Correlation - Biostatistics
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This document discusses correlation and different aspects of studying correlation. It defines correlation as the association or relationship between two variables that do not cause each other. It describes different types of correlation including positive, negative, linear, non-linear, simple, multiple and partial correlation. It also discusses various methods of studying correlation including graphic methods like scattered diagrams and correlation graphs, and algebraic methods like Karl Pearson's correlation coefficient and Spearman's rank correlation coefficient. The document explains concepts like coefficient of determination and hypothesis testing in correlation. It emphasizes that correlation indicates association but does not necessarily imply causation between variables.
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Correlation - Biostatistics
- 1. CORRELATION Fahmida Rashid Swati Assistant Professor Department of Obstetrics & Gynecology Chittagong Medical College Email:dr.fahmidaswati@gmail.com
- 8. History 1888-Francis Galton concept of correlation. kerl Pearson -1896 Reformulated Correlation coefficient ’ r’ British Physiologist E. E. Spearman in 1904, Rank Correlation
- 9. Contents •Correlation •Types of Correlation •Methods of Studying Correlation •Coefficient of Correlation •Coefficient of determination Correlation
- 10. • Association or relationship between two variables that don’t cause each other. Correlation The concept of Correlation X Co vary --- Go Together Y
- 11. Variables
- 12. Purpose of Correlation Determines values of one variable are related to another or not Y X
- 13. Independent Variables Dependent Variables Grade depends on Number of Study Hour Are these two variables Related ?
- 14. Types Correlation Positive Negative Zero Linear Non Linear Simple Multiple Partial Degree of correlation No of Variables Linearity
- 15. Positive Correlation Variables go in the SAME direction Direct Relationship between two variables Increment of one variables also ↑ another variables and vice versa. Dependent Variable Independent Variable
- 16. SUNLIGHT Growth of Plants Y value increases as X value increase Independent Variable Dependent Variable Dependent Variable-Y Independent Variable-X
- 17. Labor pain in hour- X axis Dilatation of Cervix Y-Axis Independent Variable Dependent Variable x x x
- 18. Negative Correlation Two Variable , X and Y go In OPPOSITE direction The ↑ in one variable X results in the corresponding ↓ in the other variables. Dependent Variable Independent Variable
- 21. Zero • No correlation Change of X not associated with change of Y X Y
- 23. Linear Correlation Relationship between 2 variables are in straight line , either upward or downward slopping upward downward
- 25. Non Linear/Curvilinear Ratio of changes between two variables -not constant • Relationship not in straight line, • Either upward or downward slopping curve.
- 26. upward slopping curve downward slopping curve Dependent Variable Dependent Variable Independent Variable Independent Variable
- 27. Partial • Relationship between 2 variables keeping the other variable constant or fixed Influence of 3rd variable Eliminated here.
- 28. Taking out the effect of economic state Mother Child
- 29. Multiple • The relationship among 3 or more variables at the same time. Fetal Growth Nutrition Preeclampsia Smoking
- 30. Method of Studying Correlation Graphic Scattered Diagram Correlation Graph Algebraic Karl Pearson Coefficient Spearman’s Rank Coefficient Collect Data → Compile data
- 31. Graphic
- 32. Scattered Diagram Method Each points of Graph represents a combination value - Xi & Yi One of the simplest ways of diagrammatic representation of the quantitative bi-variate. 55 Inch 10 Yr Dependent Variable Independent Variable
- 33. Positive relationship between hours of study & Grades • Points are represented by dots . • By convention, Independent variable(IV) plotted on horizontal X-axis. Dependent Variable(DV) plotted on Vertical Y-axis X Y The closer the point lie to a straight line , the stronger the linear relationship
- 34. Two information • Nature & Strength Pattern of Relationship
- 36. Advantage: •First Steps in investigating relationship between two variables. •Simple & Non mathematical •Not influenced by size of extreme values Disadvantage: Can not adopt an exact degree of correlation
- 38. Algebraic -Correlation Analysis Correlation Coefficient Karl Pearson Coefficient Spearman’s Rank Coefficient Coefficient of Determination
- 39. Means for examining the relationship between two variables systematically It measures co-variation, not causation Correlation analysis Before conducting Correlation Analysis, always should create a two-way scatter Plot Existence of linear relationship between X & Y determined Via scatter Plot
- 41. A measure of the strength & direction of a linear relationship between two variables. Correlation Coefficient Strength of Relationship Direction of relationship Size indicates strength (values closer to -1 or +1 indicate greater strength) -ive = inverse /indirect relation +ive same direction/direct relation
- 42. Correlation Coefficient Computed from sample data ‘r’ p (rho) ‘r’ has no unit
- 43. In Perfect +ive linear relationship r is +1 Range of Correlation Coefficient In Strong +ive linear relationship r close to +1 -1 to +1 In Perfect -ive linear relationship r is -1 In Strong -ive linear relationship r close to -1 In Nonlinear relationship r close to ‘0’ In Weak/No relationship r close to ‘0’
- 45. Interpretation of Value of ‘r’ Larger absolute value of r –stronger relationship
- 47. Importance of Correlation analysis Used to derive degree/strength & direction of relationship between 2 variables. Useful in presenting average relationship between 2 variables. Use to ↓ range of uncertainty in matter of prediction.
