Page 291 - Six Sigma Demystified

Part 3 s i x s i g m a to o l s 271

The K-S value reported is the p value for the null hypothesis that the data
follow the specified distribution. Values less than 0.05 generally indicate that
the fitted distribution is not a good match.

Interpretation

A useful graphic technique for determining whether there are too much data
in the tail regions of the distribution is to look for patterns near the far-left
and far-right portions of the line. Excessive data in the tails would group data
above the confidence interval on the left side (small probabilities) and below
the confidence interval on the right side (high probabilities). When normal-
distribution plots are analyzed and the data fit the distribution well, the mean
of the population can be estimated as the value of the line as it crosses the 50th
percentile. The distribution standard deviation may be estimated as the differ-
ence between the x values corresponding to the points at which the normal line
crosses the y = 50th (z = 0) and y = 84th (z = 1) percentiles.
In both the Kolmogorov-Smirnov and the Anderson-Darling tests, the null
hypothesis is that the data follow the specified distribution. Most statistical
software reports a p value, where the null hypothesis is rejected (implying that
the distribution is a poor fit) if the p value is less than a predetermined α value
(typically 0.05 or 0.10). Distributions also can be compared: The distribution
with the larger p value is the more likely distribution.
See also “Histogram” and “Distribution” topics.

Histogram

A histogram is a graphic tool used to visualize data. It is a bar chart where the
height of each bar represents the number of observations falling within a range
of rank-ordered data values.

When to Use

Measure Stage and Analyze Stage
• To graphically display the data as an aid in fitting a distribution for capa-
bility analysis or to visually detect the presence of multiple distributions