{
  "source_file": "0930",
  "source_platform": "Medium",
  "author": "Riccardo Andreoni",
  "title_listed": "Pearson vs Spearman Correlation: Find Harmony between the Variables",
  "keywords": "",
  "domain": "机器学习",
  "content_type": "深度技术解析",
  "is_paid_flag": "否",
  "url": "https://towardsdatascience.com/pearson-vs-spearman-correlation-find-harmony-between-the-variables-08e201ca9f7f/",
  "publish_date": "2024-01-18",
  "corpus_stage": "",
  "notes": "",
  "id": "f8478796dcc8",
  "collected_at": "2026-10-02T03:06:32",
  "title": "Pearson vs Spearman Correlation: Find Harmony between the Variables | Towards Data Science",
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It also helps in adverstising on the website.\n\n\n  * Cookie\nedgebucket\n  * Duration\nsession\n  * Description\nReddit sets this cookie to save the information about a log-on Reddit user, for the purpose of advertisement recommendations and updating the content.\n\n\n  * Cookie\ndid\n  * Duration\n1 year\n  * Description\nArbor sets this cookie to show targeted ads to site visitors.This cookie expires after 2 months or 1 year.\n\n\nUncategorised\nOther uncategorised cookies are those that are being analysed and have not been classified into a category as yet.\nNo cookies to display.\nReject All Save My Preferences Accept All\nToggle Search[](https://towardsdatascience.com/)Toggle Mobile Navigation\n[](https://towardsdatascience.com/)\nPublish AI, ML & data-science insights to a global community of data professionals.\nSign in[Submit an Article](https://write.insightmediagroup.io)\n[Latest](https://towardsdatascience.com/latest/)[Editor's Picks](https://towardsdatascience.com/tag/editors-pick/)[Newsletter](https://towardsdatascience.com/tag/the-variable/)[ShipAI](https://towardsdatascience.com/shipai/)\n* * *\n[Write For TDS](https://towardsdatascience.com/submissions/)\n[LinkedIn](https://www.linkedin.com/company/towards-data-science/)[X](https://x.com/TDataScience)Toggle Search\n[Artificial Intelligence](https://towardsdatascience.com/category/artificial-intelligence/)\n# Pearson vs Spearman Correlation: Find Harmony between the Variables\nWhich measure of correlation should you use for your task? Learn all you need to know about Pearson and Spearman correlations.\n[Riccardo Andreoni](https://towardsdatascience.com/author/riccardo.andreoni/)\nJanuary 18, 20246 min read\n### Which measure of correlation should you use for your task? Learn all you need to know about Pearson and Spearman correlations\nConsider a **symphony orchestra** tuning their instruments before a performance. Each musician adjusts their notes to harmonize with others, ensuring a **seamless musical experience**. In **Data Science** , the variables in a dataset can be compared to the **orchestra's musicians** : understanding the harmony or dissonances between them is crucial.\n![Image source: pixabay.com.](../images/000.jpeg)\n[Image source: pixabay.com.](https://en.wikipedia.org/wiki/Spearman%27s_rank_correlation_coefficient)\n**Correlation** is a statistical measure that acts like the conductor of the orchestra, guiding the understanding of the **complex relationships** within our data. Here we will focus on two types of correlations: [**Pearson**](https://en.wikipedia.org/wiki/Pearson_correlation_coefficient) and [**Spearman**](https://en.wikipedia.org/wiki/Spearman%27s_rank_correlation_coefficient).\nIf our data is a composition, Pearson and Spearman are our **orchestra's conductors** : they have a singular style of interpreting the symphony, each with peculiar strengths and subtleties. Understanding these two different methodologies will allow you to **extract insights** and **understand the connections** between variables.