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Carillon Technologies Limited |
Scatter Diagrams, Correlation and Measurement Analysis |
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An example of a scatter diagram:
| In this scatter diagram we can see that as the % moisture increases the tensile strength decreases (soggy corn flakes are weaker!). |  |
| Scatter diagrams are used to find the relationship between two factors. A measure of how well the factors relate is called correlation. |  |
Examples:Where correlation ranges from -1 to +1 This is an example of a correlation ratio that is equal to approximately 0.75. (this number is calculated from the data) A very good but not great predictive relationship |
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Correlation = 0 Weight and age are unrelated. Not usefull at all. |
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Correlation = 1.0 Weight and age are directly related Perfect! |
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Correlation = -1.0 Weight and age are inversely related. Also Perfect! |
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We calculate correlation by calculating the covariance of x and y and the variance of x and the variance of y. We then determine their square root (known as the standard deviation) of each of those terms and then the correlation by the formula below. A correlation ratio of 0.8 or higher or -0.8 or lower is considered as highly related.
Scatter plots can be used to help determine the critical processing factors, or analyzing measurement data. If we brainstorm the potential causes for a particular product characteristic, we can test those potential causes by making measurements (approximately 15 or so) of each of those characteristics (independent variables) and plotting each characteristics (x axis) versus the desired output or product characteristic (y axis). If the cause is related directly or indirectly a correlation will occur. The strength of the correlation ( how close does it approach +1 or -1) is an indicator of the importance of that independent variable and will help focus efforts to determine the appropriate control requirements.
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Procedure for Creating a Scatter Plot and Trendlines Using Excel |
