SlideShare a Scribd company logo
1 of 7
Spearman's correlation
Ms. Nigar K.Mujawar
Assistant Professor,
Shri.Balasaheb Mane Shikshan Prasarak Mandal Ambap
Womens College of Pharmacy, Peth-Vadgaon,
Kolhapur, M.S., INDIA.
1
Spearman's correlation
Spearman's correlation coefficient (or Spearman's rho) is a non-
parametric measure of rank correlation between two variables. It
assesses how well the relationship between two variables can be
described using a monotonic function, regardless of the scale of
measurement. Here's a detailed explanation of Spearman's correlation
coefficient:
Calculation:
1.Ranking:
1.For each variable X and Y, rank the values separately. If there are
ties (i.e., identical values), assign them the average of the ranks they
would have received if they were distinct values.
2.Computing Differences:
1.For each pair of ranked values(xi​,yi​), calculate the difference in ranks
di​=rank of xi​−rank of yi.
1.Applying the Formula:
1.Use the formula: = 1− 6∑di2 / n(n2−1)
2.6∑(2−1)ρ=1−​​ where n is the number of observations.
Interpretation:
The Spearman correlation coefficient ρ ranges between -1 and 1.
ρ=1 indicates a perfect positive monotonic relationship: as X increases,
Y tends to increase.
ρ=−1 indicates a perfect negative monotonic relationship: as X
increases, Y tends to decrease.
ρ=0 indicates no monotonic association between X and Y, but it doesn't
imply independence.
Advantages and Use Cases:
1. Non-parametric: Suitable for ordinal data or data that do not meet the
assumptions of normality required by Pearson correlation.
2. Robust: Less affected by outliers compared to Pearson correlation.
3. Interpretability: Describes the strength and direction of monotonic
relationships.
Example:
Suppose we have the following paired data representing ranks:
X:10,5,8,3,6
Y:7,4,9,2,1​
•Rank X values: Rank(10)=5,Rank(5)=3,Rank(8)=4,Rank(3)=2,Rank(6)=1
•Rank Y values: Rank(7)=4,Rank(4)=3,Rank(9)=5,Rank(2)=2,Rank(1)=1
•Compute differences:
• d1​=5−4=1
• d2​=3−3=0
• d3​=4−5=−1
• d4​=2−2=0
• d5​=1−1=0
7

More Related Content

Similar to Spearman's correlation,Formula,Advantages,

College of Doctoral StudiesRES-845 Module 8 Problem.docx
        College of Doctoral StudiesRES-845 Module 8 Problem.docx        College of Doctoral StudiesRES-845 Module 8 Problem.docx
College of Doctoral StudiesRES-845 Module 8 Problem.docx
hallettfaustina
 
Stats For Life Module7 Oc
Stats For Life Module7 OcStats For Life Module7 Oc
Stats For Life Module7 Oc
N Rabe
 
Correlational AnalysisAccording to Gogtay et al (2017) c.docx
Correlational AnalysisAccording to Gogtay et al (2017) c.docxCorrelational AnalysisAccording to Gogtay et al (2017) c.docx
Correlational AnalysisAccording to Gogtay et al (2017) c.docx
melvinjrobinson2199
 

Similar to Spearman's correlation,Formula,Advantages, (20)

Correlation - Biostatistics
Correlation - BiostatisticsCorrelation - Biostatistics
Correlation - Biostatistics
 
College of Doctoral StudiesRES-845 Module 8 Problem.docx
        College of Doctoral StudiesRES-845 Module 8 Problem.docx        College of Doctoral StudiesRES-845 Module 8 Problem.docx
College of Doctoral StudiesRES-845 Module 8 Problem.docx
 
Study of Correlation
Study of Correlation Study of Correlation
Study of Correlation
 
Stats For Life Module7 Oc
Stats For Life Module7 OcStats For Life Module7 Oc
Stats For Life Module7 Oc
 
correlation ;.pptx
correlation ;.pptxcorrelation ;.pptx
correlation ;.pptx
 
correlation.pptx
correlation.pptxcorrelation.pptx
correlation.pptx
 
Correlation
CorrelationCorrelation
Correlation
 
Regression.pptx
Regression.pptxRegression.pptx
Regression.pptx
 
RMBS - CORRELATION.pptx
RMBS - CORRELATION.pptxRMBS - CORRELATION.pptx
RMBS - CORRELATION.pptx
 
