Psychometric Function
Chart overview
A psychometric function plots the proportion of correct or detected responses as a function of stimulus intensity and fits a sigmoidal curve - typically a cumulative Gaussian or logistic function - to estimate the perceptual threshold and slope.
Key points
- Psychophysicists and sensory neuroscientists use it to characterise sensory sensitivity and the steepness of the transition from chance to ceiling performance.
- It is a cornerstone tool for measuring detection, discrimination, and recognition thresholds.
Python Tutorial
How to create a psychometric function in Python
Use the full tutorial for implementation details, troubleshooting, and chart variations in matplotlib, seaborn, and plotly.
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"Create a psychometric function plot from my behavioural data. Fit a cumulative Gaussian or logistic sigmoid to the proportion-correct values, mark the 75% threshold with dashed lines, show raw data points with binomial error bars, and format in a journal-quality style."
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Python Code Example
import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
def sigmoid(x, L ,x0, k, b):
return L / (1 + np.exp(-k*(x-x0))) + b
x_data = np.linspace(0.1, 0.9, 9)
y_data = np.array([0.05, 0.1, 0.15, 0.3, 0.55, 0.8, 0.9, 0.95, 0.98])
y_err = np.random.uniform(0.02, 0.08, len(x_data))
x_fit = np.linspace(0, 1, 100)
y_fit = sigmoid(x_fit, 1, 0.5, 10, 0)
plt.figure(figsize=(10, 6))
plt.errorbar(x_data, y_data, yerr=y_err, fmt='ko', capsize=5, label='Subject Responses')
plt.plot(x_fit, y_fit, 'b-', linewidth=2, label='Fitted Psychometric Function')
plt.axhline(0.5, color='gray', linestyle='--')
plt.axvline(0.5, color='gray', linestyle='--')
plt.title('Psychometric Function', fontsize=14, fontweight='bold', pad=20)
plt.xlabel('Stimulus Intensity', fontsize=12)
plt.ylabel('Probability of Response', fontsize=12)
plt.legend()
plt.tight_layout()
plt.savefig('plotivy-psychometric-function.png', dpi=150)
print("Psychometric function generated successfully.")
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Console Output
Psychometric function generated successfully.
Common Use Cases
- 1Measuring contrast detection thresholds in visual psychophysics experiments
- 2Estimating auditory frequency discrimination thresholds in hearing research
- 3Quantifying tactile sensitivity changes after peripheral nerve injury
- 4Comparing perceptual thresholds across age groups or clinical populations
Pro Tips
Use maximum likelihood estimation rather than least-squares for fitting proportion data
Plot binomial confidence intervals at each stimulus level, not just the fitted curve
Mark threshold and just-noticeable difference (JND) explicitly with dashed reference lines
Show the chance level (0.5 for two-alternative forced choice) as a horizontal dashed line
Long-tail keyword opportunities
High-intent chart variations
Library comparison for this chart
matplotlib
Best when you need full control over axis formatting, annotation placement, and journal-specific styling for psychometric-function.
numpy
Useful in specialized workflows that complement core Python plotting libraries for psychometric-function analysis tasks.
scipy
Useful in specialized workflows that complement core Python plotting libraries for psychometric-function analysis tasks.
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