We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
An Introduction to Uncertainty in Measurement Published online by Cambridge University Press: 06 July 2010
If it is reasonable to assume that a population consists of values that have a Gaussian distribution, then what will be the distribution of a property (a ‘statistic’) of a sample drawn from this Gaussian ‘parent’? The property might be the mean, variance or standard deviation of the sample. Each of these properties has a sampling distribution, which can be described as follows.
We imagine a very large or infinite population that has a Gaussian distribution with mean μand standard deviation ?. A sample consisting of n values is randomly drawn from this population. A property of the sample is calculated, in order to estimate the corresponding population parameter. We then draw another sample, also of size n, and calculate the same property for this second sample. The process is repeated many times. Next the distribution of that property is examined; the distribution becomes manifest as a result of taking a large number of repeated samples (all of size n). The distribution is the sampling distribution of the property in question. It is understood that, in any particular experimental situation, we do not actually need to draw a large number of samples; this process is a conceptual one that enables us to infer, from one actual sample, the variability (depicted by the shape of the sampling distribution) of our estimate of the population parameter. In section 9.1 we review the material already discussed in section 8.6.2.
To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Find out more about the Kindle Personal Document Service.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.
