

print(f"Group A SEM: {group_a_sem.get():.3f}")
print(f"Group B SEM: {group_b_sem.get():.3f}")

Related Pages

• Environment:Online_ml_River_Python_Runtime_Environment