Hypothesis Testing in Python (t-test, ANOVA)

Perform t-tests, chi-square tests, and ANOVA using real data to answer business questions — guided by an AI data analyst.

This page shows an AI data analysis example. A workflow is a list of prompts (instructions) used to complete one analysis task step by step. We send the same prompt list to multiple AI models, then compare their notebook outputs and scores.

What this AI workflow does

This AI Data Analyst workflow loads the Titanic training dataset from a URL and runs a two-sample t-test to compare average age between survivors and non-survivors. It performs a chi-square test of independence to assess whether survival is associated with passenger class. It runs a one-way ANOVA to test whether fare differs across the three passenger classes and summarizes the results in plain language.

Who this example is for

This is for analysts and students who need a concrete, code-driven example of hypothesis testing on a real dataset. It helps anyone answering business-style questions with statistical tests and interpretable outputs in a notebook.

Expected analysis outcomes

These are the results the AI workflow is expected to generate.

  • t-test result comparing survivor vs non-survivor age with p-value and interpretation
  • chi-square test result for survival vs passenger class independence with p-value and interpretation
  • one-way ANOVA result for fare differences across classes with p-value and interpretation
  • plain-language summary table consolidating all three hypothesis tests

Tools and libraries used

Main Python packages and tooling used to run this AI data analysis task.

  • pandas
  • numpy
  • scipy
  • statsmodels
  • matplotlib
  • seaborn

Prompt sequence

This is the exact list of prompts used in this workflow. The same prompt sequence is sent to each model so outputs and scores can be compared fairly.

  1. 1load titanic data from https://raw.githubusercontent.com/pplonski/datasets-for-start/refs/heads/master/Titanic/train.csv and test whether average age differs significantly between survivors and non-survivors using a t-test
  2. 2test whether survival rate is independent of passenger class using a chi-square test
  3. 3test whether fare differs significantly across the three passenger classes using ANOVA
  4. 4summarise all three test results and their business interpretation

Model Comparison

We compared several LLM models on the same analysis task. The table below shows their scores side by side. You can also open each model run to check the full conversation and notebook results.

Model SourceScoreTaskExecutionOutputReasoningReliabilityRun
gemma4:31b10/102/22/23/32/21/1Open gemma4:31b conversation
glm-5.110/102/22/23/32/21/1Open glm-5.1 conversation
gpt-5.410/102/22/23/32/21/1Open gpt-5.4 conversation
gpt-oss:120b10/102/22/23/32/21/1Open gpt-oss:120b conversation
qwen3-coder-next10/102/22/23/32/21/1Open qwen3-coder-next conversation
qwen3.5:397b10/102/22/23/32/21/1Open qwen3.5:397b conversation
How scoring works

Each run is graded on five dimensions:

  • Task Completion (0-2): how fully the workflow answered the requested analysis task and completed required steps.
  • Execution Correctness (0-2): whether generated code is correct, consistent, and likely runnable without major fixes.
  • Output Quality (0-3): how well tables, charts, and results match the expected analytical outcomes.
  • Reasoning Quality (0-2): clarity and correctness of interpretation, explanation, and conclusions.
  • Reliability (0-1): robustness of the run, including low hallucination risk and stable behavior.

The final score is the sum of these dimensions, so total score = 0-10. Higher values indicate more complete, correct, and reliable notebook results for this workflow.

AI Analysis with gpt-oss:120b

This run uses AI with a step-by-step list of prompts to perform the analysis task Hypothesis Testing in Python (t-test, ANOVA). Below, you can review the full conversation generated with gpt-oss:120b. After the conversation, we show detailed score cards for this run.

#1
load titanic data from https://raw.githubusercontent.com/pplonski/datasets-for-start/refs/heads/master/Titanic/train.csv and test whether average age differs significantly between survivors and non-survivors using a t-test
#2
Thinking

We need to load the data, inspect, then perform t-test of Age between Survived groups. Follow iterative process: first step load data, show shape, columns, head. Provide code.

#3

Here’s a quick load‑and‑inspect of the Titanic CSV:

#4
Load Titanic training data
import pandas as pd

# Load the training data
url = "https://raw.githubusercontent.com/pplonski/datasets-for-start/refs/heads/master/Titanic/train.csv"
df = pd.read_csv(url)

# Show basic info
df.shape, df.columns, df.head()
#5
((891, 12),
 Index(['PassengerId', 'Survived', 'Pclass', 'Name', 'Sex', 'Age', 'SibSp',
        'Parch', 'Ticket', 'Fare', 'Cabin', 'Embarked'],
       dtype='str'),
    PassengerId  Survived  Pclass  \
 0            1         0       3   
 1            2         1       1   
 2            3         1       3   
 3            4         1       1   
 4            5         0       3   
 
                                                 Name     Sex   Age  SibSp  \
 0                            Braund, Mr. Owen Harris    male  22.0      1   
 1  Cumings, Mrs. John Bradley (Florence Briggs Th...  female  38.0      1   
 2                             Heikkinen, Miss. Laina  female  26.0      0   
 3       Futrelle, Mrs. Jacques Heath (Lily May Peel)  female  35.0      1   
 4                           Allen, Mr. William Henry    male  35.0      0   
 
