app.py

import streamlit as st
import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import norm

# Set page config
st.set_page_config(page_title="Proportion Testing Visualizer", layout="wide")

# Sidebar controls
st.sidebar.header("Parameters")
p_0 = st.sidebar.number_input("Null Hypothesis Proportion (p₀)", min_value=0.0, max_value=1.0, value=0.50)
p_1 = st.sidebar.number_input("True Proportion (p₁)", min_value=0.0, max_value=1.0, value=0.60)
n = st.sidebar.number_input("Sample Size (n)", min_value=1, value=30)
alpha = st.sidebar.slider("Significance Level (α)", min_value=0.01, max_value=0.1, step=0.01, value=0.05)

show_alt = st.sidebar.checkbox("Show Alternative Distribution", value=False)
simulate_many = st.sidebar.checkbox("Simulate Many Samples", value=False)

# Redraw simulation button
run_simulation = False
if simulate_many:
    run_simulation = st.sidebar.button("Redraw Simulations")

# Initialize session state
if 'sample_proportions' not in st.session_state:
    st.session_state.sample_proportions = []
    st.session_state.z_scores = []
    st.session_state.decisions = []

# Calculate standard error and critical values
se = np.sqrt(p_0 * (1 - p_0) / n)
z_critical = norm.ppf(1 - alpha / 2)

# Draw sample button
if st.sidebar.button("Draw Sample"):
    # Draw a sample from the true proportion p_1
    sample = np.random.binomial(n, p_1)
    p_hat = sample / n

    # Z statistic under H₀
    z_stat = (p_hat - p_0) / se
    decision = 'Reject H₀' if abs(z_stat) > z_critical else 'Fail to Reject H₀'

    st.session_state.sample_proportions.append(p_hat)
    st.session_state.z_scores.append(z_stat)
    st.session_state.decisions.append(decision)

#####################################
# Main Plot with dynamic x-axis
#####################################

# 1) If user shows alt distribution, expand for shift
x_min, x_max = -4.0, 4.0
if show_alt:
    shift = (p_1 - p_0) / se
    x_min = min(x_min, shift - 4)
    x_max = max(x_max, shift + 4)

# 2) Also expand if the latest sample's z_stat is outside range
if st.session_state.z_scores:
    last_z = st.session_state.z_scores[-1]
    # Give a little padding around that Z value
    pad = 1.0
    x_min = min(x_min, last_z - pad)
    x_max = max(x_max, last_z + pad)

x = np.linspace(x_min, x_max, 1000)

# Null distribution (centered at 0, stdev=1)
y = norm.pdf(x, loc=0, scale=1)

fig, ax = plt.subplots(figsize=(10, 5))

# Plot null distribution
ax.plot(x, y, label='Null Distribution (Z)', color='black')
ax.fill_between(x, y, where=(x <= -z_critical) | (x >= z_critical), color='red', alpha=0.3, label='Rejection Regions')
ax.axvline(-z_critical, linestyle='--', color='red')
ax.axvline(z_critical, linestyle='--', color='red')

# Optional alternative distribution
if show_alt:
    shift = (p_1 - p_0) / se
    alt_y = norm.pdf(x, loc=shift, scale=1)
    ax.plot(x, alt_y, label='Alternative Distribution (Z)', color='blue', linestyle='--')

# Plot sample z-score
if st.session_state.z_scores:
    z_stat = st.session_state.z_scores[-1]
    color_choice = 'blue' if abs(z_stat) <= z_critical else 'red'
    ax.axvline(z_stat, color=color_choice, linestyle='-', linewidth=2,
               label=f'Z = {z_stat:.2f}')
    ax.annotate(f"Z = {z_stat:.2f}",
                xy=(z_stat, 0.05),  # arrow points here
                xytext=(z_stat + 0.4, 0.15),  # position of text box
                ha='center',
                arrowprops=dict(facecolor='black', arrowstyle='->'),
                bbox=dict(boxstyle='round,pad=0.3', facecolor='white', alpha=0.8))

ax.set_title("Z Sampling Distribution Under H₀")
ax.set_xlabel("Z-Score")
ax.set_ylabel("Probability Density")
ax.legend()
st.pyplot(fig)

# Show decision
if st.session_state.z_scores:
    st.subheader("Latest Sample Analysis")
    st.write(f"Sample Proportion (p̂): **{st.session_state.sample_proportions[-1]:.3f}**")
    st.write(f"Z-Statistic: **{st.session_state.z_scores[-1]:.2f}**")
    st.write(f"Decision: **{st.session_state.decisions[-1]}** at α = {alpha}")

# Show formulas in four columns
st.markdown("---")
st.subheader("📐 Formulas Used")

col1, col2, col3, col4 = st.columns(4)

with col1:
    st.markdown(r"""
    **Standard Error (SE):**  
    $$ SE(\hat{p}) = \sqrt{\dfrac{p_0(1 - p_0)}{n}} $$
    """)

with col2:
    st.markdown(r"""
    **Z-Statistic:**  
    $$ Z = \dfrac{\hat{p} - p_0}{\sqrt{\dfrac{p_0(1 - p_0)}{n}}} $$
    """)

with col3:
    st.markdown(r"""
    **Critical Values (Two-Tailed):**  
    $$ \pm Z_{\alpha/2} $$
    """)

with col4:
    st.markdown(r"""
    **Decision Rule:**  
    Reject $ H_0 $ if $ |Z| > |Z_{\alpha/2}| $
    """)

# Simulate many samples (Type I Error check if H₀ is actually true)
if simulate_many and run_simulation:
    st.subheader("Simulation of Many Samples")
    num_sim = 1000
    # Under H₀, the true proportion is p_0
    # Draw 1000 samples of size n from Bernoulli(p_0)
    binomial_draws = np.random.binomial(n, p_0, size=num_sim)
    p_hats = binomial_draws / n
    z_vals = (p_hats - p_0) / se
    type_I_errors = np.sum(np.abs(z_vals) > z_critical) / num_sim

    fig2, ax2 = plt.subplots(figsize=(10, 4))
    ax2.hist(z_vals, bins=50, density=True, alpha=0.6)
    ax2.axvline(-z_critical, linestyle='--', color='red')
    ax2.axvline(z_critical, linestyle='--', color='red')
    ax2.set_title("Histogram of Z-Statistics from Simulated Samples (Under H₀)")
    ax2.set_xlabel("Z-Statistic")
    ax2.set_ylabel("Density")
    st.pyplot(fig2)

    st.write(f"Empirical Rejection Rate (Type I error, H₀ true): **{type_I_errors:.3f}**")