\nLearn this step by step with the interactive [AI Engineer](https://roadmap.sh/ai-engineer), [AI and Data Scientist](https://roadmap.sh/ai-data-scientist), [Computer Science](https://roadmap.sh/computer-science), [Data Analyst](https://roadmap.sh/data-analyst) and [Machine Learning](https://roadmap.sh/machine-learning) roadmaps.\n## Pearson Correlation\nThe **Pearson correlation coefficient** , denoted as _r_ , quantifies the strength and direction of a **linear relationship** between two **continuous variables** [1]. It is calculated by dividing the covariance of the two variables by the product of their standard deviations.\n![Pearson coefficient formula](../images/001.png)\nPearson coefficient formula\nHere _X_ and _Y_ are two different variables, and _X _i_ and _Y _i_ represent individual data points. _bar{X}_ and _bar{Y}_ denote the mean values of the respective variables.\nThe interpretation of _r_ relies on its value, **ranging from -1 to 1**. A value of -1 implies a perfect negative correlation, indicating that as one variable increases, the other decreases linearly [2]. Conversely, a value of 1 signifies a perfect positive correlation, illustrating a linear increase in both variables. A value of 0 implies no linear correlation.\nPearson correlation is particularly good at capturing linear relationships between variables. Its sensitivity to linear patterns makes it a powerful tool when investigating relationships governed by a consistent linear trend. Moreover, the standardized nature of the coefficient allows for easy comparison across different datasets.\nHowever, it's crucial to note that Pearson is susceptible to the influence of [outliers](https://towardsdatascience.com/outlier-detection-with-scikit-learn-and-matplotlib-a-practical-guide-382d1411b8ec). If a dataset contains extreme values they can impact the calculation, leading to inaccurate interpretations.\nTechnical concepts can be better understood through practical examples. Let's use **Python** to show the computation of Pearson correlation and its visualization. Suppose we have two lists representing the hours spent studying (_X_) and the corresponding exam scores (_Y_).\npython\n\n```\nimport numpy as np\nfrom scipy.stats import pearsonr\nimport matplotlib.pyplot as plt\nimport seaborn as sns\n\n# Generating data points\nnp.random.seed(42)  # For reproducibility\nhours_studied = np.random.randint(8, 25, size=50)\nexam_scores = 60 + 2 * hours_studied + np.random.normal(0, 5, size=50)\n\n# Calculate Pearson correlation coefficient\npearson_corr, _ = pearsonr(hours_studied, exam_scores)\n\n# Calculate Pearson correlation line coefficients\nm, b = np.polyfit(hours_studied, exam_scores, 1)  # Fit a linear regression line\n\n# Scatter plot\nfig, ax = plt.subplots()\nax.scatter(hours_studied, exam_scores, color=sns.color_palette(\"hls\",24)[14], alpha=.9, label='Data points')\nplt.plot(hours_studied, m * np.array(hours_studied) + b, color='red', alpha=.6, label='Pearson Correlation Line')\nplt.title(\"Hours Studied vs. Exam Scores\")\nplt.xlabel(\"Hours Studied\")\nplt.ylabel(\"Exam Scores\")\nplt.legend(loc='lower right')\nax.spines['top'].set_visible(False)\nax.spines['bottom'].set_visible(False)\nax.spines['right'].set_visible(False)\nax.spines['left'].set_visible(False)\nax.xaxis.set_ticks_position('none') \nax.yaxis.set_ticks_position('none')\n```\n\n![Image by the author.](../images/002.png)\nImage by the author.\n![](../images/body-83184826073798f5c46e.png)\nPearson correlation effectiveness **diminishes** when faced **with curvilinear patterns**. This limitation arises from Pearson's inherent assumption of linearity, making it ill-suited to capture the nuances of non-linear relationships.\n![Image by the author.](../images/003.png)\nImage by the author.\nConsider a scenario where the relationship between two variables follows a quadratic curve. Pearson correlation might inaccurately suggest a weak or nonexistent relationship due to its inability to capture the non-linear relation.