CORRELATION ANALYSIS
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1 CORRELATION ANALYSIS
2 Learning Objectives Understand how correlation can be used to demonstrate a relationship between two factors. Know how to perform a correlation analysis and calculate the coefficient of linear correlation (r). Understand how a correlation analysis can be used in an improvement project.
3 How does it help? Correlation Analysis is is necessary to: show a relationship between two variables. This also sets the stage for potential cause and effect.
4 IMPROVEMENT ROADMAP Uses of Correlation Analysis Common Uses Phase 1: Measurement Breakthrough Strategy Characterization Phase 2: Analysis Phase 3: Improvement Determine and quantify the relationship between factors (x) and output characteristics (Y).. Optimization Phase 4: Control
5 KEYS TO SUCCESS Always plot the data Remember: Correlation does not always imply cause & effect Use correlation as a follow up to the Fishbone Diagram Keep it simple and do not let the tool take on a life of its own
6 WHAT IS CORRELATION? Output or y variable (dependent) Input or x variable (independent) Correlation Y= f(x) As the input variable changes, there is is an influence or bias on the output variable.
7 WHAT IS CORRELATION? A measurable relationship between two variable data characteristics. Not necessarily Cause & Effect (Y=f(x)) Correlation requires paired data sets (ie (Y 1,x 1 ), (Y 2,x 2 ), etc) The input variable is called the independent variable (x or KPIV) since it is independent of any other constraints The output variable is called the dependent variable (Y or KPOV) since it is (theoretically) dependent on the value of x. The coefficient of linear correlation r is the measure of the strength of the relationship. The square of r is the percent of the response (Y) which is related to the input (x).
8 TYPES OF CORRELATION Y=f(x) Strong Y=f(x) Weak Y=f(x) None Positive x x x Negative
9 CALCULATING r Coefficient of Linear Correlation s r xy = CALC = ( x x)( y y) i i s xy s s x y n 1 Calculate s sample covariance ( ) xy Calculate s xx and s yy for each data set Use the calculated values to to compute r CALC CALC.. Add a + for positive correlation and - for a negative correlation. While this is the most precise method to calculate Pearson s r, there is an easier way to come up with a fairly close approximation...
10 APPROXIMATING r Coefficient of Linear Correlation Plot the data on on orthogonal axis Draw an Oval around the data Measure the length and width of of the Oval Y=f(x) x W L Calculate the coefficient of of linear correlation (r) (r) based on the formulas below r W ± 1 L r = W L = positive slope - = negative slope
11 HOW DO I KNOW WHEN I HAVE CORRELATION? Ordered Pairs r CRIT The answer should strike a familiar cord at this point We have confidence (95%) that we have correlation when r CALC > r CRIT. Since sample size is a key determinate of r CRIT we need to use a table to determine the correct r CRIT given the number of ordered pairs which comprise the complete data set. So, in the preceding example we had 60 ordered pairs of data and we computed a r CALC of Using the table at the left we determine that the r CRIT value for 60 is.26. Comparing r CALC > r CRIT we get.47 >.26. Therefore the calculated value exceeds the minimum critical value required for significance. Conclusion: We are 95% confident that the observed correlation is significant.
12 Learning Objectives Understand how correlation can be used to demonstrate a relationship between two factors. Know how to perform a correlation analysis and calculate the coefficient of linear correlation (r). Understand how a correlation analysis can be used in a blackbelt story.
SIMPLE LINEAR CORRELATION. r can range from -1 to 1, and is independent of units of measurement. Correlation can be done on two dependent variables.
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