Interpret the key results for Individual Distribution Identification

Complete the following steps to interpret Individual Distribution Identification. Key output includes probability plots and p-values.

Step 1: View the fit of the distribution

Use the probability plot to assess how closely your data follow each distribution.

If the distribution is a good fit for the data, the points should fall closely along the fitted distribution line. Departures from the straight line indicate that the fit is unacceptable.

Good fit
Poor fit

In addition to the probability plots, use the goodness-of-fit measures, such as the p-values, and your practical process knowledge, to evaluate the distribution fit.

Step 2: Assess the fit of the distribution

Use the p-value to assess the fit of the distribution.

Compare the p-value for each distribution or transformation to the significance level. Usually, a significance level (denoted as α or alpha) of 0.05 works well. A significance level of 0.05 indicates a 5% risk of concluding that the data do not follow the distribution when they actually do follow the distribution.
P ≤ α: The data do not follow the distribution (Reject H0)
If the p-value is less than or equal to the significance level, you reject the null hypothesis and conclude that your data do not follow the distribution.
P > α: Cannot conclude the data do not follow the distribution (Fail to reject H0)
If the p-value is greater than the significance level, you fail to reject the null hypothesis. There is not enough evidence to conclude that the data do not follow the distribution. You can assume that the data follow the distribution.
When selecting a distribution to model your data, also rely on your process knowledge. If several distributions provide a good fit, use the following strategies to choose a distribution:
  • Choose the distribution that is most commonly used in your industry or application.
  • Choose the distribution that provides the most conservative results. For example, if you are performing capability analysis, you can perform the analysis using different distributions and then choose the distribution that produces the most conservative capability indices. For more information, go to Distribution percentiles for Individual Distribution Identification and click "Percents and percentiles".
  • Choose the simplest distribution that fits your data well. For example, if a 2-parameter and a 3-parameter distribution both provide a good fit, you might choose the simpler 2-parameter distribution.
Important

Use caution when you interpret results from a very small or a very large sample. If you have a very small sample, a goodness-of-fit test may not have enough power to detect significant deviations from the distribution. If you have a very large sample, the test may be so powerful that it detects even small deviations from the distribution that have no practical significance. Use the probability plots in addition to the p-values to evaluate the distribution fit.

Distribution Identification for Calcium

2-Parameter Exponential

* WARNING * Variance/Covariance matrix of estimated parameters does not exist. The threshold parameter is assumed fixed when calculating confidence intervals. 3-Parameter Gamma
* WARNING * Variance/Covariance matrix of estimated parameters does not exist. The threshold parameter is assumed fixed when calculating confidence intervals. Distribution ID Plot for Calcium

Distribution ID Plot for Calcium

Distribution ID Plot for Calcium

Distribution ID Plot for Calcium

Goodness of Fit Test Distribution AD P LRT P Normal 0.754 0.046 Box-Cox Transformation 0.414 0.324 Lognormal 0.650 0.085 3-Parameter Lognormal 0.341 * 0.017 Exponential 20.614 <0.003 2-Parameter Exponential 1.684 0.014 0.000 Weibull 1.442 <0.010 3-Parameter Weibull 0.230 >0.500 0.000 Smallest Extreme Value 1.656 <0.010 Largest Extreme Value 0.394 >0.250 Gamma 0.702 0.071 3-Parameter Gamma 0.268 * 0.006 Logistic 0.726 0.034 Loglogistic 0.659 0.050 3-Parameter Loglogistic 0.432 * 0.027 Johnson Transformation 0.124 0.986
Key Results: P

In these results, several distributions have a p-value that is greater than 0.05. The 3-parameter Weibull distribution (P > 0.500) and the largest extreme value distribution (P > 0.250) have the largest p-values, and appear to fit the sample data better than the other distributions. Also, the Box-Cox transformation (P = 0.353) and the Johnson transformation (P = 0.986) are effective in transforming the data to follow a normal distribution.

Note

For several distributions, Minitab also displays results for the distribution with an additional parameter. For example, for the lognormal distribution, Minitab displays results for both the 2-parameter and 3-parameter versions of the distribution. For distributions that have additional parameters, use the likelihood-ratio test p-value (LRT P) to determine whether adding another parameter significantly improves the fit of the distribution. An LRT p-value that is less than 0.05 suggests that the improvement in fit is significant. For more information, go to Goodness of fit for individual distribution identification and click "LRT P".

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