\npython\n\n```\n# Generating quadratic data\nnp.random.seed(42)\nX = np.linspace(-10, 10, 100)\nY = X**2 + np.random.normal(0, 10, size=len(X))\n\n# Calculate Pearson correlation coefficient\npearson_corr, _ = pearsonr(X, Y)\n\nm, b = np.polyfit(X, Y, 1)  # Fit a linear regression line\n\n# Scatter plot\nfig, ax = plt.subplots()\nax.scatter(X, Y, color=sns.color_palette(\"hls\",24)[14], alpha=.9, label='Data points')\nplt.plot(X, m * X + b, color='red', alpha=.6, label='Pearson Correlation Line')\nplt.title(\"X vs. Y (Quadratic Relationship)\")\nplt.xlabel(\"X\")\nplt.ylabel(\"Y\")\nplt.legend(loc='upper center')\nax.spines['top'].set_visible(False)\nax.spines['bottom'].set_visible(False)\nax.spines['right'].set_visible(False)\nax.spines['left'].set_visible(False)\nax.xaxis.set_ticks_position('none') \nax.yaxis.set_ticks_position('none') \n```\n\n![](../images/body-31ce92255b664900090f.png)\n![Image by the author.](../images/004.png)\nImage by the author.\n## Spearman Correlation\n**Spearman correlation** addresses the limitations of Pearson when applied to **non-linear relationships** or datasets containing **outliers** [3]. Spearman's rank correlation coefficient (_ρ_), denoted as _rho_ , operates on the ranked values of variables, making it less sensitive to extreme values and well-suited for capturing monotonic relationships.\n![Spearman coefficient formula](../images/005.png)\nSpearman coefficient formula\nIn the above formula, _d _i_ represents the difference between the ranks of corresponding pairs of variables, and _n_ is the number of data points.\nSimilar to Pearson, Spearman's coefficient **ranges from -1 to 1**. A value of -1 indicates a perfect negative monotonic correlation, meaning that as one variable increases, the other consistently decreases. A value of 1 signifies a perfect positive monotonic correlation, illustrating a consistent increase in both variables. A value of 0 denotes no monotonic correlation.\nUnlike Pearson, Spearman **does not assume linearity** and is robust in case of outliers. It focuses on the ordinal nature of data, making it a valuable tool when the relationship between variables is more about the order than the specific values.\n![Image by the author.](../images/006.png)\nImage by the author.\nConsider the following practical application using Python, where we have two variables 'A' and 'B' with a non-linear relationship:\npython\n\n```\nimport numpy as np\nfrom scipy.stats import spearmanr\nfrom scipy.stats import pearsonr\nimport matplotlib.pyplot as plt\n\n# Generating non-linear data\nnp.random.seed(42)\nA = np.linspace(-10, 10, 100)\nB = A**5 + np.random.normal(0, 4000, size=len(A))\n\n# Calculate Spearman correlation coefficient\nspearman_corr, _ = spearmanr(A, B)\n# Calculate Pearson correlation coefficient\npearson_corr, _ = pearsonr(A, B)\nm, b = np.polyfit(A, B, 1)  # Fit a linear regression line\n\n# Scatter plot\nfig, ax = plt.subplots()\nax.scatter(A, B, color=sns.color_palette(\"hls\",24)[14], alpha=.9, label='Data points')\nplt.plot(X, m * X + b, color='red', alpha=.6, label='Pearson Correlation Line')\nplt.title(\"A vs. B (Non-linear Relationship)\")\nplt.xlabel(\"A\")\nplt.ylabel(\"B\")\nax.spines['top'].set_visible(False)\nax.spines['bottom'].set_visible(False)\nax.spines['right'].set_visible(False)\nax.spines['left'].set_visible(False)\nax.xaxis.set_ticks_position('none') \nax.yaxis.set_ticks_position('none')\n\nplt.legend()\n```\n\n![Image by the author.](../images/007.png)\nImage by the author.\nIn this example, the scatter plot visualizes a non-linear relationship between variables 'A' and 'B.' Spearman correlation, which does not assume linearity, will be better suited to capture and quantify this non-linear association. You can see that the red line, representing the Pearson Correlation Line, misses the nature of the variables' relationship.