Statistical Analysis

Introduction

Statistical analysis is a core skill for data scientists, allowing you to summarize, interpret, and draw conclusions from data.

This tutorial covers:

✅ Descriptive statistics.
✅ Inferential statistics.
✅ Hypothesis testing.
✅ Practical Python implementation.

Descriptive Statistics

Descriptive statistics summarize your dataset’s main characteristics.

Key metrics:

• Mean, Median, Mode
• Standard Deviation, Variance
• Range, Percentiles, IQR

Example:

import pandas as pd

data = {'Scores': [75, 88, 92, 68, 81, 95, 77, 85, 89]}
df = pd.DataFrame(data)

print(df.describe())

Inferential Statistics

Inferential statistics allow you to draw conclusions about a population based on a sample.

Key concepts:

✅ Sampling and sample distributions.
✅ Confidence intervals.
✅ Hypothesis testing.

Hypothesis Testing

What is Hypothesis Testing?

A statistical method to test an assumption (hypothesis) about a population parameter.

Steps: 1️⃣ Formulate null (H0) and alternative (H1) hypotheses.
2️⃣ Choose a significance level (alpha, typically 0.05).
3️⃣ Select and compute the test statistic.
4️⃣ Determine the p-value and interpret results.

Example: One-Sample t-Test

We will test if the average score in our dataset differs from 80.

from scipy import stats

sample_scores = [75, 88, 92, 68, 81, 95, 77, 85, 89]

t_stat, p_value = stats.ttest_1samp(sample_scores, 80)

print("T-statistic:", t_stat)
print("P-value:", p_value)

if p_value < 0.05:
    print("Reject the null hypothesis: The mean is significantly different from 80.")
else:
    print("Fail to reject the null hypothesis: No significant difference from 80.")

Visualization for Statistical Analysis

Visualize distributions to support your statistical analysis:

import matplotlib.pyplot as plt
import seaborn as sns

sns.histplot(sample_scores, kde=True)
plt.axvline(x=80, color='red', linestyle='--', label='Test Value (80)')
plt.title('Score Distribution')
plt.xlabel('Scores')
plt.ylabel('Frequency')
plt.legend()
plt.show()

Best Practices

✅ Always visualize your data before running statistical tests.
✅ Check assumptions of the test you are using (e.g., normality for t-tests).
✅ Report effect sizes and confidence intervals alongside p-values.
✅ Interpret results in the context of your business or research questions.

Conclusion

You now understand: ✅ The difference between descriptive and inferential statistics.
✅ How to perform and interpret hypothesis tests using Python.
✅ How to use statistical analysis to support your data science projects.

What’s Next?

✅ Explore ANOVA, Chi-Squared, and non-parametric tests for broader analysis capabilities.
✅ Move forward to feature selection using statistical methods.
✅ Continue with machine learning model building using statistically informed decisions.

Join our SuperML Community to share your statistical analysis workflows and get feedback from fellow data scientists.

Happy Analyzing! 📊