Goodness-of-fit test for a pattern of data?

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Jonathan Cheng 2017-4-19

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https://ww2.mathworks.cn/matlabcentral/answers/336201-goodness-of-fit-test-for-a-pattern-of-data

I’m trying to determine whether a pattern of 7 bars follows an “average” pattern of a large population of the same set of 7 bars, as shown in the attached Figure 1 as 10 sets of 7 bars. Let’s call the 10 sets 10 independent observations, as shown by 10 separate bar clusters. Each bar is a discrete integer number. As you can see, most of the clusters follow a pattern, with the order of bar 4, then bar 1, bar 7, … To visualize the values of the 7 bars in relation to each other, I normalized each bar against the most frequent maximum bar position amongst the observations, bar number 4. The normalized values (ratios) are plotted in Figure 2. Now, I would like to find a statistical test to determine a statistical score (perhaps a goodness-of-fit score?) for each observation against the population of all 10 observations. For example, observation cluster 6 would be identified as an outlier. The other output I would like is simply which one of the bars 1 thru 7 in each observation is “abnormal” out of the population of bars 1 thru 7. For example, bar 1 in observation cluster 8 would be an outlier. I’m thinking that some kind of regression test would be relevant, but I’m not sure which one. Any help is appreciated.