The Essential Python Cheat Sheet for Statistical Analysis

Descriptive statistics provide a snapshot of your dataset. They help you understand central tendency, variability, and relationships between variables.

1.1 Measures of Central Tendency

Central tendency measures give insight into the “average” behavior of your data:

• Mean – The arithmetic average.

import statistics data = [10, 20, 30, 40, 50] mean = statistics.mean(data) print("Mean:", mean)

• Median – The middle value when the data is sorted.

median = statistics.median(data) print("Median:", median)

• Mode – The most frequent value.

data_with_mode = [10, 20, 20, 30, 40] mode = statistics.mode(data_with_mode) print("Mode:", mode)

1.2 Measures of Dispersion

Dispersion metrics assess how spread out your data is:

• Variance

variance = statistics.variance(data) print("Variance:", variance)

• Standard Deviation

std_dev = statistics.stdev(data) print("Standard Deviation:", std_dev)

• Range

data_range = max(data) - min(data) print("Range:", data_range)

1.3 Correlation and Covariance

These metrics describe relationships between two variables:

import numpy as np x = [10, 20, 30] y = [5, 10, 15] correlation = np.corrcoef(x, y)[0, 1] print("Pearson Correlation:", correlation)

covariance = np.cov(x, y)[0, 1] print("Covariance:", covariance)

1.4 Data Distribution: Percentiles and Quantiles

import numpy as np data = np.random.normal(0, 1, 1000) p_25 = np.percentile(data, 25) q1, q2, q3 = np.quantile(data, [0.25, 0.5, 0.75]) print(f"25th Percentile: {p_25}")

2. Probability Distributions in Python

Probability distributions describe how data is spread across possible outcomes. Python supports major distributions—normal, binomial, Poisson, exponential, uniform, chi-square, and gamma—using libraries like numpy and scipy. These are fundamental for simulations, predictions, and hypothesis testing. Visualizing these distributions with matplotlib helps identify patterns, randomness, and fit in real-world datasets.

2.1 Normal Distribution

data = np.random.normal(loc=0, scale=1, size=1000) plt.hist(data, bins=30) plt.title("Normal Distribution") plt.show()

2.2 Binomial Distribution

n, p = 10, 0.5 binomial_data = np.random.binomial(n, p, 1000) plt.hist(binomial_data, bins=10) plt.title("Binomial Distribution") plt.show()

2.3 Poisson Distribution

poisson_data = np.random.poisson(lam=3, size=1000) plt.hist(poisson_data, bins=10) plt.title("Poisson Distribution") plt.show()

2.4 Exponential Distribution

exponential_data = np.random.exponential(scale=1.0, size=1000) plt.hist(exponential_data, bins=30) plt.title("Exponential Distribution") plt.show()

2.5 Uniform Distribution

uniform_data = np.random.uniform(low=0, high=10, size=1000) plt.hist(uniform_data, bins=30) plt.title("Uniform Distribution") plt.show()

2.6 Chi-Square Distribution

from scipy.stats import chi2 chi_square_data = chi2.rvs(df=2, size=1000) plt.hist(chi_square_data, bins=30) plt.title("Chi-Square Distribution") plt.show()

2.7 Gamma Distribution

from scipy.stats import gamma gamma_data = gamma.rvs(a=2, scale=1, size=1000) plt.hist(gamma_data, bins=30) plt.title("Gamma Distribution") plt.show()

3. Inferential Statistics in Python

Inferential statistics allow us to draw conclusions about populations from samples. Using Python’s scipy.stats, you can perform hypothesis testing (t-tests, ANOVA, chi-square), calculate p-values, and construct confidence intervals. These tools help assess significance, compare groups, and validate assumptions—making them crucial for data-driven decision-making and academic research analysis.

3.1 Hypothesis Testing Terms

• Null Hypothesis (H₀): No effect.
• Alternative Hypothesis (H₁): Effect exists.
• p-value: If < 0.05, reject H₀.

3.2 t-tests

from scipy.stats import ttest_1samp, ttest_ind, ttest_rel t_stat, p_val = ttest_1samp(group1, 50)

3.3 ANOVA

from scipy.stats import f_oneway f_stat, p_value = f_oneway(group1, group2, group3)

3.4 Chi-Square Test

from scipy.stats import chi2_contingency table = [[50, 30], [20, 40]] chi2, p, dof, expected = chi2_contingency(table)

3.5 Mann-Whitney U Test

from scipy.stats import mannwhitneyu u_stat, p_value = mannwhitneyu(group1, group2)

3.6 Confidence Intervals

import scipy.stats as stats mean = np.mean(data) sem = stats.sem(data) conf_interval = stats.t.interval(0.95, len(data)-1, loc=mean, scale=sem) print("95% CI:", conf_interval)

4. Regression Analysis in Python

Regression analysis models relationships between dependent and independent variables. Python’s scikit-learn supports linear and logistic regression for prediction and classification tasks.

4.1 Linear Regression

from sklearn.linear_model import LinearRegression X = np.array([[1], [2], [3]]) y = np.array([2, 4, 6]) model = LinearRegression() model.fit(X, y)

4.2 Logistic Regression

from sklearn.linear_model import LogisticRegression X = np.array([[1], [2], [3], [4], [5]]) y = np.array([0, 0, 0, 1, 1]) model = LogisticRegression() model.fit(X, y)

5. Data Visualization with Python

5.1 Histogram

plt.hist(data, bins=20, color='skyblue') plt.title('Histogram') plt.show()

5.2 Box Plot

sns.boxplot(data=data, color='skyblue') plt.title('Box Plot') plt.show()

5.3 Scatter Plot

plt.scatter(x, y, color='skyblue') plt.title('Scatter Plot') plt.show()

5.4 Pair Plot

sns.pairplot(data) plt.show()

5.5 Line Plot

plt.plot(x, y, color='skyblue') plt.title('Line Plot') plt.show()

Final Thoughts

This Python statistical analysis cheat sheet is built to help you get unstuck during assignments and boost your confidence in both programming and statistics. From descriptive summaries to complex regression models, the code snippets above are battle-tested and used by our own statistics experts when helping students across various levels. If you're still struggling with understanding or applying any of these concepts, our expert team at StatisticsHomeworkHelper.com is here to support you with detailed walkthroughs, tutoring, and customized solutions.