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I have two measurement devices accelerometer A and B. The measurement is the step time of a person walking in a corridor. A is the gold standard. I want to check the validity and reliability of B. how well B can estimate the step time of the person. My question is How many times should I repeat the test (ask the person to walk with accelerometer A and B) and do the measurement so that my test has a power of 80%? and whether I need a number of subjects to do the same test?

chl
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Naima Abiad
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    Normally, comparing two measurement systems isn't done with a hypothesis test nor does the concept of power apply to it: you want to assess how the two measurements relate to each other over an expected range of results. You might find [our threads on measurement calibration](https://stats.stackexchange.com/search?q=calibration+measurement) to be useful. – whuber Jan 15 '20 at 20:46
  • @whuber You can check the measurement of one device against another (this is what calibration does). Your null in this case would be that the two measurements are equal and you have to calculate the uncertainty of each measurement. This comes from domain knowledge such as repeatability of mounting the sensor, temp/humidity, etc. You want to keep as many things consistent as possible (i.e. same person wears both devices). – M Waz Jan 15 '20 at 21:51
  • @MWaz I still don't see how such a null hypothesis test would be useful. The only possible conclusions would be (a) we cannot detect a difference between B and A and (b) we do detect a difference between B and A. Wouldn't it be far more useful to achieve a *quantitative characterization* of the relation between B and A? The latter is my understanding of calibration. – whuber Jan 15 '20 at 21:56
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    @whuber Depends on what you are using the data for later down stream. In OP's case, it seems that he only wants to verify that B is giving similar measurements to A. In this case he only needs to determine if there is a difference. However, from a hypothesis test, you can always construct a confidence interval. If however, you are using the device to measure an unknown then yes, you want to characterize how your sensor responds to some "known." – M Waz Jan 15 '20 at 22:26
  • I want to study whether the acclerometer in the cellphone B is good enough to detect step time. for that I think I have to compare it aganist a dedicated accelerometer A. But to compare it, I don't know what type of test I should do. The cellphone is already calibrated. It is just a test of quality. whether the quality of the cellphone is enough or not. how many times should I do the test so that I can properly judge the device. If say it is a hypothesis test with a confidence interval how will I know? @whuber – Naima Abiad Jan 17 '20 at 12:31
  • That can be solved once you indicate--quantitatively--what "quality" is and how much is "enough." Without such information we would all just be guessing. – whuber Jan 17 '20 at 13:41
  • As @whuber pointed out, statistical test of null hypothesis are meaningless in such scenario, and you may want to rely on [method comparison](https://stats.stackexchange.com/q/527/930) approach, for which sample size may usually be derived from the limits of agreement. – chl Oct 25 '20 at 08:59

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