Learning Statistics with Python

Statistics organizes, analyzes, interprets, and presents data. It guides drawing conclusions, inferences, understanding patterns, relationships, and variability.

Why is statistics necessary for data scientists?

Data scientists need to know statistics for several reasons:

Data Analysis and Interpretation: is key for data analysis. Techniques summarize, visualize, and reveal patterns, aiding data scientists in understanding trends and relationships;
Statistical Inference: data scientists use samples to infer about populations. Stats inference, estimates parameters, tests hypotheses, and predicts using sample data;
Modeling and Machine Learning: stats forms ML's core. Data scientists train, assess models, and decide using statistical methods, ensuring effective choices and tuning;
Experimental Design and A/B Testing: in data science, stats guides experiments, A/B tests. Vital for design, sample size, and hypothesis testing;
Dealing with Uncertainty: manages real data's uncertainty, missing values, and outliers, ensuring robust analysis;
Interpreting Research and Literature: research papers use stats for conclusions. Data scientists must grasp these analyses for interpretation and building on research;
Communication and Collaboration: aids data scientists in clear stakeholder communication, results presentation, and justifying data-driven choices.

In summary, statistics is a crucial tool for data scientists, providing a framework for data analysis, modeling, inference, and decision-making. It equips data scientists with the necessary skills to extract insights from data, build accurate models, and make informed decisions in a wide range of applications across industries.

Statistics vs. Probability Theory

Probability Theory	Statistics
Probability theory deals with the study of random events and uncertainty	Statistics involves the collection, organization, analysis, interpretation, and presentation of data
Deals with the study of random events and uncertainty	Uses probability theory as a foundation to draw conclusions and make inferences from data
Focuses on probability, quantifying outcome likelihood in random experiments	Analyzes real-world data, summarizes for insights, data-driven decisions
Models randomnesses like dice, coins, and cards	Involves descriptive stats: mean, median, variance, and graphs describe data
Covers probability distributions, conditional/joint probability, Bayes' theorem, and random variables	Includes inferential stats, using samples to predict populations

Example of task

As a data analyst, compare two email campaign versions for higher purchase rates. A/B testing checks mean conversion rates, identifying significant differences.


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import numpy as np
from scipy.stats import ttest_ind

# Sample data for Group A and Group B (number of conversions)
np.random.seed(42)  # For reproducibility

group_a_conversions = np.random.normal(loc=100, scale=15, size=100)  # Mean=100, Standard Deviation=15
group_b_conversions = np.random.normal(loc=110, scale=20, size=100)  # Mean=110, Standard Deviation=20

# Calculate the means of the two samples
mean_a = np.mean(group_a_conversions)
mean_b = np.mean(group_b_conversions)

# Perform the independent two-sample t-test
t_statistic, p_value = ttest_ind(group_a_conversions, group_b_conversions)

# Print the results
print(f'Mean conversion rate for Group A is {mean_a}')
print(f'Mean conversion rate for Group B is  {mean_b}')
print(f'T-statistic is  {t_statistic}')
print(f'P-value is {p_value}')

# Print the result of the test
if p_value < 0.05:
    print('The difference in mean conversion rates between the two groups is statistically significant.')
    if mean_b > mean_a:
        print('Layout 2 (Group B) has a higher mean conversion rate than Layout 1 (Group A).')
    else:
        print('Layout 1 (Group A) has a higher mean conversion rate than Layout 2 (Group B).')
else:
    print('There is no statistically significant difference in mean conversion rates between the two groups.')

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