Six Sigma SPC - Statistical Process Control

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Scatter plot - X Y chart

Graph used to show relationship or correlation between two factors or variables. i.e. X-Y or XY or X Y chart. (can be used in conjunction with correlation coefficient below)

Each factor or variable should be drawn on a graph, (a piece of grid paper would work), with X plotted on the vertical axis and Y plotted on the horizontal axis, or visa-versa. Each factor or variable should be graphed in such a way that they intersect both axis making one point for each of the X-Y paired numbers.

Scatter Plot X-Y Example Chart

Scatter Plot  X-Y Example Chart

Correlation Coefficient

The output is the degree of similarity between two data sets. The calculation is below. (be sure to see precautions to observe below)

Correlation Coefficient Formula

As an example, data indicated that when teachers are unemployed, the alcohol consumption rises. In that case, there was no correlation.

Meaning of (r) in the Correlation Coefficient

Relationship Between X and Y

r = + 1.0 Strong - Positive As X goes up, Y always also goes up
r = + 0.5 Weak - Positive As X goes up, Y tends to usually also go up
r = 0 - No Correlation - X and Y are not correlated
r = - 0.5 Weak - Negative As X goes up, Y tends to usually go down
r = - 1.0 Strong - Negative As X goes up, Y always goes down

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Precautions to observe

Be careful when using the correlation coefficient. One should think about the following rules.

  • The result of the calculation, (r), is a measure of the linear association between X and Y as it exists in any given set of number pairs. Even when there is high value of (r), it does not necessarily imply that X and Y are related in any way as a cause and effect. It is not unheard of to obtain a high degree of statistical association with no causal connection whatsoever. It is also not impossible that two variables which are not related may both be related to a third variable. This could cause the first two variables to show a statistical association when there are not is necessarily any real cause and effect.

    You should make sure that there are sound engineering reasons for the relations before trying to draw any deductions from a calculated (r).
  • Whereas unassociated pairs of data could have zero correlation the average, specific pairs may have correlation as a consequence of sampling variation, and thus will have values of (r) above or below zero. Due to the fact that (r) is sometimes above or below zero does not automatically point to two sets of numbers being related.

    Do not draw any conclusions based on the correlation coefficient until you have tested it for significance as follows...

    • Multiply r by the square root of n, where n is the number of pairs used to determine (r). We will call this (t).
    • If (t) is larger than 3, deem the correlation is significant. If (t) is smaller than 3, the correlation may not be significant. The smaller the value of (t), the lesser the probability that the correlation will be significant. If the correlation is not absolutely significant, as prescribed above, this could be due to...
      • (a) A genuine lack of correlation
      • (b) Inadequate data. If you should have reason to think that a correlation should exist you may wish to acquire more data pairs, calculate a new value of (r), and retest the new values for significance.

Not all can see the relation between the scatter plot and the correlation coefficient, but it can aid in evaluations of a process.


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Last Updated: Monday, 06-Mar-06 04:17:19 PST