Hjalkarsson
Member
- Joined
- Jun 15, 2020
- Messages
- 36
you have a sampling of values.
you can't use that sample to predict what another such sampling WILL BE. that is, you can't be 100.000% sure.
but, you can use the average and standard deviation, to figure out what is the most likely distribution, at a certain degree of certainty.
that's called a "confidence interval". when added to both sides of the average, that is called the "confidence limits" (CL).
you calculate the confidence interval with the following:
Z * s / sqrt(n)
where
Z is a number from a table of what confidence you want to have
s = standard deviation
n = number of samples in the group
the table is:
80%, 1.282
90%, 1.645
95%, 1.960
99%, 2.576
99.5%, 2.807
the full table is much bigger than that, but this is just to give you an idea. far and away the 95% confidence level is suitable for most purposes. that's what most people use.
as you can see, a larger confidence interval results in a larger Z value. the spread will have to be bigger if you want to be more confident.
so for example, you have a group of 5 shots:
1.24"
1.86"
0.83"
2.37"
1.45"
the average is 1.55", the standard deviation is 0.59".
for 95% confidence, Z= 1.960
then from the equation above,
1.960 * 0.59 / sqrt(5) = 0.52"
therefore, given the sampling you have observed, 95% of the shots will be 1.55" plus or minus 0.52".
do you want to be sure? then use 99.9% confidence. Z= 3.291 and the CL is +/- 0.87
do you want to be sure sure? absolutely positively sure? then use 99.999% confidence. Z= 4.417 and the CL is +/- 1.16"
at that point, you can be 99.999% confident that you won't have a shot more than 2.71"
you can't use that sample to predict what another such sampling WILL BE. that is, you can't be 100.000% sure.
but, you can use the average and standard deviation, to figure out what is the most likely distribution, at a certain degree of certainty.
that's called a "confidence interval". when added to both sides of the average, that is called the "confidence limits" (CL).
you calculate the confidence interval with the following:
Z * s / sqrt(n)
where
Z is a number from a table of what confidence you want to have
s = standard deviation
n = number of samples in the group
the table is:
80%, 1.282
90%, 1.645
95%, 1.960
99%, 2.576
99.5%, 2.807
the full table is much bigger than that, but this is just to give you an idea. far and away the 95% confidence level is suitable for most purposes. that's what most people use.
as you can see, a larger confidence interval results in a larger Z value. the spread will have to be bigger if you want to be more confident.
so for example, you have a group of 5 shots:
1.24"
1.86"
0.83"
2.37"
1.45"
the average is 1.55", the standard deviation is 0.59".
for 95% confidence, Z= 1.960
then from the equation above,
1.960 * 0.59 / sqrt(5) = 0.52"
therefore, given the sampling you have observed, 95% of the shots will be 1.55" plus or minus 0.52".
do you want to be sure? then use 99.9% confidence. Z= 3.291 and the CL is +/- 0.87
do you want to be sure sure? absolutely positively sure? then use 99.999% confidence. Z= 4.417 and the CL is +/- 1.16"
at that point, you can be 99.999% confident that you won't have a shot more than 2.71"