Statistics-In-Python

Let's build your roadmap.

Category 1: The Bedrock - Descriptive Statistics

(You can't build a house without a foundation. These describe the basic features of your data.)

1. Measures of Central Tendency:

   • Question: "What is the typical or central value in my data?" (Mean, Median, Mode)
   • Project Idea: Analyze a real estate dataset. Calculate the mean and median house price. Explain why the median is often a better measure for house prices than the mean due to outliers (mansions).

2. Measures of Dispersion/Variability:

   • Question: "How spread out is my data?" (Variance, Standard Deviation, IQR)
   • Project Idea: Using the same real estate data, calculate the standard deviation of prices for two different neighborhoods. Use the IQR to create box plots and visually show which neighborhood has more price variability.

3. Distributions, Skewness & Kurtosis:

   • Question: "What is the shape of my data's distribution? Is it symmetric or lopsided?"
   • Project Idea: Analyze customer age in a marketing dataset. Plot a histogram and calculate skewness to determine if the customer base is skewed towards younger or older individuals.

4. Correlation Matrix & Heatmaps:

   • Question: "How are my numerical variables related to each other at a high level?"
   • Project Idea: Use the Spotify dataset. Create a correlation matrix for all the audio features (danceability, energy, loudness, etc.) and visualize it with a Seaborn heatmap. Identify the strongest positive and negative correlations.

Category 2: The Core of Inference - Hypothesis Testing

(This is where you move from describing to making statistically-backed claims.)

5. One-Sample T-Test:

   • Question: "Is the mean of my sample significantly different from a known or hypothesized value?"
   • Project Idea: Analyze a dataset of student test scores. The national average score is 75. Is the average score of students at your sample school significantly different from the national average?

6. Independent Samples T-Test:

   • Question: "Is there a significant difference in the means of a variable between two independent groups?"
   • Project Idea: Using the Titanic dataset, test if the mean Age of passengers who survived is significantly different from the mean Age of those who did not.

7. Paired Samples T-Test:

   • Question: "Is there a significant difference in the means of two related groups (e.g., before-and-after)?"
   • Project Idea: Analyze a dataset of patients' blood pressure measured before and after taking a new medication. Is there a statistically significant reduction in blood pressure?

8. Analysis of Variance (ANOVA):

   • Question: "Is there a significant difference in the means of a variable across three or more independent groups?"
   • Project Idea: Use the Spotify dataset. Test if the mean popularity is significantly different across three distinct genres (e.g., 'pop', 'rock', 'hip-hop').

9. Post-Hoc Tests (e.g., Tukey's HSD):

   • Question: (After a significant ANOVA) "Okay, a difference exists, but which specific groups are different from each other?"
   • Project Idea: Following your ANOVA project, apply Tukey's HSD to determine which specific genre pairs (pop vs. rock? pop vs. hip-hop?) have significantly different mean popularity scores.

10. Chi-Squared Test for Independence:

    • Question: "Is there a statistically significant association between two categorical variables?"
    • Project Idea: Using the Titanic dataset, test if there is a significant association between Pclass (1st, 2nd, 3rd) and Survived status.

11. Proportion Z-Test (One and Two Sample):

    • Question: "Is the proportion of successes in a group different from a known value? OR, are the proportions of successes in two groups different?" (The heart of A/B testing).
    • Project Idea: You have two versions of a website (A and B). Analyze a dataset showing which version users saw and whether they clicked a "buy" button. Is the conversion rate of version B significantly higher than version A?

Category 3: The Predictors - Regression Modeling

12. Simple Linear Regression:

    • Question: "Can I use one numerical variable to predict another numerical variable?"
    • Project Idea: Use a dataset of cars. Can you predict a car's MPG (Miles Per Gallon) based on its Weight? Plot the regression line.

13. Multiple Linear Regression:

    • Question: "Can I use multiple numerical variables to create a better prediction of another numerical variable?"
    • Project Idea: Extend your car project. Predict MPG using Weight, Horsepower, and Engine Size. Report the R-squared value and interpret the coefficients.

14. Residual Analysis for Regression:

    • Question: "How good is my regression model? Are its predictions biased? Do they meet the assumptions of linear regression?"
    • Project Idea: For your multiple linear regression project, plot the residuals (prediction errors). Check for patterns, normality (using a Q-Q plot), and homoscedasticity (constant variance). This is a CRITICAL step for any serious regression analysis.

15. Logistic Regression:

    • Question: "Can I use one or more variables (numerical or categorical) to predict a binary outcome (Yes/No, 1/0)?"
    • Project Idea: Use a dataset from a bank to predict customer churn (Yes/No) based on their account balance, age, and number of products.

Category 4: The Robust Toolkit - Non-Parametric Tests

(Use these when your data violates the assumptions of the standard tests, like not being normally distributed.)

16. Mann-Whitney U Test:

    • Question: (Alternative to Independent T-Test) "Are the distributions of a variable different between two independent groups?"
    • Project Idea: You have customer satisfaction scores (on a 1-10 scale, which is ordinal, not continuous) for two different store locations. Use the Mann-Whitney U test to see if one store has significantly higher satisfaction scores.

17. Kruskal-Wallis H Test:

    • Question: (Alternative to ANOVA) "Are the distributions of a variable different across three or more independent groups?"
    • Project Idea: You have employee performance ratings (ordinal data) for three different departments. Use the Kruskal-Wallis test to see if there's a significant difference in performance between the departments.

