Topic: Python SciPy – From Easy to Top: Part 5 of 6: Working with SciPy Statistics

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1. Introduction to `scipy.stats`

• The scipy.stats module contains a large number of probability distributions and statistical functions.
• You can perform tasks like descriptive statistics, hypothesis testing, sampling, and fitting distributions.

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2. Descriptive Statistics

Use these functions to summarize and describe data characteristics:

from scipy import stats
import numpy as np

data = [2, 4, 4, 4, 5, 5, 7, 9]

mean = np.mean(data)
median = np.median(data)
mode = stats.mode(data, keepdims=True)
std_dev = np.std(data)

print("Mean:", mean)
print("Median:", median)
print("Mode:", mode.mode[0])
print("Standard Deviation:", std_dev)

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3. Probability Distributions

SciPy has built-in continuous and discrete distributions such as normal, binomial, Poisson, etc.

Normal Distribution Example

from scipy.stats import norm

# PDF at x = 0
print("PDF at 0:", norm.pdf(0, loc=0, scale=1))

# CDF at x = 1
print("CDF at 1:", norm.cdf(1, loc=0, scale=1))

# Generate 5 random numbers
samples = norm.rvs(loc=0, scale=1, size=5)
print("Random Samples:", samples)

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4. Hypothesis Testing

One-sample t-test – test if the mean of a sample is equal to a known value:

sample = [5.1, 5.3, 5.5, 5.7, 5.9]
t_stat, p_val = stats.ttest_1samp(sample, popmean=5.0)

print("T-statistic:", t_stat)
print("P-value:", p_val)

Interpretation: If the p-value is less than 0.05, reject the null hypothesis.

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5. Two-sample t-test

Test if two samples come from populations with equal means:

group1 = [20, 22, 19, 24, 25]
group2 = [28, 27, 26, 30, 31]

t_stat, p_val = stats.ttest_ind(group1, group2)

print("T-statistic:", t_stat)
print("P-value:", p_val)

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6. Chi-Square Test for Independence

Use to test independence between two categorical variables:

# Example contingency table
data = [[10, 20], [20, 40]]
chi2, p, dof, expected = stats.chi2_contingency(data)

print("Chi-square statistic:", chi2)
print("P-value:", p)

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7. Correlation and Covariance

Measure linear relationship between variables:

x = [1, 2, 3, 4, 5]
y = [2, 4, 6, 8, 10]

corr, _ = stats.pearsonr(x, y)
print("Pearson Correlation Coefficient:", corr)

Covariance:

cov_matrix = np.cov(x, y)
print("Covariance Matrix:\n", cov_matrix)

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8. Fitting Distributions to Data

You can fit a distribution to real-world data:

data = np.random.normal(loc=50, scale=10, size=1000)
params = norm.fit(data)  # returns mean and std dev

print("Fitted mean:", params[0])
print("Fitted std dev:", params[1])

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9. Sampling from Distributions

Generate random numbers from different distributions:

# Binomial distribution
samples = stats.binom.rvs(n=10, p=0.5, size=10)
print("Binomial Samples:", samples)

# Poisson distribution
samples = stats.poisson.rvs(mu=3, size=10)
print("Poisson Samples:", samples)

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10. Summary

• scipy.stats is a powerful tool for statistical analysis.
• You can compute summaries, perform tests, model distributions, and generate random samples.

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Exercise

• Generate 1000 samples from a normal distribution and compute mean, median, std, and mode.
• Test if a sample has a mean significantly different from 5.
• Fit a normal distribution to your own dataset and plot the histogram with the fitted PDF curve.

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#Python #SciPy #Statistics #HypothesisTesting #DataAnalysis

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💡 Pandas Cheatsheet

A quick guide to essential Pandas operations for data manipulation, focusing on creating, selecting, filtering, and grouping data in a DataFrame.

1. Creating a DataFrame
The primary data structure in Pandas is the DataFrame. It's often created from a dictionary.

import pandas as pd

data = {'Name': ['Alice', 'Bob', 'Charlie'],
        'Age': [25, 32, 28],
        'City': ['New York', 'Paris', 'New York']}
df = pd.DataFrame(data)

print(df)
#       Name  Age       City
# 0    Alice   25   New York
# 1      Bob   32      Paris
# 2  Charlie   28   New York

• A dictionary is defined where keys become column names and values become the data in those columns. pd.DataFrame() converts it into a tabular structure.