MCA_UNIT-4_Computer Oriented Numerical Statistical Methods
MCA_UNIT-4_Computer Oriented Numerical Statistical MethodsMCA_UNIT-4_Computer Oriented Numerical Statistical Methods
MCA_UNIT-4_Computer Oriented Numerical Statistical Methods
 
Data Processing and Statistical Treatment: Spreads and Correlation
Data Processing and Statistical Treatment: Spreads and CorrelationData Processing and Statistical Treatment: Spreads and Correlation
Data Processing and Statistical Treatment: Spreads and Correlation
 
Correlational Research
Correlational ResearchCorrelational Research
Correlational Research
 
Factor Extraction method in factor analysis with example in R studio.pptx
Factor Extraction method in factor analysis with example in R studio.pptxFactor Extraction method in factor analysis with example in R studio.pptx
Factor Extraction method in factor analysis with example in R studio.pptx
 
Four Methods in testing reliability
Four Methods in testing reliabilityFour Methods in testing reliability
Four Methods in testing reliability
 
Class 9 Covariance & Correlation Concepts.pptx
Class 9 Covariance & Correlation Concepts.pptxClass 9 Covariance & Correlation Concepts.pptx
Class 9 Covariance & Correlation Concepts.pptx
 
Correlation and Path analysis in breeding experiments
Correlation and Path analysis in breeding experimentsCorrelation and Path analysis in breeding experiments
Correlation and Path analysis in breeding experiments
 
Association between-variables
Association between-variablesAssociation between-variables
Association between-variables
 
Correlational AnalysisAccording to Gogtay et al (2017) c.docx
Correlational AnalysisAccording to Gogtay et al (2017) c.docxCorrelational AnalysisAccording to Gogtay et al (2017) c.docx
Correlational AnalysisAccording to Gogtay et al (2017) c.docx
 
Inferential statistics correlations
Inferential statistics correlationsInferential statistics correlations
Inferential statistics correlations
 
Research Methodology-Chapter 14
Research Methodology-Chapter 14Research Methodology-Chapter 14
Research Methodology-Chapter 14
 

More from Nigar Kadar Mujawar,Womens College of Pharmacy,Peth Vadgaon,Kolhapur,416112

More from Nigar Kadar Mujawar,Womens College of Pharmacy,Peth Vadgaon,Kolhapur,416112 (9)

Plagiarism,forms,understand about plagiarism,avoid plagiarism,key significanc...
Plagiarism,forms,understand about plagiarism,avoid plagiarism,key significanc...Plagiarism,forms,understand about plagiarism,avoid plagiarism,key significanc...
Plagiarism,forms,understand about plagiarism,avoid plagiarism,key significanc...
 
Introduction to Research ,Need for research, Need for design of Experiments, ...
Introduction to Research ,Need for research, Need for design of Experiments, ...Introduction to Research ,Need for research, Need for design of Experiments, ...
Introduction to Research ,Need for research, Need for design of Experiments, ...
 
Chi-Square Test Non Parametric Test Categorical Variable
Chi-Square Test Non Parametric Test Categorical VariableChi-Square Test Non Parametric Test Categorical Variable
Chi-Square Test Non Parametric Test Categorical Variable
 
Problems on Mean,Mode,Median Standard Deviation
Problems on Mean,Mode,Median Standard DeviationProblems on Mean,Mode,Median Standard Deviation
Problems on Mean,Mode,Median Standard Deviation
 
Least Significance Difference:Biostatics and Research Methodology
Least Significance Difference:Biostatics and Research MethodologyLeast Significance Difference:Biostatics and Research Methodology
Least Significance Difference:Biostatics and Research Methodology
 
ANOVA Parametric test: Biostatics and Research Methodology
ANOVA Parametric test: Biostatics and Research MethodologyANOVA Parametric test: Biostatics and Research Methodology
ANOVA Parametric test: Biostatics and Research Methodology
 
t-test Parametric test Biostatics and Research Methodology
t-test Parametric test Biostatics and Research Methodologyt-test Parametric test Biostatics and Research Methodology
t-test Parametric test Biostatics and Research Methodology
 