18. Spearman Rank Correlation:

    • Question: (Alternative to Pearson Correlation) "Is there a monotonic relationship (as one variable increases, the other consistently increases or decreases, but not necessarily linearly) between two variables?"
    • Project Idea: Analyze the relationship between a country's "ranking in press freedom" and its "ranking in happiness." Since this is ordinal (rank) data, Spearman is more appropriate than Pearson.

Category 5: The Specialists - Advanced & Domain-Specific Techniques

19. Principal Component Analysis (PCA):

    • Question: "Can I reduce the number of correlated features in my dataset into a smaller set of uncorrelated 'principal components' while retaining most of the information?"
    • Project Idea: Use the Spotify dataset with its many audio features. Apply PCA to reduce them to just 2 or 3 components and then create a scatter plot of the components, colored by genre, to see if they separate.

20. Time Series Decomposition:

    • Question: "Can I break down my time-series data into its core components: Trend, Seasonality, and Residuals?"
    • Project Idea: Analyze a dataset of monthly airline passenger numbers. Decompose the time series to visually identify the long-term upward trend and the clear yearly seasonality.

21. Autocorrelation (ACF) and Partial Autocorrelation (PACF) Plots:

    • Question: "How does a value in my time series correlate with its own past values?"
    • Project Idea: Using the same airline passenger data, create ACF and PACF plots. Interpret them to understand the strength of the seasonality (e.g., a strong spike at lag 12 would indicate a yearly pattern).

22. Survival Analysis (Kaplan-Meier Curve):

    • Question: "What is the probability of an event (e.g., customer churn, product failure) happening over time?"
    • Project Idea: Use a telecom customer churn dataset. Create a Kaplan-Meier plot to visualize the probability of a customer remaining subscribed over a period of months.

23. Cox Proportional Hazards Model:

    • Question: (Advanced Survival Analysis) "Which features have a significant impact on the 'hazard rate' or the rate at which an event occurs?"
    • Project Idea: Extend your Kaplan-Meier project. Use a Cox model to determine if features like monthly contract vs. yearly contract significantly impact the likelihood of a customer churning at any given time.

24. Cluster Analysis (K-Means):

    • Question: "Can I segment my data into distinct groups (clusters) based on their features, without any pre-existing labels?"
    • Project Idea: Use a dataset of mall customers with age, annual income, and spending score. Use K-Means to segment them into distinct personas (e.g., "young big spenders," "frugal seniors").

25. Silhouette Score Analysis:

    • Question: (For Clustering) "How good are my clusters? Are they dense and well-separated?"
    • Project Idea: For your K-Means project, calculate the silhouette score for different numbers of clusters (k=2, 3, 4, 5...) to help you determine the optimal number of clusters for your data.

26. Factor Analysis (EFA/CFA):

    • Question: "Is there an underlying, unobserved 'latent variable' or 'factor' that explains the correlations among my observed variables?"
    • Project Idea: Analyze survey data where you have multiple questions about "job satisfaction." Use Factor Analysis to see if these questions all load onto a single underlying "satisfaction" factor.

27. Bayesian Inference / A/B Testing:

    • Question: "Instead of a simple yes/no from a p-value, what is the actual probability that version B is better than version A, and by how much?"
    • Project Idea: Re-do your Proportion Z-Test (A/B test) project using a Bayesian approach (e.g., with the pymc library). Instead of a p-value, your output will be a full probability distribution of the difference in conversion rates.

Category 6: The Foundation of Trust - Experimental Design

28. Power Analysis & Sample Size Calculation:

    • Question: "How many samples do I need to collect for my experiment to have a good chance of detecting a real effect if one exists?" (To be done before an experiment).
    • Project Idea: Plan an A/B test. Assume you want to detect a 2% lift in conversion rate. Use a power analysis tool/script to calculate how many users you need to show each version of the website to achieve 80% statistical power.

29. Bootstrapping:

    • Question: "How can I estimate the uncertainty (like a confidence interval) of a statistic (e.g., the median) when I don't know the underlying distribution of the data?"
    • Project Idea: Take a small sample of salaries from a company. Calculate the median salary. Use bootstrapping (resampling with replacement) to generate a 95% confidence interval for that median salary.

30. Stratified Sampling:

    • Question: "How can I draw a sample from a population in a way that ensures my sample is representative of key subgroups?"
    • Project Idea: You have a population of university students (70% undergrad, 30% grad). Write a Python script to draw a sample of 100 students using stratified sampling, ensuring your sample also contains exactly 70 undergrads and 30 grads. Compare this to a simple random sample to show how the latter might be unbalanced by chance.

I wish someone had done this for me when i started my career

• Focus on Interpretation: For every project, the code is only 30% of the work. The other 70% is interpreting the results in plain English. What does the p-value mean? What is the business implication? Why did you choose this test? What are its assumptions?
• Check Assumptions: For every test, make it a habit to list its assumptions (e.g., normality, independence, equal variances) and write code to check them. This is what separates amateurs from professionals.
• Visualize Everything: A plot is worth a thousand statistics. Before and after every test, visualize your data. A box plot before a t-test, a scatter plot before a correlation, etc.

This roadmap is a serious undertaking, but completing it will give you a level of practical statistical fluency that is exceptionally rare and valuable. Godspeed. You have a fantastic journey ahead of you.