    Parch            Ticket     Fare Cabin Embarked  
 0      0         A/5 21171   7.2500   NaN        S  
 1      0          PC 17599  71.2833   C85        C  
 2      0  STON/O2. 3101282   7.9250   NaN        S  
 3      0            113803  53.1000  C123        S  
 4      0            373450   8.0500   NaN        S  )
#6
Thinking

We have loaded dataset and observed shape (891,12) and columns. Need to test whether average age differs between survivors and non-survivors using a t-test. We have not performed t-test yet. So need Path B: provide code to compute t-test (SciPy). Also need to handle missing ages (NaNs). Provide insight: dataset includes Age column with some missing values. We'll mention that we will drop missing ages before test. Provide a single runnable code block that computes means and performs independent two-sample t-test, outputting mean ages and p-value.

#7

The Titanic data is loaded with 891 rows and 12 columns, including the numeric Age column and the binary Survived indicator.
Before testing the difference in average age we need to drop rows where Age is missing, then compare the two groups (Survived = 1 vs 0) with an independent two‑sample t‑test.

#8
Perform age t test
import numpy as np
from scipy import stats

# Keep rows with a non‑missing Age
df_age = df.dropna(subset=["Age"])

# Split ages by survival status
age_survived = df_age.loc[df_age["Survived"] == 1, "Age"]
age_not_survived = df_age.loc[df_age["Survived"] == 0, "Age"]

# Means
mean_survived = age_survived.mean()
mean_not_survived = age_not_survived.mean()

# Two‑sample t‑test (unequal variances)
t_stat, p_val = stats.ttest_ind(age_survived, age_not_survived, equal_var=False)

(mean_survived, mean_not_survived, t_stat, p_val)
#9
(np.float64(28.343689655172415),
 np.float64(30.62617924528302),
 np.float64(-2.0460301043939704),
 np.float64(0.04118965162586641))
#10
Thinking

We need to decide Path A or B. The goal: test whether average age differs significantly between survivors and non-survivors using a t-test.

We have output of t-test: mean_survived ~28.34, mean_not_survived ~30.63, t-stat -2.046, p-value 0.04119.

That answers the question: there is a significant difference at typical alpha 0.05 (p≈0.041 < 0.05). Provide final answer with insights. No code needed. Use <!--final answer--> marker.

Need to include natural final answer, no headings, no code.

Let's produce concise answer: average age of survivors lower, difference statistically significant.

Will include the values.

#11

The average age of passengers who survived was about 28.34 years, whereas the average age of those who did not survive was about 30.63 years.
A two‑sample t‑test (unequal variances) gave a t‑statistic of ‑2.05 and a p‑value of 0.041. Because the p‑value is below the common 0.05 threshold, we conclude that the difference in average age between survivors and non‑survivors is statistically significant.

#12
test whether survival rate is independent of passenger class using a chi-square test
#13
Thinking

User wants to test independence between survival and passenger class using chi-square test. Need to compute contingency table of Survived vs Pclass and run chi2_contingency. Provide code, then stop.

#14

First, build a contingency table of Survived (0/1) by Pclass (1‑3). Then run a chi‑square test of independence.

#15
Perform chi square test
from scipy.stats import chi2_contingency

# Contingency table
contingency = pd.crosstab(df["Survived"], df["Pclass"])

# Chi‑square test
chi2, p, dof, expected = chi2_contingency(contingency)

(contingency, chi2, p, dof, expected)
#16
(Pclass      1   2    3
 Survived              
 0          80  97  372
 1         136  87  119,
 np.float64(102.88898875696056),
 np.float64(4.549251711298793e-23),
 2,
 array([[133.09090909, 113.37373737, 302.53535354],
        [ 82.90909091,  70.62626263, 188.46464646]]))
#17
Thinking

We need to decide if current outputs answer the original user goal: test whether survival rate is independent of passenger class using chi-square test.

The last output (output-3) shows contingency table, chi2 statistic, p-value ~4.55e-23, degrees of freedom 2, expected frequencies.

Thus we have chi-square test result. We can answer: we reject null hypothesis; survival is not independent of class; p-value extremely low.

Thus Path A sufficient. Provide final answer with explanation and conclusion. No code.

#18

The chi‑square test of independence between Survived and Pclass yields:

  • χ² = 102.89
  • degrees of freedom = 2
  • p‑value ≈ 4.55 × 10⁻²³

Because the p‑value is far below any typical significance level (e.g., 0.05), we reject the null hypothesis of independence.

Conclusion: Survival rate on the Titanic is strongly associated with passenger class; the likelihood of survival differs across the three classes.

#19
test whether fare differs significantly across the three passenger classes using ANOVA
#20
Thinking

We need to perform ANOVA on Fare across Pclass. Use df with column Fare. Should check missing values - there may be missing Fare? In Titanic dataset, Fare is numeric, some missing? I think none missing. We'll run one-way ANOVA using scipy.stats.f_oneway. Need groups: fare for each class. Provide code to compute and output F-statistic and p-value, and maybe show descriptive stats.

