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I'm making an app to measure anxiety in special needs children. Children will regularly score their anxiety using a subjective units of distress scale, which is a 0-10 scoring system. I will record the time of the measurement. Each data item is therefore a tuple: [time, 0-10 score].

Children will score their anxiety on two or three occasions per day. I wasn't planning to enforce strict rules in this regard, but if it strongly affects the quality of the statistics, I could do that.

For each child, I would like to answer these questions:

  • Is anxiety increasing or decreasing over time? I would like to answer that both generally (across all times of the day) but also for subsets of the data (e.g. the morning).
  • Is a particular score, or set of scores, statistically higher or lower than normal? E.g. is this morning's score of 3 just normal variation or should we be concerned that it's significantly different to normal?

What would be appropriate statistical approaches to these questions, given the type of data I'm recording? Also, how many data items would need to be collected before I can present meaningful statistics for a child?

Apologies, I'm not sure which tags would be appropriate for this question

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The easiest way to measure if the anxiety is changing over time is to apply a Moving average.

The second question is very hard to answer: first, you have to know, what the distribution of your data is like? Is it Gaussian normal? Is it uniform? Has it fat tails? Once you determined the nature of your distribution, you can figure out, how probable a given value is, and then say something like "ok, a 2 has a probability of 10%, so it is ok, a 1 has a probability of 1%, so I have to interfere". This last statement comes from the idea, that the most important events are events of high negative impact and low probability of occurence. Obviously, you have to define the threshold where you interefere by yourself.

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  • $\begingroup$ Moving average sounds sensible, thanks. I'm surprised by the second answer. My distant statistics memories had me thinking standard deviations (or something similar) might be involved... $\endgroup$
    – Duncan Jones
    Commented May 19, 2019 at 14:51
  • $\begingroup$ Standard deviations make sense if you consider distributions like the Gaussian or uniform. Let's say you have a skewed distribution like the log-normal, in this case standard deviations make really no sense. As a rule of thumb: if your distrbution is not symmetrical, then standard deviations hardly contain any real information. $\endgroup$
    – Rho.Pi
    Commented May 19, 2019 at 15:04

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