Hypothesis Testing in Python (t-test, ANOVA)

The user wants to analyze the Titanic dataset. Specifically, they want to:

1. Load the data from a provided URL.
2. Test if the average age differs significantly between survivors and non-survivors using a t-test.

Following the "AI Data Analyst" persona rules:

• I must work iteratively.
• I cannot provide the full pipeline at once.
• The first step for any dataset that isn't loaded is to load and inspect: shape, columns, and head().
• I should only provide one Python code block per response.
• I must use the specified currency formatting (though not applicable here).
• I must follow the visualization/ML rules (though not applicable yet).

Plan: Step 1: Load the data from the URL and inspect it. Step 2: (In subsequent turns) Handle missing values for the 'Age' column and 'Survived' column. Step 3: (In subsequent turns) Perform the t-test.

Current step: Load and inspect.

The user wants to test whether the average age differs significantly between survivors and non-survivors using a t-test. The dataset is loaded. The columns Survived and Age exist. To perform a t-test, I need to separate the Age values into two groups based on Survived (0 or 1). I must handle missing values in the Age column, as t-tests cannot be performed on NaN values.

Plan:

1. Extract Age for Survived == 1 and Survived == 0.
2. Remove NaN values from these groups.
3. Run scipy.stats.ttest_ind.
4. Display the results.

The latest output confirms the presence of Survived and Age columns. Now I need to perform the actual statistical test.

The user wants to know if the average age differs significantly between survivors and non-survivors using a t-test.

Looking at the notebook state:

• Data loaded: df.
• Groups created: survived_age (mean ~28.34, count 290) and not_survived_age (mean ~30.63, count 424).
• T-test performed: $T$-statistic = -2.0667, $P$-value = 0.0391.

Interpretation:

• The $p$-value (0.0391) is less than the standard significance level of 0.05.
• This indicates that the difference in average age between survivors and non-survivors is statistically significant.
• On average, survivors were younger (28.34 years) than non-survivors (30.63 years).

The original goal was: "load titanic data ... and test whether average age differs significantly between survivors and non-survivors using a t-test".

The results are fully available in output-2. Path A is appropriate.

Final answer construction:

• State the observed means.
• State the p-value.
• Conclude whether the difference is significant.

The user wants to test if survival rate is independent of passenger class using a chi-square test.

- `df` is already loaded and contains `Survived` and `Pclass`.
- Survival is binary (0 or 1).
- Pclass is categorical (1, 2, 3).

- A chi-square test of independence requires a contingency table (cross-tabulation) of the two variables.
- I can use `pd.crosstab` to create the table.
- I can use `scipy.stats.chi2_contingency` to perform the test.

- Import `stats` from `scipy` (already done in previous cell, but good to keep it in mind or re-import if necessary, though in a notebook it's usually persistent).
- Create a contingency table of `Survived` vs `Pclass`.
- Run the chi-square test.
- Display the table and the p-value.

The user wants to test whether survival rate is independent of passenger class using a chi-square test.

Looking at the notebook state:

• cell-3 performed the chi-square test of independence between Survived and Pclass.
• The contingency_table shows the counts of survivors (1) and non-survivors (0) across the three passenger classes (1, 2, 3).
• The output shows:
  • Chi-square statistic: 102.8890
  • P-value: 0.0000 (which is $< 0.05$)
• The contingency table shows a clear difference in survival proportions (e.g., class 1 has more survivors than non-survivors, whereas class 3 has significantly more non-survivors).

Conclusion:

• The p-value is extremely low ($p < 0.0001$), which means we reject the null hypothesis of independence.
• Therefore, survival rate is not independent of passenger class; there is a statistically significant association between the two.

Decision: Path A. The outputs are sufficient to answer the goal.

The user wants to test if the Fare differs significantly across the three passenger classes (Pclass) using ANOVA (Analysis of Variance).

*   `df`: Titanic dataset (DataFrame) containing `Fare` and `Pclass`.
*   Columns of interest: `Fare` (numeric) and `Pclass` (categorical/ordinal).

*   Objective: ANOVA test to compare means of `Fare` across `Pclass`.
*   Step 1: Group `Fare` by `Pclass`.
*   Step 2: Use `scipy.stats.f_oneway` to perform the ANOVA.
*   Step 3: Provide descriptive statistics (means per class) for context.

*   The `Fare` column might have NaNs? Checking the first load output... `Fare` seems okay, but it's good practice to handle missing values. In the Titanic dataset, `Fare` usually doesn't have NaNs in the train set, but I should ensure the arrays passed to `f_oneway` are clean.
*   `Pclass` has values 1, 2, 3.

*   Group `Fare` values based on `Pclass`.
*   Run `stats.f_oneway`.
*   Print results.

The user wants to know if the fare differs significantly across the three passenger classes using ANOVA.

Looking at the notebook state:

• Cell 4 executed stats.f_oneway(*fares_by_class).
• The output shows:
  • Mean Fare for Pclass 1: 84.154687
  • Mean Fare for Pclass 2: 20.662183
  • Mean Fare for Pclass 3: 13.675550
  • F-statistic: 242.3442
  • P-value: 0.0000

The p-value is essentially 0, which is much lower than the standard significance level of 0.05. This means we reject the null hypothesis that the means are equal. There is a statistically significant difference in fares across the three passenger classes. The means clearly show that first-class passengers paid significantly more (84.15 USD) than second-class (20.66 USD) and third-class (13.68 USD) passengers.

Current outputs are sufficient to answer the original goal. I will choose Path A.

Currency rule: Use USD instead of $.

• The user wants a summary of three statistical tests performed in the notebook and their business (or practical) interpretation.

  • The notebook contains:

    1. T-test: Age vs. Survived.
    2. Chi-square test: Pclass vs. Survived.
    3. ANOVA: Fare vs. Pclass.

  • Test 1 (T-test): Age vs. Survival.

    • Mean Age (Survived): 28.34
    • Mean Age (Not Survived): 30.63
    • P-value: 0.0391 (Significant at 0.05).
    • Interpretation: There is a statistically significant difference in age between those who survived and those who didn't. Younger passengers were slightly more likely to survive.

  • Test 2 (Chi-square): Pclass vs. Survival.

    • P-value: 0.0000 (Highly significant).
    • Crosstab: Pclass 1 has a higher survival rate relative to its count compared to Pclass 3.
    • Interpretation: Passenger class is strongly associated with survival. Being in a higher class significantly increased the chances of survival.

  • Test 3 (ANOVA): Fare vs. Pclass.

    • Mean Fares: Pclass 1 (84.15 USD), Pclass 2 (20.66 USD), Pclass 3 (13.68 USD).
    • P-value: 0.0000 (Highly significant).
    • Interpretation: There is a significant difference in ticket prices across the three classes, as expected. This confirms that the class system was clearly delineated by cost.

  • Ensure currency is formatted as USD per the system prompt.

  • Avoid using $ symbols for money.

  • Keep it professional and data-driven.