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import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
import pingouin as pg
from scipy.stats import t, gaussian_kde, bartlett, levene
# ============================================================
# One-sample t-test
# ============================================================
def plot_ttest_mean_distribution(
numeric_col: str,
sample: np.ndarray,
mu0: float,
df_output: pd.DataFrame,
alternative: str,
bootstrap_samples: int,
):
"""
Plot bootstrap sampling distribution of the mean vs. theoretical t under H0,
shading the p-value region.
"""
plt.style.use("seaborn-v0_8-whitegrid")
# Pingouin output
p_val = df_output["p-val"].values[0]
df = df_output["dof"].values[0]
# Sample stats
n = len(sample)
sample_mean = np.mean(sample)
sample_std = np.std(sample, ddof=1)
se = sample_std / np.sqrt(n)
# Theoretical t-distribution under H0
x = np.linspace(mu0 - 5 * se, mu0 + 5 * se, 1000)
t_density = t.pdf((x - mu0) / se, df) / se
# Bootstrap sampling distribution of the mean
boot_means = np.array(
[
np.mean(np.random.choice(sample, size=n, replace=True))
for _ in range(bootstrap_samples)
]
)
# KDE for bootstrap means (off-screen fig to get line data)
fig_tmp, ax_tmp = plt.subplots()
sns.kdeplot(boot_means, bw_adjust=1.2, ax=ax_tmp)
x_kde, y_kde = ax_tmp.lines[0].get_data()
plt.close(fig_tmp)
# Final figure
fig, ax = plt.subplots(figsize=(8, 5))
# Bootstrap KDE
ax.plot(
x_kde,
y_kde,
color="rebeccapurple",
label="Bootstrap sampling dist.",
linewidth=2,
)
# Theoretical t under H0
ax.plot(
x,
t_density,
color="gray",
linestyle="--",
linewidth=2,
label=r"$t$-distribution ($H_0$)",
)
# Shade p-value region
if alternative == "two-sided":
delta = abs(sample_mean - mu0)
lower = mu0 - delta
upper = mu0 + delta
mask = (x <= lower) | (x >= upper)
elif alternative == "greater":
mask = x >= sample_mean
elif alternative == "less":
mask = x <= sample_mean
else:
raise ValueError("alternative must be 'two-sided', 'greater', or 'less'")
ax.fill_between(
x,
0,
t_density,
where=mask,
color="red",
alpha=0.3,
label=f"p-value ≈ {p_val:.3f}",
)
# Reference lines
ax.axvline(
mu0,
color="tab:orange",
linestyle="--",
linewidth=2,
label=rf"$\mu_0 = {mu0}$",
)
ax.axvline(
sample_mean,
color="black",
linestyle="-",
linewidth=1.5,
label=rf"Sample mean = {sample_mean:.2f}",
)
# Formatting
ax.set_title(
f"Sampling Distribution of the Mean ({numeric_col})",
fontsize=14,
)
ax.set_xlabel("Sample Mean", fontsize=12)
ax.set_ylabel("Density", fontsize=12)
ax.grid(True, linestyle="--", alpha=0.5)
ax.legend()
plt.tight_layout()
return fig
def one_sample_ttest(
sample: np.ndarray,
mu0: float,
alternative: str,
*,
numeric_col: str,
bootstrap_samples: int,
include_graph: bool,
) -> tuple[pd.DataFrame, plt.Figure | None]:
"""
One-sample Student's t-test and optional sampling distribution plot.
"""
if sample.size == 0:
raise ValueError("No valid data in the selected column.")
df_output = pg.ttest(
x=sample,
y=mu0,
alternative=alternative,
paired=False,
)
fig = None
if include_graph:
fig = plot_ttest_mean_distribution(
numeric_col=numeric_col,
sample=sample,
mu0=mu0,
df_output=df_output,
alternative=alternative,
bootstrap_samples=bootstrap_samples,
)
return df_output, fig
# ============================================================
# Two-sample t-test (means)
# ============================================================
def mirror_plot(
numeric_col: str,
group1: np.ndarray,
name_group1: str,
group2: np.ndarray,
name_group2: str,
df_output: pd.DataFrame,
):
"""
Mirror histogram + KDE plot for two groups.
