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I have six measurements taken at different time-points in an experiment, and I want to show if these measurements have a dependence on time (i.e. are they random or not). I originally presented the data as a line graph (measurement vs time) as I felt that a sample size of 6 was too small for any meaningful statistical analysis. There doesn't appear to be any trend when observing the graph. I included a linear trendline (which had a tiny gradient and a poor fit!) and stated that there did not appear to be any dependence on time.

However, two reviewers of my data are unhappy with the lack of statistical testing, and want me to perform a test of randomness. I have used runs tests before on larger sample sizes, but as far as I can tell, six samples is too small to perform a Runs test on (table of critical values doesn't go down that low). I am not sure how to proceed and satisfy the reviewers.

In case it helps, my (time, measurement) data points are as follows (ignore the slight polynomial appearance): (37.79, 72.71) (43.43, 69.74) (49.90, 69.95) (57.33, 70.51) (65.87, 70.38) (75.69, 72.99) Many thanks in advance! CC

Extra info as requested: I have six repeated measurements of the same image quality metric, taken at 6 different time points which are represented by a level of radioactivity. For example, data point (37.79, 72.71) means that the image quality metric was 72.71% when the radioactivity was 37.79MBq. The image quality wavers around the 70% as the radioactivity decreased, and does not appear to be directly affected by the level of radioactivity (random, no dependence). It is a very simple, stand-alone group of measurements. So simple, in fact, that I think the use of statistics is questionable. Obviously it would be better if I had been able to take more measurements, but it wasn't possible (I wont bore you with the reasons!)

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  • $\begingroup$ We need more information. Six metrics, got that, but measured at how many points in time? What's the sample size? Is there any structure to the information, eg, test vs control groups or heterarchical nesting? $\endgroup$ – DJohnson Feb 2 '16 at 17:14
  • $\begingroup$ Thank you for your comment. I have six repeated measurements of the same image quality metric, taken at 6 different time points which are represented by a level of radioactivity. For example, data point (37.79, 72.71) means that the image quality metric was 72.71% when the radioactivity was 37.79MBq. The image quality wavers around the 70% as the radioactivity decreased, and does not appear to be directly affected by the level of radioactivity (random, no dependence). It is a very simple, stand-alone group of measurements. So simple, in fact, that I think the use of statistics is questionable. $\endgroup$ – user102759 Feb 3 '16 at 10:04
  • $\begingroup$ A sample size of six is standard in human clinical trials. From my perspective, there would seem to be two broad avenues to address it: first, frequentist based on leveraging either a Fisher's Exact Test or bootstrapping or, second, Bayesian. But I will defer to others on CV who are the real experts in designs of this type. In particular, you might want to reach out to @frankharrell with this question -- stats.stackexchange.com/users/4253/frank-harrell He will have the best advice. $\endgroup$ – DJohnson Feb 3 '16 at 14:25

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