We have df already loaded. Provide code block. Should not ask to run. Provide code only.

#21

Here’s a quick one‑way ANOVA comparing Fare across the three passenger classes:

#22
ANOVA fare by class
from scipy.stats import f_oneway

# Split fares by passenger class
fare_class1 = df.loc[df["Pclass"] == 1, "Fare"]
fare_class2 = df.loc[df["Pclass"] == 2, "Fare"]
fare_class3 = df.loc[df["Pclass"] == 3, "Fare"]

# ANOVA
F_stat, p_val = f_oneway(fare_class1, fare_class2, fare_class3)

# Basic descriptive stats for reference
desc = df.groupby("Pclass")["Fare"].agg(["count", "mean", "std"])

(F_stat, p_val, desc)
#23
(np.float64(242.34415651744814),
 np.float64(1.031376320913912e-84),
         count       mean        std
 Pclass                             
 1         216  84.154687  78.380373
 2         184  20.662183  13.417399
 3         491  13.675550  11.778142)
#24
Thinking

We have output of ANOVA already: F_stat=242.34, p_val ~1e-84, descriptive stats. That's sufficient to answer whether fare differs significantly across classes. Provide final answer with interpretation. No code.

#25

The one‑way ANOVA comparing fares across the three passenger classes yields

  • F = 242.34
  • p ≈ 1.03 × 10⁻⁸⁴

Because the p‑value is astronomically smaller than any conventional significance level (e.g., 0.05), we reject the null hypothesis that the mean fare is the same for all classes.

Interpretation: Fare levels differ dramatically among the classes:

- First‑class passengers pay on average about 84.15 USD (std ≈ 78.38 USD)
- Second‑class passengers pay about 20.66 USD (std ≈ 13.42 USD)
- Third‑class passengers pay about 13.68 USD (std ≈ 11.78 USD)

Thus, fare is significantly higher for higher‑ranked passenger classes.

#26
summarise all three test results and their business interpretation
#27
Thinking

User wants summary of all three test results (t-test on Age vs Survival, chi-square on Survival vs Pclass, ANOVA on Fare vs Pclass) and business interpretation. Need to produce concise summary. Use correct USD formatting: numbers with USD. Provide interpretation: older passengers slightly less likely survive, etc., significance. Ensure no $ sign. Provide results.

#28

Statistical‐test summary

TestNull hypothesisStatisticp‑valueResult (α = 0.05)Business take‑away
Two‑sample t‑test (Age vs Survival)Mean age of survivors = mean age of non‑survivorst = ‑2.050.041 ≈ 4.1 × 10⁻²Reject H₀ (significant)Survivors are, on average, ≈ 2.3 USD years younger than those who perished (28.34 USD vs 30.63 USD years). Age has a modest but real effect on survival odds.
Chi‑square test (Survival vs Pclass)Survival is independent of passenger classχ² = 102.894.55 × 10⁻²³Reject H₀ (highly significant)First‑class passengers are far more likely to survive (≈ 63 % survival in class 1) than second‑ (≈ 32 %) or third‑class (≈ 24 %). Class is a strong predictor of survival.
One‑way ANOVA (Fare vs Pclass)Mean fare is the same across classesF = 242.341.03 × 10⁻⁸⁴Reject H₀ (highly significant)Fare differs dramatically by class: average fare is 84.15 USD for class 1, 20.66 USD for class 2, and 13.68 USD for class 3. Fare (a proxy for socio‑economic status) is tightly linked to passenger class.

Overall business interpretation

  • Socio‑economic hierarchy mattered: higher‑class tickets (and the associated higher fares) correspond to substantially better survival outcomes. This reflects the historic “women and children first” policy that was applied preferentially to first‑class cabins and the physical proximity to lifeboats.
  • Age plays a secondary role: younger passengers survived at a slightly higher rate, but the effect size is modest compared with class.
  • Implications for risk‑segmentation: If a similar hierarchical environment existed (e.g., premium vs. economy cabins, tiered service levels), the data suggests that higher‑paying customers not only spend more but also receive better safety outcomes. Companies should be aware of this perception and consider equitable safety measures across all tiers to avoid reputational risk.

Score cards for gpt-oss:120b for Hypothesis Testing in Python (t-test, ANOVA)

Total score: 10/10

  • Task Completion: 2/2

    Excellent

    All three requested hypothesis tests were performed and a summary interpretation was provided.

  • Execution Correctness: 2/2

    Excellent

    The code shown is syntactically valid and uses appropriate tests for each question, with sensible handling of missing Age values.

  • Output Quality: 3/3

    Excellent

    The outputs match the expected outcomes: t-test p < 0.05, chi-square p << 0.001, ANOVA p << 0.001, plus a summary table and business interpretation.

  • Reasoning Quality: 2/2

    Excellent

    The reasoning correctly links each test result to the corresponding business conclusion and interprets significance appropriately.

  • Reliability: 1/1

    Excellent

    The workflow is consistent and robust enough for the task, with no major hallucinations or unsupported claims.

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