Probability Problems, Biostatics and Research Methodology
Probability Problems, Biostatics and Research MethodologyProbability Problems, Biostatics and Research Methodology
Probability Problems, Biostatics and Research Methodology
 
Probability Biostatics and Research Methodology
Probability Biostatics and Research MethodologyProbability Biostatics and Research Methodology
Probability Biostatics and Research Methodology
 

Recently uploaded

SURVEY I created for uni project research
SURVEY I created for uni project researchSURVEY I created for uni project research
SURVEY I created for uni project research
CaitlinCummins3
 
The basics of sentences session 4pptx.pptx
The basics of sentences session 4pptx.pptxThe basics of sentences session 4pptx.pptx
The basics of sentences session 4pptx.pptx
heathfieldcps1
 

Recently uploaded (20)

SURVEY I created for uni project research
SURVEY I created for uni project researchSURVEY I created for uni project research
SURVEY I created for uni project research
 
philosophy and it's principles based on the life
philosophy and it's principles based on the lifephilosophy and it's principles based on the life
philosophy and it's principles based on the life
 
The basics of sentences session 4pptx.pptx
The basics of sentences session 4pptx.pptxThe basics of sentences session 4pptx.pptx
The basics of sentences session 4pptx.pptx
 
Software testing for project report .pdf
Software testing for project report .pdfSoftware testing for project report .pdf
Software testing for project report .pdf
 
Dementia (Alzheimer & vasular dementia).
Dementia (Alzheimer & vasular dementia).Dementia (Alzheimer & vasular dementia).
Dementia (Alzheimer & vasular dementia).
 
An Overview of the Odoo 17 Discuss App.pptx
An Overview of the Odoo 17 Discuss App.pptxAn Overview of the Odoo 17 Discuss App.pptx
An Overview of the Odoo 17 Discuss App.pptx
 
Pragya Champions Chalice 2024 Prelims & Finals Q/A set, General Quiz
Pragya Champions Chalice 2024 Prelims & Finals Q/A set, General QuizPragya Champions Chalice 2024 Prelims & Finals Q/A set, General Quiz
Pragya Champions Chalice 2024 Prelims & Finals Q/A set, General Quiz
 
“O BEIJO” EM ARTE .
“O BEIJO” EM ARTE                       .“O BEIJO” EM ARTE                       .
“O BEIJO” EM ARTE .
 
The Last Leaf, a short story by O. Henry
The Last Leaf, a short story by O. HenryThe Last Leaf, a short story by O. Henry
The Last Leaf, a short story by O. Henry
 
How to Analyse Profit of a Sales Order in Odoo 17
How to Analyse Profit of a Sales Order in Odoo 17How to Analyse Profit of a Sales Order in Odoo 17
How to Analyse Profit of a Sales Order in Odoo 17
 
Stl Algorithms in C++ jjjjjjjjjjjjjjjjjj
Stl Algorithms in C++ jjjjjjjjjjjjjjjjjjStl Algorithms in C++ jjjjjjjjjjjjjjjjjj
Stl Algorithms in C++ jjjjjjjjjjjjjjjjjj
 
ANTI PARKISON DRUGS.pptx
ANTI         PARKISON          DRUGS.pptxANTI         PARKISON          DRUGS.pptx
ANTI PARKISON DRUGS.pptx
 
Championnat de France de Tennis de table/
Championnat de France de Tennis de table/Championnat de France de Tennis de table/
Championnat de France de Tennis de table/
 
24 ĐỀ THAM KHẢO KÌ THI TUYỂN SINH VÀO LỚP 10 MÔN TIẾNG ANH SỞ GIÁO DỤC HẢI DƯ...
24 ĐỀ THAM KHẢO KÌ THI TUYỂN SINH VÀO LỚP 10 MÔN TIẾNG ANH SỞ GIÁO DỤC HẢI DƯ...24 ĐỀ THAM KHẢO KÌ THI TUYỂN SINH VÀO LỚP 10 MÔN TIẾNG ANH SỞ GIÁO DỤC HẢI DƯ...
24 ĐỀ THAM KHẢO KÌ THI TUYỂN SINH VÀO LỚP 10 MÔN TIẾNG ANH SỞ GIÁO DỤC HẢI DƯ...
 