\nWe can quantify this measure by comparing the two coefficients:\n![](../images/body-116f26aab8eb69c0abb3.png)\nSpearman coefficient is sensibly higher, as it is more suited for this type of relationship.\n## Conclusion: Pearson vs. Spearman\nConcluding this introductory guide, let's point out the **pros and cons** of the two measures.\n![Image by the author.](../images/008.png)\nImage by the author.\nPearson Correlation coefficient is indeed **efficient** for **linear relationship** , and can provide a **standardized measure** for easy comparison across different datasets.\nOn the other hand, Pearson coefficient is highly **sensitive to outliers**. Also, assuming linearity may **mislead in non-linear scenarios**.\nMost of Pearson coefficient's downsides are addressed by Spearman Correlation coefficient: it is **robust** in the presence of **outliers** , and, as it relies on the **rank of data points** , it is suitable for **non-linear relationships**.\nIt is important, however, to keep in mind that Spearman coefficient has also some criticalities. In my opinion the most relevant ones are its **lower efficiency** on large datasets, and the **potential loss of information** in case of tied ranks.\nIn order to keep this guide **concise and practical** , my advice is to **choose Pearson** for linear relationships in normally distributed data without outliers. **Opt for Spearman** when facing non-linear relationships, ordinal data, or datasets with outliers, as it excels in capturing monotonic associations.\nRemember that this choice heavily relies on the characteristics of the data. Keep also in mind that this introduction, while touching most important aspects, merely scratched the surface of statistical methodologies. For further study, you can find an interesting **set of resources** below!\n## References\nIn-text references:\n[1] [Laerd Statistics - Pearson Product-Moment Correlation](https://statistics.laerd.com/statistical-guides/pearson-correlation-coefficient-statistical-guide.php)\n[2] [Boston University - Correlation and Regression with R](https://sphweb.bumc.bu.edu/otlt/MPH-Modules/BS/R/R5_Correlation-Regression/R5_Correlation-Regression_print.html)\n[3] [Analytics Vidhya - Pearson vs Spearman Correlation Coefficients](https://www.analyticsvidhya.com/blog/2021/03/comparison-of-pearson-and-spearman-correlation-coefficients/)\n[4] [Statistics by Jim - Spearman's Correlation Explained](https://statisticsbyjim.com/basics/spearmans-correlation/)\nOther material:\n  * [An Introduction to Statistical Learning by Gareth James, Daniela Witten, Trevor Hastie, and Robert Tibshirani](https://www.statlearning.com/)\n  * [Statistics by Robert S. Witte and John S. Witte](https://www.wiley.com/en-us/Statistics,+11th+Edition-p-9781119254515)\n  * [Understanding Correlation by Kristoffer Magnusson](https://rpsychologist.com/correlation/)\n  * [A Gentle Introduction to Correlation and Causation by David M Diez](https://baselbiometrics.github.io/home/docs/trainings/20210202/1_Moffa.pdf)\n  * [Discovering Statistics Using IBM SPSS Statistics by Andy Field](https://uk.sagepub.com/en-gb/eur/discovering-statistics-using-ibm-spss-statistics/book257672)\n  * [Applied Multivariate Statistical Analysis by Richard A. Johnson and Dean W. Wichern](https://www.webpages.uidaho.edu/~stevel/519/Applied%20Multivariate%20Statistical%20Analysis%20by%20Johnson%20and%20Wichern.pdf)\n\n\n## Register Now to Continue Reading\n### Unlock Towards Data Science with a Free Account\nAll articles on Towards Data Science are available to registered users. 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It also helps in adverstising on the website.