Introduction to Statistics for Data Science

1. Introduction

The goal of this tutorial is to provide an introduction to the essential statistics concepts used in data science. By the end of the tutorial, you will have a basic understanding of key statistical concepts that are fundamental to data analysis and interpretation.

You Will Learn:

• Descriptive and inferential statistics
• Probability theory and distributions
• Hypothesis testing
• Regression analysis

Prerequisites:

• Basic understanding of Python programming
• Familiarity with mathematical concepts such as mean, median, mode, and standard deviation

2. Step-by-Step Guide

Descriptive Statistics:

Descriptive statistics summarize and organize characteristics of a data set. A data set may have one or many variables. Variables can be numerical or categorical.

Inferential Statistics:

Inferential statistics make predictions or inferences about a population based on a sample of data taken from the population in question.

Probability Theory and Distributions:

Probability theory is a fundamental concept in statistics. It’s used to draw inferences about the possible outcomes. Probability distribution is a function that describes the likelihood of obtaining the possible values that a random variable can assume.

Hypothesis Testing:

Hypothesis testing is a statistical method that is used in making statistical decisions using experimental data. It’s a method that uses statistical analysis to test claims or hypotheses about a group or population.

Regression Analysis:

Regression analysis is a form of predictive modeling technique which investigates the relationship between a dependent and independent variable.

3. Code Examples

Let's start with importing necessary libraries.

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
from scipy import stats

Descriptive Statistics with Python:

Let's create a simple data set and calculate some basic descriptive statistics.

# Create a simple data set
data = [4, 7, 5, 9, 8, 6, 7, 7, 8, 5]

# Calculate mean
mean = np.mean(data)
print("Mean: ", mean)

# Calculate median
median = np.median(data)
print("Median: ", median)

# Calculate mode
mode = stats.mode(data)
print("Mode: ", mode)

# Calculate standard deviation
std_dev = np.std(data)
print("Standard Deviation: ", std_dev)

In this code snippet:
1. We create a simple data set using a Python list.
2. We calculate and print the mean, median, mode, and standard deviation of the data set using numpy and scipy.

Inferential Statistics with Python:

Let's perform a simple t-test using scipy.

# Create two data sets
data1 = [5, 7, 6, 8, 6, 7, 7, 8, 7, 6]
data2 = [8, 7, 7, 7, 8, 8, 8, 7, 7, 8]

# Perform t-test
t_statistic, p_value = stats.ttest_ind(data1, data2)

print("t statistic: ", t_statistic)
print("p value: ", p_value)

In this code snippet:
1. We create two data sets using Python lists.
2. We perform a t-test on the two data sets using scipy and print the t statistic and p value.

4. Summary

In this tutorial, we covered the basics of statistics for data science, including descriptive statistics, inferential statistics, probability theory and distributions, hypothesis testing, and regression analysis. We also learned how to calculate basic statistics and perform a t-test in Python.

Next Steps:

• Practice working with different types of data
• Learn more about other types of statistical tests
• Learn more about different types of regression analysis

Additional Resources:

• Python for Data Analysis
• Think Stats: Probability and Statistics for Programmers

5. Practice Exercises

1. Calculate the mean, median, mode, and standard deviation of the following data set: [6, 7, 5, 7, 7, 8, 7, 6, 9, 7]
2. Perform a t-test on the following data sets: [7, 7, 5, 6, 6, 8, 7, 6, 7, 7] and [7, 7, 7, 7, 7, 7, 7, 7, 7, 7]

Solutions and explanations will be provided upon request. For further practice, create your own data sets and perform the same statistical tests.