What is a probability plot?

A probability plot is graph that you can use to evaluate the fit of a distribution to your data, estimate percentiles, and compare different sample distributions. A probability plot does the following:
  • Creates an estimated cumulative distribution function (cdf) from your sample by plotting the value of each observation against its estimated cumulative probability. The scales are transformed so that the fitted distribution forms a straight line. A good distribution fit is one where the observations are near the fitted line.
  • Displays the approximate 95% confidence intervals for the percentiles. These confidence intervals are point-wise, meaning that they are calculated separately for each point on the fitted distribution without controlling for family-wise error. Thus, if you use them to estimate more than one parameter per sample, your chance of making a type I error is greater than your chosen alpha level.
  • Displays a table with distribution parameter estimates along with the Anderson-Darling statistic and p-value to help you evaluate the distribution fit to your data.
Tip

If you hold the pointer on a plotted point, Minitab displays the row number and x- and y-values for the point. If you hold the pointer on the fitted line or confidence intervals, Minitab displays values for multiple fitted percentiles and associated confidence bounds.

A probability plot serves a similar function as an empirical CDF plot. An advantage of a probability plot is that you can judge the distribution fit by viewing how the points fall about the line.

Example of a probability plot

A manager at a fast food restaurant would like to know the percentage of customers who have to wait the target time of 4 minutes or less for their food. The manager records the wait times for 15 customers and plots them.

This probability plot reveals the following:
  • The data points approximately follow the straight line, the p-value is greater than 0.05, and the Anderson-Darling statistic is low. Therefore, the normal distribution appears to fit the sample data fairly well, and the manager can use the fitted line to estimate percentiles. If the normal distribution is not a good fit for the data, Minitab provides other choices.
  • The mean wait time is 3.573; the standard deviation is 0.5700.
  • It seems that about 80% of the data fall below 4.0. The manager can hold the pointer over one of the lines to get exact numbers, or add a percentile line at 4 minutes.

The preceding plot shows observations from only one restaurant. The manager could also display and compare data for several restaurants on the same probability plot.

Note

The normal probability plot available through Graph > Probability Plot is not the same as the normal probability plot of the effects in a DOE analysis.

  • The DOE plot shows the statistical significance and magnitude of standardized effects. Points farther from the line denote a more significant effect.
  • The Graph plot assesses how closely the data follow a normal distribution.

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