Why statistics quantifies uncertainty in SciPy

Introduction

Statistics helps us understand how sure or unsure we are about data and results. It puts numbers on uncertainty so we can make better decisions.

When you want to know how reliable a survey result is.

When you need to predict outcomes but data has natural randomness.

When comparing two groups and want to see if differences are real or by chance.

When measuring quality control in manufacturing to detect problems.

When estimating the chance of an event happening based on past data.

Syntax

SciPy

import scipy.stats as stats

# Example: Calculate confidence interval for a sample mean
confidence_interval = stats.norm.interval(alpha=0.95, loc=sample_mean, scale=sample_std / (n**0.5))

The interval function gives a range where the true value likely lies.

The alpha parameter sets the confidence level (e.g., 0.95 means 95%).

Examples

This shows the range where the true average likely falls with 95% confidence.

SciPy

import scipy.stats as stats

# 95% confidence interval for mean 50, std 10, sample size 25
ci = stats.norm.interval(0.95, loc=50, scale=10 / (25**0.5))
print(ci)

The p-value tells how likely the observed data would happen if the true mean was zero.

SciPy

import scipy.stats as stats

# Calculate p-value for a t-test comparing sample mean to 0
t_stat, p_value = stats.ttest_1samp([2,3,5,6,9], 0)
print(f"p-value: {p_value}")

Sample Program

This program calculates the average height and shows a range where the true average height likely lies with 95% confidence. It uses statistics to quantify uncertainty in the average.

SciPy

import scipy.stats as stats

# Sample data: heights in cm
data = [170, 172, 168, 165, 174, 169, 171, 173, 167, 170]

# Calculate sample mean and standard deviation
sample_mean = sum(data) / len(data)
sample_std = (sum((x - sample_mean)**2 for x in data) / (len(data) - 1))**0.5

# Calculate 95% confidence interval for the mean
confidence_interval = stats.norm.interval(0.95, loc=sample_mean, scale=sample_std / (len(data)**0.5))

print(f"Sample mean: {sample_mean:.2f} cm")
print(f"95% confidence interval: ({confidence_interval[0]:.2f}, {confidence_interval[1]:.2f}) cm")

Important Notes

Uncertainty is natural in data because of randomness and measurement limits.

Statistics gives tools to measure and communicate this uncertainty clearly.

Summary

Statistics helps us put numbers on how uncertain we are about data.

Confidence intervals and p-values are common ways to show uncertainty.

Using these tools helps make better, informed decisions.