\n\n\n  * Cookie\nedgebucket\n  * Duration\nsession\n  * Description\nReddit sets this cookie to save the information about a log-on Reddit user, for the purpose of advertisement recommendations and updating the content.\n\n\n  * Cookie\ndid\n  * Duration\n1 year\n  * Description\nArbor sets this cookie to show targeted ads to site visitors.This cookie expires after 2 months or 1 year.\n\n\nUncategorised\nOther uncategorised cookies are those that are being analysed and have not been classified into a category as yet.\nNo cookies to display.\nReject All Save My Preferences Accept All\nToggle Search[](https://towardsdatascience.com/)Toggle Mobile Navigation\n[](https://towardsdatascience.com/)\nPublish AI, ML & data-science insights to a global community of data professionals.\nSign in[Submit an Article](https://write.insightmediagroup.io)\n[Latest](https://towardsdatascience.com/latest/)[Editor's Picks](https://towardsdatascience.com/tag/editors-pick/)[Newsletter](https://towardsdatascience.com/tag/the-variable/)[ShipAI](https://towardsdatascience.com/shipai/)\n* * *\n[Write For TDS](https://towardsdatascience.com/submissions/)\n[LinkedIn](https://www.linkedin.com/company/towards-data-science/)[X](https://x.com/TDataScience)Toggle Search\n[Artificial Intelligence](https://towardsdatascience.com/category/artificial-intelligence/)\n# Pearson vs Spearman Correlation: Find Harmony between the Variables\nWhich measure of correlation should you use for your task? Learn all you need to know about Pearson and Spearman correlations.\n[Riccardo Andreoni](https://towardsdatascience.com/author/riccardo.andreoni/)\nJanuary 18, 20246 min read\n### Which measure of correlation should you use for your task? Learn all you need to know about Pearson and Spearman correlations\nConsider a **symphony orchestra** tuning their instruments before a performance. Each musician adjusts their notes to harmonize with others, ensuring a **seamless musical experience**. In **Data Science** , the variables in a dataset can be compared to the **orchestra's musicians** : understanding the harmony or dissonances between them is crucial.\n![Image source: pixabay.com.](https://assets.insightmediagroup.io/media/wp-content/uploads/2024/01/1pLaKbsPX0c6w3nss3bKG_Q.jpeg)\n[Image source: pixabay.com.](https://en.wikipedia.org/wiki/Spearman%27s_rank_correlation_coefficient)\n**Correlation** is a statistical measure that acts like the conductor of the orchestra, guiding the understanding of the **complex relationships** within our data. Here we will focus on two types of correlations: [**Pearson**](https://en.wikipedia.org/wiki/Pearson_correlation_coefficient) and [**Spearman**](https://en.wikipedia.org/wiki/Spearman%27s_rank_correlation_coefficient).\nIf our data is a composition, Pearson and Spearman are our **orchestra's conductors** : they have a singular style of interpreting the symphony, each with peculiar strengths and subtleties. Understanding these two different methodologies will allow you to **extract insights** and **understand the connections** between variables.\nLearn this step by step with the interactive [AI Engineer](https://roadmap.sh/ai-engineer), [AI and Data Scientist](https://roadmap.sh/ai-data-scientist), [Computer Science](https://roadmap.sh/computer-science), [Data Analyst](https://roadmap.sh/data-analyst) and [Machine Learning](https://roadmap.sh/machine-learning) roadmaps.\n## Pearson Correlation\nThe **Pearson correlation coefficient** , denoted as _r_ , quantifies the strength and direction of a **linear relationship** between two **continuous variables** [1]. It is calculated by dividing the covariance of the two variables by the product of their standard deviations.\n![Pearson coefficient formula](https://assets.insightmediagroup.io/media/wp-content/uploads/2024/01/11xm0y3Wh8F05xd9CtYUe6w.png)\nPearson coefficient formula\nHere _X_ and _Y_ are two different variables, and _X _i_ and _Y _i_ represent individual data points. _bar{X}_ and _bar{Y}_ denote the mean values of the respective variables.