Let's talk about sample **variances**. The measure of scattering is well visualized by the **violin plot**. 

It is similar in use to **boxplot**. Consider an example from life. Let's compare the data on annual incomes in the USA and Canada in 2020:

The graph tells us that they are quite close. 

The white dot in the center of the graph indicates the **median** of the **distribution**. 

The bolder part of the line means the first quantile (bottom) and the third quantile (top). Anything outside the horizontal line is an outlier. Now let's compare the data on annual incomes in the USA and Brazil in 2020:

The graph tells us that they are quite close. In this graph, the **distributions** are clearly different. The **violin plot** for income in Brazil is below.
Let's build a **violin plot** of the `'Impression'` columns for the test and control groups:

# Import libraries
import matplotlib.pyplot as plt
import pandas as pd
import seaborn as sns

# Read .csv files
df_control = pd.read_csv('https://codefinity-content-media.s3.eu-west-1.amazonaws.com/c3b98ad3-420d-403f-908d-6ab8facc3e28/ab_control.csv', delimiter=';')
df_test = pd.read_csv('https://codefinity-content-media.s3.eu-west-1.amazonaws.com/c3b98ad3-420d-403f-908d-6ab8facc3e28/ab_test.csv', delimiter=';')

# Define colors for graphs
colors_list = ['#ff8a00', '#33435c']

# Add to the dataframes columns-labels, which mean belonging to either the control or the test group
df_control['group'] = 'Contol group'
df_test['group'] = 'Test group'

# Concat the dataframes
df_combined = pd.concat([df_control, df_test])

# Plotting violin plots
sns.violinplot(data=df_combined, x='group', y='Impression', palette=colors_list)

# Sign the axes
plt.xlabel('')
plt.ylabel('Impression')
plt.title('Comparison of Impressions')

# Show the results
plt.show()

The **swarm plot** goes well with the **violin plot**. Let's look at their combination:

# Import libraries
import matplotlib.pyplot as plt
import pandas as pd
import seaborn as sns

# Read .csv files
df_control = pd.read_csv('https://codefinity-content-media.s3.eu-west-1.amazonaws.com/c3b98ad3-420d-403f-908d-6ab8facc3e28/ab_control.csv', delimiter=';')
df_test = pd.read_csv('https://codefinity-content-media.s3.eu-west-1.amazonaws.com/c3b98ad3-420d-403f-908d-6ab8facc3e28/ab_test.csv', delimiter=';')

# Define colors for graphs
colors_list = ['#ff8a00', '#33435c']

# Add to the dataframes columns-labels, which mean belonging to either the control or the test group
df_control['group'] = 'Contol group'
df_test['group'] = 'Test group'

# Concat the dataframes
df_combined = pd.concat([df_control, df_test])

# Plotting violin plots
sns.violinplot(data=df_combined, x='group', y='Impression', palette=colors_list)

# Plotting swarm plots
sns.swarmplot(data=df_combined, x='group', y='Impression', color="r", alpha=0.8)

# Sign the axes
plt.xlabel('')
plt.ylabel('Impression')
plt.title('Comparison of Impressions')

# Show the results
plt.show()

Now we have a visual representation of data scatter. But are these variances equal? Alas, we cannot draw such a conclusion by looking only at the graphs. As you might have guessed, statistics have a tool to check. But first, practice time!

This course is a comprehensive and practical online program designed to equip individuals with the knowledge and skills necessary to conduct effective A/B tests. 

In this course, participants will learn the fundamental principles of A/B testing, including experimental design, sample size determination, hypothesis testing, and statistical analysis.

Welcome to the A/B testing course. In this section, we will tell you what controlled experiments are, where they are used, and why they are used. We will look at a specific example of a controlled experiment and talk about A/A testing. The Python programming language will help us with this. Well, let's get started!

Before conducting a controlled experiment, we need to determine the characteristics of the sample. The type of tests that we will conduct a little later will depend on these characteristics. You will learn to build distribution histograms, box plots, and check the normality of the distribution. Let's get started right now!

The last thing to do before conducting a controlled experiment is to check the sampling variances. Some types of graphs and Levene's test will help us with this. Let's talk about it in more detail in this section!

So we got to A/B testing. Soon you will make your first parametric tests, or as they are also called - T-tests. We'll use all the knowledge we've learned in the previous sections: metric definition, normality testing, variance testing, and plotting. All this will help us get statistically significant results. Well, to work!

It turns out that sometimes the samples do not have a normal distribution. This means that we cannot perform parametric testing. What to do in such a situation? Non-parametric testing. We will talk about him in the last section.

The Art of A/B Testing

Violin and Swarm Plots