Libraries
First, you need to install the following librairies:
- matplotlib is used for plot creating the charts
- pandas is used to put the data into a dataframe
- numpy is used to generate some data
The Anova test will be done using scipy: install it using the pip install scipy command
import pandas as pd
import matplotlib.pyplot as plt
import numpy as np
import scipy.stats as stats
Dataset
Let's create a dummy dataset. Three groups are made up: A, B and C.
For each of them, 100 random values are created thanks to the np.random.normal() function, but with different mean values.
sample_size = 100
groupA = np.random.normal(10, 10, sample_size)
groupB = np.random.normal(70, 10, sample_size)
groupC = np.random.normal(40, 10, sample_size)
category = ['GroupA']*sample_size + ['GroupB']*sample_size + ['GroupC']*sample_size
df = pd.DataFrame({'value': np.concatenate([groupA, groupB, groupC]),
'category': category})
Get statistical values
First, we'll start by retrieving the values we want to add on the plot: the p value and the F statistic. For this, we need to use the f_oneway() function from scipy.
Also, we retrieve the mean of each group.
Important: This post does not cover any statistical/math details
# groups
groupA = df[df['category']=='GroupA']['value']
groupB = df[df['category']=='GroupB']['value']
groupC = df[df['category']=='GroupC']['value']
# Perform a paired t-test
F_statistic, p_value = stats.f_oneway(groupA, groupB, groupC)
# Get means
mean_groupA = groupA.mean()
mean_groupB = groupB.mean()
mean_groupC = groupC.mean()
# Print the results
print("T-statistic:", F_statistic)
print("P-value:", p_value)
print("Mean groupA:", mean_groupA)
print("Mean groupB:", mean_groupB)
print("Mean groupC:", mean_groupC)
T-statistic: 960.8980055803397
P-value: 2.0225642197230424e-130
Mean groupA: 8.745526783582141
Mean groupB: 70.56101076624377
Mean groupC: 40.310280651985394
Let's round them in order to make the chart more readable at the end
F_statistic = round(F_statistic,2)
p_value = round(p_value,5) # more decimal since it's a lower value in general
mean_groupA = round(mean_groupA,2)
mean_groupB = round(mean_groupB,2)
mean_groupC = round(mean_groupC,2)
Boxplot with statistical elements
Now let's use the stats we got above and add them to the plot of boxplots of each group using the text() function from matplotlib.
For this graph, we'll also add the average of each group next to its associated boxplot.
# Group our dataset with our 'Group' variable
grouped = df.groupby('category')['value']
# Init a figure and axes
fig, ax = plt.subplots(figsize=(8, 6))
# Create the plot with different colors for each group
boxplot = ax.boxplot(x=[group.values for name, group in grouped],
labels=grouped.groups.keys(),
patch_artist=True,
medianprops={'color': 'black'}
)
# Define colors for each group
colors = ['orange', 'purple', '#69b3a2']
# Assign colors to each box in the boxplot
for box, color in zip(boxplot['boxes'], colors):
box.set_facecolor(color)
# Add the p value and the t
p_value_text = f'p-value: {p_value}'
ax.text(0.7, 50, p_value_text, weight='bold')
f_value_text = f'F-value: {F_statistic}'
ax.text(0.7, 45, f_value_text, weight='bold')
# Add the mean for each group
ax.text(1.2, mean_groupA, f'Mean of Group A: {mean_groupA}', fontsize=10)
ax.text(2.2, mean_groupB, f'Mean of Group B: {mean_groupB}', fontsize=10)
ax.text(2, mean_groupC, f'Mean of Group C: {mean_groupC}', fontsize=10)
# Add a title and axis label
ax.set_title('One way Anova between group A, B and C')
# Add a legend
legend_labels = ['Group A', 'Group B', 'Group C']
legend_handles = [plt.Rectangle((0,0),1,1, color=color) for color in colors]
ax.legend(legend_handles, legend_labels)
# Display it
plt.show()
Violin plot with statistical elements
# Group our dataset with our 'Group' variable
grouped = df.groupby('category')['value']
# Init a figure and axes
fig, ax = plt.subplots(figsize=(8, 6))
# Create the plot with different colors for each group
violins = ax.violinplot([group.values for name, group in grouped],
#labels=grouped.groups.keys()
)
# Define colors for each group
colors = ['orange', 'purple', '#69b3a2']
# Assign colors to each box in the boxplot
for violin, color in zip(violins['bodies'], colors):
violin.set_facecolor(color)
# Add the p value and the t
p_value_text = f'p-value: {p_value}'
ax.text(0.7, 50, p_value_text, weight='bold')
F_value_text = f'F-value: {F_statistic}'
ax.text(0.7, 45, F_value_text, weight='bold')
# Add the mean for each group
ax.text(1.25, mean_groupA, f'Mean of Group A: {mean_groupA}', fontsize=10)
ax.text(2.25, mean_groupB, f'Mean of Group B: {mean_groupB}', fontsize=10)
ax.text(2, mean_groupC, f'Mean of Group C: {mean_groupC}', fontsize=10)
# Add a title and axis label
ax.set_title('One way Anova between group A, B and C')
# Add a legend
legend_labels = ['Group A', 'Group B', 'Group C']
legend_handles = [plt.Rectangle((0,0),1,1, color=color) for color in colors]
ax.legend(legend_handles, legend_labels)
# Display it
plt.show()
Customized violin plot with statistics
# Group our dataset with our 'Group' variable
grouped = df.groupby('category')['value']
# Init a figure and axes
fig, ax = plt.subplots(figsize=(8, 6))
# Create the plot with different colors for each group
violins = ax.violinplot([group.values for name, group in grouped],
#labels=grouped.groups.keys()
)
# Define colors for each group
colors = ['orange', 'purple', '#69b3a2']
# Assign colors to each box in the boxplot
for violin, color in zip(violins['bodies'], colors):
violin.set_facecolor(color)
# Add the p value and the t
p_value_text = f'p-value: {p_value}'
ax.text(0.7, 60, p_value_text)
F_value_text = f'F-value: {F_statistic}'
ax.text(0.7, 55, F_value_text)
# Add the mean for each group
ax.text(1.3, mean_groupA, f'Mean Group A: {mean_groupA}',
style='italic', fontsize=8)
ax.text(2.3, mean_groupB, f'Mean Group B: {mean_groupB}',
style='italic', fontsize=8)
ax.text(2.2, mean_groupC, f'Mean Group C: {mean_groupC}',
style='italic', fontsize=8)
# Remove axis labels
ax.set_xticks([])
ax.set_yticks([])
# Removes spines
ax.spines[['right', 'top', 'left', 'bottom']].set_visible(False)
# Add a title and axis label
ax.set_title('One way Anova\nbetween group A, B and C', weight='bold')
# Add a legend
legend_labels = ['Group A', 'Group B', 'Group C']
legend_handles = [plt.Rectangle((0,0),1,1, color=color, alpha=0.5) for color in colors]
ax.legend(legend_handles, legend_labels, loc='upper left')
# Display it
plt.show()
Going further
This post explains how to represent the results of an Anova in a violin plot and a boxplot.
For more examples of charts with statistics, see the statistics section. You may also be interested in how to represent Student t-test results.