\nThe interpretation of _r_ relies on its value, **ranging from -1 to 1**. A value of -1 implies a perfect negative correlation, indicating that as one variable increases, the other decreases linearly [2]. Conversely, a value of 1 signifies a perfect positive correlation, illustrating a linear increase in both variables. A value of 0 implies no linear correlation.\nPearson correlation is particularly good at capturing linear relationships between variables. Its sensitivity to linear patterns makes it a powerful tool when investigating relationships governed by a consistent linear trend. Moreover, the standardized nature of the coefficient allows for easy comparison across different datasets.\nHowever, it's crucial to note that Pearson is susceptible to the influence of [outliers](https://towardsdatascience.com/outlier-detection-with-scikit-learn-and-matplotlib-a-practical-guide-382d1411b8ec). If a dataset contains extreme values they can impact the calculation, leading to inaccurate interpretations.\nTechnical concepts can be better understood through practical examples. Let's use **Python** to show the computation of Pearson correlation and its visualization. Suppose we have two lists representing the hours spent studying (_X_) and the corresponding exam scores (_Y_).\npython\n\n```\nimport numpy as np\nfrom scipy.stats import pearsonr\nimport matplotlib.pyplot as plt\nimport seaborn as sns\n\n# Generating data points\nnp.random.seed(42)  # For reproducibility\nhours_studied = np.random.randint(8, 25, size=50)\nexam_scores = 60 + 2 * hours_studied + np.random.normal(0, 5, size=50)\n\n# Calculate Pearson correlation coefficient\npearson_corr, _ = pearsonr(hours_studied, exam_scores)\n\n# Calculate Pearson correlation line coefficients\nm, b = np.polyfit(hours_studied, exam_scores, 1)  # Fit a linear regression line\n\n# Scatter plot\nfig, ax = plt.subplots()\nax.scatter(hours_studied, exam_scores, color=sns.color_palette(\"hls\",24)[14], alpha=.9, label='Data points')\nplt.plot(hours_studied, m * np.array(hours_studied) + b, color='red', alpha=.6, label='Pearson Correlation Line')\nplt.title(\"Hours Studied vs. Exam Scores\")\nplt.xlabel(\"Hours Studied\")\nplt.ylabel(\"Exam Scores\")\nplt.legend(loc='lower right')\nax.spines['top'].set_visible(False)\nax.spines['bottom'].set_visible(False)\nax.spines['right'].set_visible(False)\nax.spines['left'].set_visible(False)\nax.xaxis.set_ticks_position('none') \nax.yaxis.set_ticks_position('none')\n```\n\n![Image by the author.](https://assets.insightmediagroup.io/media/wp-content/uploads/2024/01/12YnGIiqQDpfSCEnp6BznZw.png)\nImage by the author.\n![](https://assets.insightmediagroup.io/media/wp-content/uploads/2024/01/1i_bUHFG2tfqx_MyMAJbohg.png)\nPearson correlation effectiveness **diminishes** when faced **with curvilinear patterns**. This limitation arises from Pearson's inherent assumption of linearity, making it ill-suited to capture the nuances of non-linear relationships.\n![Image by the author.](https://assets.insightmediagroup.io/media/wp-content/uploads/2024/01/1J8o7tTct_XPCYldltr5yBA.png)\nImage by the author.\nConsider a scenario where the relationship between two variables follows a quadratic curve. Pearson correlation might inaccurately suggest a weak or nonexistent relationship due to its inability to capture the non-linear relation.