"""
t_val = df_output["T"].values[0]
p_val = df_output["p-val"].values[0]
mean1 = np.mean(group1)
mean2 = np.mean(group2)
fig, ax = plt.subplots(figsize=(10, 6))
# Shared binning
combined = np.concatenate([group1, group2])
x_min, x_max = float(np.min(combined)), float(np.max(combined))
bin_range = np.linspace(x_min, x_max, 30)
bin_centers = (bin_range[:-1] + bin_range[1:]) / 2
bin_width = np.diff(bin_range)[0]
x_vals = np.linspace(x_min, x_max, 200)
# Group 1 (top)
sns.histplot(
group1,
bins=bin_range,
stat="density",
kde=False,
color="rebeccapurple",
label=name_group1,
alpha=0.6,
ax=ax,
)
kde1 = gaussian_kde(group1)
ax.plot(x_vals, kde1(x_vals), color="rebeccapurple", linewidth=2)
ax.axvline(
mean1,
color="rebeccapurple",
linestyle="--",
linewidth=2,
label=f"{name_group1} mean = {mean1:.2f}",
)
# Group 2 (bottom, mirrored)
heights2, _ = np.histogram(group2, bins=bin_range, density=True)
ax.bar(
bin_centers,
-heights2,
width=bin_width,
color="tab:orange",
edgecolor="black",
alpha=0.6,
label=name_group2,
)
kde2 = gaussian_kde(group2)
ax.plot(x_vals, -kde2(x_vals), color="tab:orange", linewidth=2)
ax.axvline(
mean2,
color="tab:orange",
linestyle="--",
linewidth=2,
label=f"{name_group2} mean = {mean2:.2f}",
)
ax.axhline(0, color="black", linewidth=1)
ax.set_title("Mirror Plot: Two-Sample Distribution Comparison", fontsize=14)
ax.set_xlabel(numeric_col)
ax.set_ylabel("Density (Top ↑ vs. Bottom ↓)", fontsize=11)
ax.text(
0.01,
0.95,
f"p = {p_val:.3f}",
transform=ax.transAxes,
fontsize=11,
verticalalignment="top",
bbox=dict(boxstyle="round", facecolor="white", alpha=0.6),
)
ax.legend()
plt.tight_layout()
return fig
def plot_mean_distribution(
group1: np.ndarray,
name_group1: str,
group2: np.ndarray,
name_group2: str,
bootstrap_samples: int,
df_output: pd.DataFrame,
):
"""
Bootstrap distributions of the two sample means.
"""
p_val = df_output["p-val"].values[0]
mean1 = np.mean(group1)
mean2 = np.mean(group2)
boot1 = [
np.mean(np.random.choice(group1, size=len(group1), replace=True))
for _ in range(bootstrap_samples)
]
boot2 = [
np.mean(np.random.choice(group2, size=len(group2), replace=True))
for _ in range(bootstrap_samples)
]
fig, ax = plt.subplots(figsize=(8, 5))
sns.kdeplot(
boot1,
label=f"{name_group1} mean",
fill=True,
color="rebeccapurple",
alpha=0.6,
ax=ax,
)
sns.kdeplot(
boot2,
label=f"{name_group2} mean",
fill=True,
color="tab:orange",
alpha=0.6,
ax=ax,
)
ax.axvline(mean1, color="rebeccapurple", linestyle="--", linewidth=2)
ax.axvline(mean2, color="tab:orange", linestyle="--", linewidth=2)
ax.set_title("Bootstrap Mean Distributions", fontsize=14)
ax.set_xlabel("Mean", fontsize=12)
ax.set_ylabel("Density", fontsize=12)
ax.grid(True, linestyle="--", alpha=0.5)
ax.text(
0.98,
0.95,
f"p = {round(p_val, 3)}\n"
f"Mean({name_group1}) = {round(mean1, 2)}\n"
f"Mean({name_group2}) = {round(mean2, 2)}",
transform=ax.transAxes,
ha="right",
va="top",
bbox=dict(boxstyle="round", facecolor="white", alpha=0.7),
fontsize=11,
)
ax.legend()
plt.tight_layout()
return fig
def two_sample_ttest(
group1: np.ndarray,
group2: np.ndarray,
*,
numeric_col: str,
name_group1: str,
name_group2: str,
alternative: str,
correction: bool,
plot_type: str,
bootstrap_samples: int,
include_graph: bool,
) -> tuple[pd.DataFrame, plt.Figure | None]:
"""
Two-sample Student's t-test (pingouin.ttest) plus optional plots.
"""
if group1.size == 0 or group2.size == 0:
raise ValueError("One or both groups are empty after filtering.")
df_output = pg.ttest(
x=group1,
y=group2,
alternative=alternative,
paired=False,
correction=correction,
)
fig = None
if include_graph:
if plot_type == "Sample Histogram":
fig = mirror_plot(
numeric_col=numeric_col,
group1=group1,
name_group1=name_group1,
group2=group2,
name_group2=name_group2,
df_output=df_output,
)
elif plot_type == "Mean Density":
fig = plot_mean_distribution(
group1=group1,
name_group1=name_group1,
group2=group2,
name_group2=name_group2,
bootstrap_samples=bootstrap_samples,
df_output=df_output,
)
return df_output, fig
# ============================================================
# Variance tests (Bartlett / Levene)
# ============================================================
def plot_variance_distribution(
p: float,
group1: np.ndarray,
name_group1: str,
var1: float,
group2: np.ndarray,
name_group2: str,
var2: float,
method: str,
bootstrap_samples: int,
):
"""
Bootstrap distributions of sample variances for two groups.
