Understanding Descriptive vs Inferential Statistics: A Complete Guide for Beginners

📗 Chapter 4: Comparing Descriptive and Inferential Statistics

Know When to Describe and When to Predict – The Complete Comparison Guide

🧠 Introduction

Understanding data is more than just looking at averages or charts. It’s about knowing what story the data tells and whether we’re reading it or predicting the next chapter. This is where the two main branches of statistics come into play: descriptive and inferential statistics.

While descriptive statistics help us summarize data, inferential statistics help us conclude or predict beyond it.

This chapter dives deep into comparing both, not just in theory — but with real-life examples, side-by-side code, and practical tips on when and how to use each approach effectively.

📘 Section 1: Recap – What Are Descriptive & Inferential Statistics?

📊 Descriptive Statistics:

Summarize and describe the features of a dataset.

• Focused on the data you have
• No assumptions about broader context
• Easy to visualize and calculate

🔍 Inferential Statistics:

Use sample data to make predictions or inferences about a larger population.

• Makes probabilistic statements
• Involves confidence intervals, hypothesis testing, modeling
• Requires assumptions (random sampling, independence, etc.)

📘 Section 2: Key Differences at a Glance

📘 Section 3: Real-World Comparison Examples

🏥 Scenario 1: Healthcare Data

Goal: Understand average BMI of patients.

• Descriptive: Calculate mean, SD, and median of BMI in the sample.
• Inferential: Test whether BMI in this sample is significantly higher than national average using a one-sample t-test.

python

import pandas as pd

import numpy as np

import scipy.stats as stats

bmi_data = np.random.normal(28, 4, 100)

mean_bmi = np.mean(bmi_data)

std_bmi = np.std(bmi_data)

# Descriptive

print("Mean BMI:", mean_bmi)

print("Standard Deviation:", std_bmi)

# Inferential: Test if BMI > 25

t_stat, p_val = stats.ttest_1samp(bmi_data, 25)

print("T-Statistic:", t_stat, "P-Value:", p_val)

📊 Scenario 2: Marketing A/B Testing

Goal: Compare response rates for two ad versions.

• Descriptive: Plot average click-through rate (CTR) for Group A and B.
• Inferential: Use a two-sample t-test to check if the CTR difference is statistically significant.

python

group_A = np.random.binomial(1, 0.12, 100)

group_B = np.random.binomial(1, 0.17, 100)

print("Mean CTR A:", np.mean(group_A))

print("Mean CTR B:", np.mean(group_B))

# Inferential

t_stat, p_val = stats.ttest_ind(group_A, group_B)

print("T-Statistic:", t_stat, "P-Value:", p_val)

📘 Section 4: Visualization – Descriptive vs Inferential

Histogram (Descriptive)

python

import matplotlib.pyplot as plt

import seaborn as sns

sns.histplot(bmi_data, kde=True)

plt.title("BMI Distribution")

plt.show()

Confidence Interval Plot (Inferential)

python

import statsmodels.stats.api as sms

ci = sms.DescrStatsW(bmi_data).tconfint_mean()

print("95% Confidence Interval for BMI:", ci)

📘 Section 5: When to Use Each – Practical Guidelines

📘 Section 6: Risks of Misuse

📘 Section 7: Combining Descriptive & Inferential Statistics

In most real-world projects, both are used together:

• Descriptive: EDA → find patterns, check for outliers, build summary tables.
• Inferential: Model building, testing assumptions, drawing final conclusions.

📌 Example Workflow:

📋 Summary Table