As the sample size increases, the statistical power of the test also increases. Distribution tests are like other hypothesis tests. Q-Q plots are especially useful in cases where the distribution tests are too powerful. These plots are similar to Empirical CDF plots except that they transform the axes so the fitted distribution follows a straight line. Probability plots are also known as quantile-quantile plots, or Q-Q plots. If all the data points line up within the area of a fat pencil laid over the center straight line, you can conclude that your data follow the distribution. Informally, this process is called the “fat pencil” test. If your data follow the straight line on the graph, the distribution fits your data. Probability plots might be the best way to determine whether your data follow a particular distribution. Related post: Understanding the Weibull Distribution Using Probability Plots to Identify the Distribution of Your Data Let’s consider the three-parameter Weibull distribution and lognormal distribution to be our top two candidates. The lognormal distribution has the next highest p-value of 0.345. For the three-parameter Weibull, the LRT P is significant (0.000), which means that the third parameter significantly improves the fit. The highest p-value is for the three-parameter Weibull distribution (>0.500). However, we’ll disregard the transformations because we want to identify our probability distribution rather than transform it. If we need to transform our data to follow the normal distribution, the high p-values indicate that we can use these transformations successfully. The Box-Cox transformation and the Johnson transformation both have high p-values. The p-value is less than 0.005, which indicates that we can reject the null hypothesis that these data follow the normal distribution. We’re looking for higher p-values in the Goodness-of-Fit Test table below.Īs we expected, the Normal distribution does not fit the data. I’m using Minitab, which can test 14 probability distributions and two transformations all at once. Goodness of Fit Test Results for the Distribution Tests NORMAL PROBABILITY PLOT MINITAB SOFTWARETypically, you don’t interpret this statistic directly, but the software uses it to calculate the p-value for the test. It’s like the t-value for t-tests or the F-value for F-tests. The Anderson-Darling statistic is the test statistic. The test I’ll use for our data is the Anderson-Darling test. However, we want to identify the probability distribution that our data follow rather than the distributions they don’t follow! Consequently, distribution tests are a rare case where you look for high p-values to identify candidate distributions.īefore we test our data to identify the distribution, here are some measures you need to know:Īnderson-Darling statistic (AD): There are different distribution tests. H 1: The sample data do not follow the hypothesized distribution.įor distribution tests, small p-values indicate that you can reject the null hypothesis and conclude that your data were not drawn from a population with the specified distribution.H 0: The sample data follow the hypothesized distribution.The sizes of the drill holes might be right-skewed away from the minimum possible size. On the other hand, drill holes can’t be smaller than the drill bit. For example, purity can’t be greater than 100%, which might cause the data to cluster near the upper limit and skew left towards lower values. If a process has a natural limit, data tend to skew away from the limit. For instance, income data are typically right skewed. However, in some areas, you should actually expect nonnormal distributions. You might think of nonnormal data as abnormal. NORMAL PROBABILITY PLOT MINITAB HOW TOIn this post, I show you how to identify the probability distribution of your data. You can picture the symmetric normal distribution, but what about the Weibull or Gamma distributions? This uncertainty might leave you feeling unsettled. Unfortunately, not all data are normally distributed or as intuitive to understand. The normal distribution is that nice, familiar bell-shaped curve. You’re probably familiar with data that follow the normal distribution.
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