\npython\n\n```\n# Generating quadratic data\nnp.random.seed(42)\nX = np.linspace(-10, 10, 100)\nY = X**2 + np.random.normal(0, 10, size=len(X))\n\n# Calculate Pearson correlation coefficient\npearson_corr, _ = pearsonr(X, Y)\n\nm, b = np.polyfit(X, Y, 1)  # Fit a linear regression line\n\n# Scatter plot\nfig, ax = plt.subplots()\nax.scatter(X, Y, color=sns.color_palette(\"hls\",24)[14], alpha=.9, label='Data points')\nplt.plot(X, m * X + b, color='red', alpha=.6, label='Pearson Correlation Line')\nplt.title(\"X vs. Y (Quadratic Relationship)\")\nplt.xlabel(\"X\")\nplt.ylabel(\"Y\")\nplt.legend(loc='upper center')\nax.spines['top'].set_visible(False)\nax.spines['bottom'].set_visible(False)\nax.spines['right'].set_visible(False)\nax.spines['left'].set_visible(False)\nax.xaxis.set_ticks_position('none') \nax.yaxis.set_ticks_position('none') \n```\n\n![](https://assets.insightmediagroup.io/media/wp-content/uploads/2024/01/1_LB5zlj4Ca59RZug-mJOMw.png)\n![Image by the author.](https://assets.insightmediagroup.io/media/wp-content/uploads/2024/01/1iPmv0G_N6axZ3P6Lhl4mRg.png)\nImage by the author.\n## Spearman Correlation\n**Spearman correlation** addresses the limitations of Pearson when applied to **non-linear relationships** or datasets containing **outliers** [3]. Spearman's rank correlation coefficient (_ρ_), denoted as _rho_ , operates on the ranked values of variables, making it less sensitive to extreme values and well-suited for capturing monotonic relationships.\n![Spearman coefficient formula](https://assets.insightmediagroup.io/media/wp-content/uploads/2024/01/1PwAr1l_Rm1rlI_V35cexwQ.png)\nSpearman coefficient formula\nIn the above formula, _d _i_ represents the difference between the ranks of corresponding pairs of variables, and _n_ is the number of data points.\nSimilar to Pearson, Spearman's coefficient **ranges from -1 to 1**. A value of -1 indicates a perfect negative monotonic correlation, meaning that as one variable increases, the other consistently decreases. A value of 1 signifies a perfect positive monotonic correlation, illustrating a consistent increase in both variables. A value of 0 denotes no monotonic correlation.\nUnlike Pearson, Spearman **does not assume linearity** and is robust in case of outliers. It focuses on the ordinal nature of data, making it a valuable tool when the relationship between variables is more about the order than the specific values.\n![Image by the author.](https://assets.insightmediagroup.io/media/wp-content/uploads/2024/01/1vgknv_TyZlBeMMPrUx-yJQ.png)\nImage by the author.\nConsider the following practical application using Python, where we have two variables 'A' and 'B' with a non-linear relationship:\npython\n\n```\nimport numpy as np\nfrom scipy.stats import spearmanr\nfrom scipy.stats import pearsonr\nimport matplotlib.pyplot as plt\n\n# Generating non-linear data\nnp.random.seed(42)\nA = np.linspace(-10, 10, 100)\nB = A**5 + np.random.normal(0, 4000, size=len(A))\n\n# Calculate Spearman correlation coefficient\nspearman_corr, _ = spearmanr(A, B)\n# Calculate Pearson correlation coefficient\npearson_corr, _ = pearsonr(A, B)\nm, b = np.polyfit(A, B, 1)  # Fit a linear regression line\n\n# Scatter plot\nfig, ax = plt.subplots()\nax.scatter(A, B, color=sns.color_palette(\"hls\",24)[14], alpha=.9, label='Data points')\nplt.plot(X, m * X + b, color='red', alpha=.6, label='Pearson Correlation Line')\nplt.title(\"A vs. B (Non-linear Relationship)\")\nplt.xlabel(\"A\")\nplt.ylabel(\"B\")\nax.spines['top'].set_visible(False)\nax.spines['bottom'].set_visible(False)\nax.spines['right'].set_visible(False)\nax.spines['left'].set_visible(False)\nax.xaxis.set_ticks_position('none') \nax.yaxis.set_ticks_position('none')\n\nplt.legend()\n```\n\n![Image by the author.](https://assets.insightmediagroup.io/media/wp-content/uploads/2024/01/1Vsu7Lrcx05wpV3yRYdphVg.png)\nImage by the author.\nIn this example, the scatter plot visualizes a non-linear relationship between variables 'A' and 'B.' Spearman correlation, which does not assume linearity, will be better suited to capture and quantify this non-linear association. You can see that the red line, representing the Pearson Correlation Line, misses the nature of the variables' relationship.