Published online by Cambridge University Press: 03 February 2022
Many scientific questions lead to hypotheses about random vectors. For instance, the question of whether global warming has occurred over a geographic region is a question about whether temperature has changed at each spatial location within the region. One approach to addressing such a question is to apply a univariate test to each location separately and then use the results collectively to make a decision. This approach is called multiple testing or multiple comparisons and is common in genomics for analyzing gene expressions. The disadvantage of this approach is that it does not fully account for correlation between variables. Multivariate techniques provide a framework for hypothesis testing that takes into account correlations between variables. Although multivariate tests are more comprehensive, they require estimating more parameters and therefore have low power when the number of variables is large. Multivariate statistical analysis draws heavily on linear algebra and includes a generalization of the normal distribution, called the multivariate normal distribution, whose population parameters are the mean vector and the covariance matrix.
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.