"""
boot1 = [
np.var(np.random.choice(group1, size=len(group1), replace=True), ddof=1)
for _ in range(bootstrap_samples)
]
boot2 = [
np.var(np.random.choice(group2, size=len(group2), replace=True), ddof=1)
for _ in range(bootstrap_samples)
]
fig, ax = plt.subplots(figsize=(8, 5))
sns.kdeplot(
boot1,
label=f"{name_group1} variance",
fill=True,
color="rebeccapurple",
alpha=0.6,
ax=ax,
)
sns.kdeplot(
boot2,
label=f"{name_group2} variance",
fill=True,
color="tab:orange",
alpha=0.6,
ax=ax,
)
ax.axvline(var1, color="rebeccapurple", linestyle="--", linewidth=2)
ax.axvline(var2, color="tab:orange", linestyle="--", linewidth=2)
ax.set_title(f"Bootstrap Variance Distributions\n{method}", fontsize=14)
ax.set_xlabel("Variance", fontsize=12)
ax.set_ylabel("Density", fontsize=12)
ax.grid(True, linestyle="--", alpha=0.5)
ax.text(
0.98,
0.95,
f"{method}\n"
f"p = {round(p, 3)}\n"
f"Var({name_group1}) = {round(var1, 2)}\n"
f"Var({name_group2}) = {round(var2, 2)}",
transform=ax.transAxes,
ha="right",
va="top",
bbox=dict(boxstyle="round", facecolor="white", alpha=0.7),
fontsize=11,
)
ax.legend()
plt.tight_layout()
return fig
def variance_test(
group1: np.ndarray,
group2: np.ndarray,
*,
name_group1: str,
name_group2: str,
test_type: str,
include_graph: bool,
bootstrap_samples: int,
) -> tuple[pd.DataFrame, plt.Figure | None]:
"""
Bartlett or Levene test + optional bootstrap variance plots.
"""
if group1.size == 0 or group2.size == 0:
raise ValueError("One or both groups are empty after filtering.")
if test_type == "Bartlett":
stat, p = bartlett(group1, group2)
method = "Bartlett's test"
elif test_type == "Levene":
stat, p = levene(group1, group2, center="mean")
method = "Levene's test"
else:
raise ValueError("Invalid test type selected.")
var1 = float(np.var(group1, ddof=1))
var2 = float(np.var(group2, ddof=1))
df_output = pd.DataFrame(
{
"Test": [method],
"Statistic": [stat],
"p-value": [p],
f"Var({name_group1})": [var1],
f"Var({name_group2})": [var2],
}
)
fig = None
if include_graph:
fig = plot_variance_distribution(
p=p,
group1=group1,
name_group1=name_group1,
var1=var1,
group2=group2,
name_group2=name_group2,
var2=var2,
method=method,
bootstrap_samples=bootstrap_samples,
)
return df_output, fig
# ============================================================
# One-way ANOVA
# ============================================================
def one_way_anova_plot(
data_group: pd.DataFrame,
numeric_col: str,
cat_col: str,
df_output: pd.DataFrame,
):
"""
KDE plot of group distributions with F/p annotation.
"""
p_val = df_output["p-unc"].values[0]
groups = sorted(data_group[cat_col].dropna().unique())
palette = sns.color_palette("tab10", n_colors=len(groups))
group_color_map = dict(zip(groups, palette))
fig, ax = plt.subplots(figsize=(8, 5))
for group in groups:
subset = data_group[data_group[cat_col] == group][numeric_col].dropna()
sns.kdeplot(
subset,
fill=True,
common_norm=False,
color=group_color_map[group],
alpha=0.5,
linewidth=1,
label=str(group),
ax=ax,
)
overall_mean = data_group[numeric_col].mean()
ax.axvline(
overall_mean,
color="black",
linestyle=":",
linewidth=1.2,
label="Overall mean",
)
group_means = data_group.groupby(cat_col)[numeric_col].mean()
for group, mean_val in group_means.items():
ax.axvline(
mean_val,
color=group_color_map[group],
linestyle="--",
linewidth=1.5,
label=f"{group} mean",
)
ax.text(
0.98,
0.95,
f"p = {p_val:.3f}",
transform=ax.transAxes,
ha="right",
va="top",
bbox=dict(boxstyle="round", facecolor="white", alpha=0.7),
fontsize=11,
)
ax.set_title("Group Distributions for One-way ANOVA", fontsize=14)
ax.set_xlabel(numeric_col, fontsize=12)
ax.set_ylabel("Density", fontsize=12)
ax.grid(True, linestyle="--", alpha=0.3)
ax.legend(title=cat_col)
plt.tight_layout()
return fig
def one_way_anova(
data_group: pd.DataFrame,
*,
numeric_col: str,
cat_col: str,
) -> tuple[pd.DataFrame, plt.Figure]:
"""
One-way ANOVA (pingouin.anova) + distribution plot.
"""
if data_group.empty:
raise ValueError("Dataset is empty after filtering.")
df_output = pg.anova(
dv=numeric_col,
between=cat_col,
data=data_group,
detailed=True,
)
fig = one_way_anova_plot(
data_group=data_group,
numeric_col=numeric_col,
cat_col=cat_col,
df_output=df_output,
)
return df_output, fig
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