Post History
#2: Post edited
by
tommi
·
2024-04-23T11:35:49Z (7 months ago)
- I am checking the temperature I have at home with accuracy of one tenth of a grade (Celsius). The easily publicly available information is temperature in grades, with no decimals.
- I am doing very basic hypothesis testing: My null hypothesis is that temperatures I measure do not have a systematic bias upwards or downwards from the public data, while my alternative hypothesis is that the temperatures I measure are systematically higher or systematically lower. I am doing a simple T-test and checking if the average of the differences is far from zero.
Does it make a difference whether I round my own measurements to integers, or, (essentially equivalently,) round the differences to integers? In particular, is there a bias in a particular direction, towards throwing away the null hypothesis or the opposite, if my data has more accuracy then what I am comparing it to?
- I am checking the temperature I have at home with accuracy of one tenth of a grade (Celsius). The easily publicly available information is temperature in grades, with no decimals.
- I am doing very basic hypothesis testing: My null hypothesis is that temperatures I measure do not have a systematic bias upwards or downwards from the public data, while my alternative hypothesis is that the temperatures I measure are systematically higher or systematically lower. I am doing a simple T-test and checking if the average of the differences is far from zero.
- Does it make a difference whether I round my own measurements to integers, or, (essentially equivalently,) round the differences to integers? In particular, is there a bias in a particular direction, towards throwing away the null hypothesis or the opposite, if my data has more accuracy then what I am comparing it to?
- **Notes**
- This project breaks assumptions of hypothesis testing; at least independence of measurements and possibly the normal distribution of the differences.
- The point of the question is not these, but rather the possible effect of rounding or different precision in the ground truth data and the measurements on the hypothesis test.
#1: Initial revision
by
tommi
·
2024-04-23T09:34:19Z (7 months ago)
The effect of measurement accuracy and rounding on hypothesis testing
I am checking the temperature I have at home with accuracy of one tenth of a grade (Celsius). The easily publicly available information is temperature in grades, with no decimals. I am doing very basic hypothesis testing: My null hypothesis is that temperatures I measure do not have a systematic bias upwards or downwards from the public data, while my alternative hypothesis is that the temperatures I measure are systematically higher or systematically lower. I am doing a simple T-test and checking if the average of the differences is far from zero. Does it make a difference whether I round my own measurements to integers, or, (essentially equivalently,) round the differences to integers? In particular, is there a bias in a particular direction, towards throwing away the null hypothesis or the opposite, if my data has more accuracy then what I am comparing it to?