2. Selecting Data with .loc and .iloc
Use .loc for label-based selection and .iloc for integer-position based selection.

# Select the first row by its integer position (0)
print(df.iloc[0])

# Select the row with index label 1 and only the 'Name' column
print(df.loc[1, 'Name'])

# Output for df.iloc[0]:
# Name       Alice
# Age           25
# City    New York
# Name: 0, dtype: object
#
# Output for df.loc[1, 'Name']:
# Bob

• .iloc[0] gets all data from the row at index position 0.
• .loc[1, 'Name'] gets the data at the intersection of index label 1 and column label 'Name'.

3. Filtering Data
Select subsets of data based on conditions.

# Select rows where Age is greater than 27
filtered_df = df[df['Age'] > 27]
print(filtered_df)
#       Name  Age       City
# 1      Bob   32      Paris
# 2  Charlie   28   New York

• The expression df['Age'] > 27 creates a boolean Series (True/False).
• Using this Series as an index df[...] returns only the rows where the value was True.

4. Grouping and Aggregating
The "group by" operation involves splitting data into groups, applying a function, and combining the results.

# Group by 'City' and calculate the mean age for each city
city_ages = df.groupby('City')['Age'].mean()
print(city_ages)
# City
# New York    26.5
# Paris       32.0
# Name: Age, dtype: float64

• .groupby('City') splits the DataFrame into groups based on unique city values.
• ['Age'].mean() then calculates the mean of the 'Age' column for each of these groups.

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Top 30 Pandas Functions & Methods

This lesson covers 30 essential Pandas functions for data manipulation and analysis, each with a standalone example and its output.

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1. pd.DataFrame()
Creates a new DataFrame (a 2D labeled data structure) from various inputs like dictionaries or lists.

import pandas as pd
data = {'col1': [1, 2], 'col2': [3, 4]}
df = pd.DataFrame(data)
print(df)

col1  col2
0     1     3
1     2     4

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2. pd.Series()
Creates a new Series (a 1D labeled array).

import pandas as pd
s = pd.Series([10, 20, 30, 40], name='MyNumbers')
print(s)

0    10
1    20
2    30
3    40
Name: MyNumbers, dtype: int64

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3. pd.read_csv()
Reads data from a CSV file into a DataFrame. (Assuming a file data.csv exists).

# Create a dummy csv file first
with open('data.csv', 'w') as f:
    f.write('Name,Age\nAlice,25\nBob,30')

df = pd.read_csv('data.csv')
print(df)

Name  Age
0  Alice   25
1    Bob   30

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4. df.to_csv()
Writes a DataFrame to a CSV file.

import pandas as pd
df = pd.DataFrame({'Name': ['Charlie'], 'Age': [35]})
# index=False prevents writing the DataFrame index to the file
df.to_csv('output.csv', index=False)
# You can check that 'output.csv' has been created.
print("File 'output.csv' created.")

File 'output.csv' created.

#PandasIO #DataFrame #Series

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5. df.head()
Returns the first n rows of the DataFrame (default is 5).

import pandas as pd
data = {'Name': ['A', 'B', 'C', 'D', 'E', 'F'], 'Value': [1, 2, 3, 4, 5, 6]}
df = pd.DataFrame(data)
print(df.head(3))

Name  Value
0    A      1
1    B      2
2    C      3

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6. df.tail()
Returns the last n rows of the DataFrame (default is 5).

import pandas as pd
data = {'Name': ['A', 'B', 'C', 'D', 'E', 'F'], 'Value': [1, 2, 3, 4, 5, 6]}
df = pd.DataFrame(data)
print(df.tail(2))

Name  Value
4    E      5
5    F      6

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7. df.info()
Provides a concise summary of the DataFrame, including data types and non-null values.

import pandas as pd
import numpy as np
data = {'col1': [1, 2, 3], 'col2': [4.0, 5.0, np.nan], 'col3': ['A', 'B', 'C']}
df = pd.DataFrame(data)
df.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 3 entries, 0 to 2
Data columns (total 3 columns):
 #   Column  Non-Null Count  Dtype  
---  ------  --------------  -----  
 0   col1    3 non-null      int64  
 1   col2    2 non-null      float64
 2   col3    3 non-null      object 
dtypes: float64(1), int64(1), object(1)
memory usage: 200.0+ bytes

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8. df.shape
Returns a tuple representing the dimensionality (rows, columns) of the DataFrame.

import pandas as pd
df = pd.DataFrame({'A': [1, 2], 'B': [3, 4], 'C': [5, 6]})
print(df.shape)

(2, 3)

#DataInspection #PandasBasics

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9. df.describe()
Generates descriptive statistics for numerical columns (count, mean, std, min, max, etc.).

import pandas as pd
df = pd.DataFrame({'Age': [22, 38, 26, 35, 29]})
print(df.describe())