如何实现基于用户输入指定样本的双样本t检验？

Hey there! Let's fix up your code so you can use user-specified sample values instead of generating random Gaussian distributions. Your initial input logic was targeting distribution parameters (like mean/variance), but we need to capture actual sample data instead. Here's a complete, working solution:

Full Modified Code #

import numpy as np
from scipy import stats

# Get user input for Sample A
sample_a_str = input("Enter Sample A values separated by commas (e.g., 1.2, 3.4, 5.6): ")
# Convert input string to a numpy array of floats
a = np.array([float(val.strip()) for val in sample_a_str.split(',')])

# Get user input for Sample B
sample_b_str = input("Enter Sample B values separated by commas (e.g., 2.3, 4.5, 6.7): ")
b = np.array([float(val.strip()) for val in sample_b_str.split(',')])

# Confirm the input samples
print("\nSample A:", a)
print("Sample B:", b)

# Calculate sample sizes
n_a = len(a)
n_b = len(b)

# Compute unbiased variances (ddof=1 uses n-1 for degrees of freedom)
var_a = a.var(ddof=1)
var_b = b.var(ddof=1)

# Calculate pooled standard deviation (adjust for equal/unequal sample sizes)
if n_a == n_b:
    pooled_std = np.sqrt((var_a + var_b) / 2)
else:
    pooled_std = np.sqrt(((n_a - 1)*var_a + (n_b - 1)*var_b) / (n_a + n_b - 2))

# Compute t-statistic
t_stat = (a.mean() - b.mean()) / (pooled_std * np.sqrt(1/n_a + 1/n_b))

# Calculate degrees of freedom
df = n_a + n_b - 2

# Compute two-tailed p-value
p_val = 2 * (1 - stats.t.cdf(np.abs(t_stat), df=df))

# Print manual calculation results
print("\nManual Calculation Results:")
print(f"t-statistic = {t_stat:.4f}")
print(f"p-value = {p_val:.4f}")

# Cross-validate with scipy's built-in function
t_scipy, p_scipy = stats.ttest_ind(a, b, equal_var=True)
print("\nScipy Built-in Function Results:")
print(f"t-statistic = {t_scipy:.4f}")
print(f"p-value = {p_scipy:.4f}")

Key Improvements & Explanations #

• Sample Input Handling: We now accept comma-separated numerical values from the user, convert them into numpy arrays—this lets us directly work with the exact sample data you need.
• Flexible Sample Sizes: The code checks if sample sizes are equal and adjusts the pooled standard deviation formula accordingly, making it work for both equal and unequal sample sizes.
• Two-Tailed Test Alignment: The manual p-value calculation uses the absolute t-statistic and multiplies by 2, matching the default two-tailed output of scipy.stats.ttest_ind.
• Validation: We keep the scipy cross-check to ensure our manual calculations match the trusted library implementation.

Example Usage #

If you input:

• Sample A: 2.1, 1.9, 2.3, 2.0, 1.8
• Sample B: 0.2, -0.1, 0.3, 0.0, -0.2

You'll get output showing a significant difference between the two sample means (low p-value), just like your original random sample example.

内容的提问来源于stack exchange，提问作者Petkes Balás