\nWe can quantify this measure by comparing the two coefficients:\n![](https://assets.insightmediagroup.io/media/wp-content/uploads/2024/01/1D7_P3zCOP9GGoDxOw0PhJA.png)\nSpearman coefficient is sensibly higher, as it is more suited for this type of relationship.\n## Conclusion: Pearson vs. Spearman\nConcluding this introductory guide, let's point out the **pros and cons** of the two measures.\n![Image by the author.](https://assets.insightmediagroup.io/media/wp-content/uploads/2024/01/12fBtyQmLUps9dApMhoClig.png)\nImage by the author.\nPearson Correlation coefficient is indeed **efficient** for **linear relationship** , and can provide a **standardized measure** for easy comparison across different datasets.\nOn the other hand, Pearson coefficient is highly **sensitive to outliers**. Also, assuming linearity may **mislead in non-linear scenarios**.\nMost of Pearson coefficient's downsides are addressed by Spearman Correlation coefficient: it is **robust** in the presence of **outliers** , and, as it relies on the **rank of data points** , it is suitable for **non-linear relationships**.\nIt is important, however, to keep in mind that Spearman coefficient has also some criticalities. In my opinion the most relevant ones are its **lower efficiency** on large datasets, and the **potential loss of information** in case of tied ranks.\nIn order to keep this guide **concise and practical** , my advice is to **choose Pearson** for linear relationships in normally distributed data without outliers. **Opt for Spearman** when facing non-linear relationships, ordinal data, or datasets with outliers, as it excels in capturing monotonic associations.\nRemember that this choice heavily relies on the characteristics of the data. Keep also in mind that this introduction, while touching most important aspects, merely scratched the surface of statistical methodologies. For further study, you can find an interesting **set of resources** below!\n## References\nIn-text references:\n[1] [Laerd Statistics - Pearson Product-Moment Correlation](https://statistics.laerd.com/statistical-guides/pearson-correlation-coefficient-statistical-guide.php)\n[2] [Boston University - Correlation and Regression with R](https://sphweb.bumc.bu.edu/otlt/MPH-Modules/BS/R/R5_Correlation-Regression/R5_Correlation-Regression_print.html)\n[3] [Analytics Vidhya - Pearson vs Spearman Correlation Coefficients](https://www.analyticsvidhya.com/blog/2021/03/comparison-of-pearson-and-spearman-correlation-coefficients/)\n[4] [Statistics by Jim - Spearman's Correlation Explained](https://statisticsbyjim.com/basics/spearmans-correlation/)\nOther material:\n  * [An Introduction to Statistical Learning by Gareth James, Daniela Witten, Trevor Hastie, and Robert Tibshirani](https://www.statlearning.com/)\n  * [Statistics by Robert S. Witte and John S. Witte](https://www.wiley.com/en-us/Statistics,+11th+Edition-p-9781119254515)\n  * [Understanding Correlation by Kristoffer Magnusson](https://rpsychologist.com/correlation/)\n  * [A Gentle Introduction to Correlation and Causation by David M Diez](https://baselbiometrics.github.io/home/docs/trainings/20210202/1_Moffa.pdf)\n  * [Discovering Statistics Using IBM SPSS Statistics by Andy Field](https://uk.sagepub.com/en-gb/eur/discovering-statistics-using-ibm-spss-statistics/book257672)\n  * [Applied Multivariate Statistical Analysis by Richard A. Johnson and Dean W. Wichern](https://www.webpages.uidaho.edu/~stevel/519/Applied%20Multivariate%20Statistical%20Analysis%20by%20Johnson%20and%20Wichern.pdf)\n\n\n## Register Now to Continue Reading\n### Unlock Towards Data Science with a Free Account\nAll articles on Towards Data Science are available to registered users. 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