- 49. Step 1: Kind of Scale
- 51. Continuous Scale
- 53. Combination of 3 Scale
- 54. Formula N - Number of Paired Data X - Independent Variable Y - Dependent Variable
- 55. Correlation between Age and Blood Pressure X-Age Y-Blood Pressure XY- Age X BP X2-Age 2 Y2- BP2 With Formula: r = .897 X Y XY X2 Y2 Suggests a strong +ive relationship between age & blood pressure
- 56. Association Between Height & Weight Association between Likert Scale on work satisfaction and work output Two continuous Variables Pearson Linear Relationship One continuous and One categorical Variable(Ordinal)/Ranked order scale Spearman Step 2 &3: Decide And Calculate Correlation Coefficient:
- 57. Interval /Ratio Measure Most Popular Normally distributed linear relationship Quantitative variable
- 58. Gives precise numerical value of degree of linear relationship between two variable. Measures strength and direction of linear relationship between two variables. A ‘r’ = 0.9 (+/-) - very strong Association ‘r’- value has nothing to do with 90% CI
- 59. • Not need to know exact formulas. • Not need to be able to do by hand.
- 60. Non parametric statistical Measure Non Normal distribution & ordinal scale Used to study strength of association between two ranked variable Observed value qualitative/ quantitative converted to Rank
- 61. • r= Rank correlation Coefficient • D= Difference between ranks(R1-R2) • N= Number of paired observations • In case of r -1 ≤ R ≤ +1 • The sum of the total Rank difference is always equal to Zero ,i.e.ED=0 • Not need to know exact formulas. • Not need to be able to do by hand.
- 62. •If Spearman Correlation Coefficient is - 0.108 & p is 0.117 •Compared values against Spearman Table •Value 0.117 < 0.364 (P = 0.05.) •Here P is > 0.05 Inference: There is no significant association between hours of TV watched/week & IQ
- 63. • ‘r’ and rs similar Meaning • Difference is :
- 65. Coefficient of Determination(CoD) Used for interpretation of correlation & comparing 2 or More correlation coefficient Square of Correlation Coefficient i.e. r2 Explain % of variation in dependent variable Y that can be explained in terms of independent variable X. If r=0.8 , r2= 0.64, It implies that 64% of total variations in Y occurs due to X. The remaining 34% variation occurs due to external factors.
- 66. So, CoD = r2= Total Variance Explained variance
- 67. If Pearson r = -0.5 r2= 0.25 Expression: 1/4th or 25% of variability in GPA scores accounted by depression (remaining 75% of variability is other factors, habits, ability, motivation, courses studied , etc) Correlation of Depression with GPA grade:
- 68. If ‘r’ = 0.5 r2 = 0.25 If ‘r’ = 0.7 r2 = 0.49 r2 tells us that - r = 0.7 accounts for about 2 fold variability relative to r= 0.5 While ‘r’ = 0.5 Vs 0.7 might not look so different in terms of strength. 0.49 0.25
- 69. Correlation Hypothesis Testing: Step1:Identify Population, distribution and assumption Step 2:State null Hypothesis and Research Hypothesis Step 3: Determine Characteristics of comparison distribution Step 4: Determine The critical Value Step5: Calculate The test Statistic(t) Step 6: Make a decision
- 71. Causation: Cause & Effect Relation Correlation : •Interdependency among Variables for correlating 2 phenomenon. •Should have cause-effect relationship & Otherwise can not be correlated . Two variables vary in such away that movement in one accompanied by movement in other. Causation always implies correlation but correlation does not necessarily implies causation.
- 72. With large sample , even a small correlation can be statistically significant Correlation measure association not causation. Correlation assumes linear relationship. Take Home Massage : Statistically significant correlation may not be practically significant. A low correlation is still a low correlation
- 73. Values between -1 & +1 measure strength & direction of the relationship In simple linear Correlation Coefficient – variables normally distributed. In Spearman’s Rank Correlation Coefficient – variables doesn’t follow normal distribution.
- 74. সম্পর্ক গুল ো কর্মন অদ্ভু ত! কর্ছু কর্ছু সম্পলর্ক র কর্োন নোম হয় নো। কতোমোর র্োন্নোয় আমোর ক োখ কিলে উলে কতোমোর র্থোয় সব ি ু ল ছুটি নতু ন পলথ। বৃকিলত হোত ধলর কিেলত ইলে হয় ইলে হয় কতোমোর পোাঁ লে কথলর্ র্কর কবশ্ব কর্ েয় । মুলেো মুলেো খুকের আড়োল কতোমোয় হোকরলয় কে োর খুব িয় হয়! Dependent Variable - আমি Independent Variable – ত ু মি Qualitative Variable – ততোিোর -কথো—কোন্নো আিোর -বৃমি তেজো – মবশ্ব জয়- খুমি- েয় CC: Spearman Correlation Coefficient Hypothesis– Null- ততোিোর কথোর সোথথ আিোর খুিীর তকোন সম্পক ক নোই। Alternate- ততোিোর কথোর সোথথ আিোর খুিীর সম্পক ক আথে ।
- 76. Choosing the ‘right Method’ for the data is the key statistical expertise one need to have .
- 77. Do we need to know the formulas? • Not need to know exact formulas. • Not need to be able to do correlation & regression by hand. •Need to understand concept behind them & general statistical concepts to use the formula.
- 78. Relationship between immediate postpartum umbilical cord pH, fetal distress and neonatal outcome Correlation of biological parameters with placental parameters and pregnancy outcomes in pre-eclamptic women