Capitol Tech Univ Doctoral Presentation -May 2024
Capitol Tech Univ Doctoral Presentation -May 2024Capitol Tech Univ Doctoral Presentation -May 2024
Capitol Tech Univ Doctoral Presentation -May 2024
 
size separation d pharm 1st year pharmaceutics
size separation d pharm 1st year pharmaceuticssize separation d pharm 1st year pharmaceutics
size separation d pharm 1st year pharmaceutics
 
BỘ LUYỆN NGHE TIẾNG ANH 8 GLOBAL SUCCESS CẢ NĂM (GỒM 12 UNITS, MỖI UNIT GỒM 3...
BỘ LUYỆN NGHE TIẾNG ANH 8 GLOBAL SUCCESS CẢ NĂM (GỒM 12 UNITS, MỖI UNIT GỒM 3...BỘ LUYỆN NGHE TIẾNG ANH 8 GLOBAL SUCCESS CẢ NĂM (GỒM 12 UNITS, MỖI UNIT GỒM 3...
BỘ LUYỆN NGHE TIẾNG ANH 8 GLOBAL SUCCESS CẢ NĂM (GỒM 12 UNITS, MỖI UNIT GỒM 3...
 
An Overview of the Odoo 17 Knowledge App
An Overview of the Odoo 17 Knowledge AppAn Overview of the Odoo 17 Knowledge App
An Overview of the Odoo 17 Knowledge App
 
Removal Strategy _ FEFO _ Working with Perishable Products in Odoo 17
Removal Strategy _ FEFO _ Working with Perishable Products in Odoo 17Removal Strategy _ FEFO _ Working with Perishable Products in Odoo 17
Removal Strategy _ FEFO _ Working with Perishable Products in Odoo 17
 
Navigating the Misinformation Minefield: The Role of Higher Education in the ...
Navigating the Misinformation Minefield: The Role of Higher Education in the ...Navigating the Misinformation Minefield: The Role of Higher Education in the ...
Navigating the Misinformation Minefield: The Role of Higher Education in the ...
 

Spearman's correlation,Formula,Advantages,

  • 1. Spearman's correlation Ms. Nigar K.Mujawar Assistant Professor, Shri.Balasaheb Mane Shikshan Prasarak Mandal Ambap Womens College of Pharmacy, Peth-Vadgaon, Kolhapur, M.S., INDIA. 1
  • 2. Spearman's correlation Spearman's correlation coefficient (or Spearman's rho) is a non- parametric measure of rank correlation between two variables. It assesses how well the relationship between two variables can be described using a monotonic function, regardless of the scale of measurement. Here's a detailed explanation of Spearman's correlation coefficient: Calculation: 1.Ranking: 1.For each variable X and Y, rank the values separately. If there are ties (i.e., identical values), assign them the average of the ranks they would have received if they were distinct values. 2.Computing Differences: 1.For each pair of ranked values(xi​,yi​), calculate the difference in ranks di​=rank of xi​−rank of yi.
  • 3. 1.Applying the Formula: 1.Use the formula: = 1− 6∑di2 / n(n2−1) 2.6∑(2−1)ρ=1−​​ where n is the number of observations. Interpretation: The Spearman correlation coefficient ρ ranges between -1 and 1. ρ=1 indicates a perfect positive monotonic relationship: as X increases, Y tends to increase. ρ=−1 indicates a perfect negative monotonic relationship: as X increases, Y tends to decrease. ρ=0 indicates no monotonic association between X and Y, but it doesn't imply independence.
  • 4. Advantages and Use Cases: 1. Non-parametric: Suitable for ordinal data or data that do not meet the assumptions of normality required by Pearson correlation. 2. Robust: Less affected by outliers compared to Pearson correlation. 3. Interpretability: Describes the strength and direction of monotonic relationships. Example: Suppose we have the following paired data representing ranks: X:10,5,8,3,6 Y:7,4,9,2,1​ •Rank X values: Rank(10)=5,Rank(5)=3,Rank(8)=4,Rank(3)=2,Rank(6)=1 •Rank Y values: Rank(7)=4,Rank(4)=3,Rank(9)=5,Rank(2)=2,Rank(1)=1
  • 5. •Compute differences: • d1​=5−4=1 • d2​=3−3=0 • d3​=4−5=−1 • d4​=2−2=0 • d5​=1−1=0
  • 6.
  • 7. 7