IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-1-4615-8615-9_7.html
   My bibliography  Save this book chapter

Normal sampling theory: test for difference between several sample means, analysis of variance, design of experiments

In: Essentials of Statistics for Scientists and Technologists

Author

Listed:
  • C. Mack

    (Institute of Technology, Applied Mathematics)

Abstract

In Chapter 6 the t test was used to decide whether the difference between two sample means was too great for them to come from the same population. We now describe the test for the case of more than two samples (Note: applying the t test to the difference between largest and smallest mean will give the wrong answer). This test is based on the fact that the mean of a sample of size n from a normal population with given σ, is itself normally distributed with variance σ2/n (see Section 5.7). If, then, we have m samples, and their means have a greater variance than would be expected from m individuals from a population whose variance is σ2/n, we conclude that, very probably, there are some real physical differences between the means. Unfortunately, σ2 is not usually known and so has to be estimated from the variance within each sample (it is assumed that all population variances are the same).

Suggested Citation

  • C. Mack, 1966. "Normal sampling theory: test for difference between several sample means, analysis of variance, design of experiments," Springer Books, in: Essentials of Statistics for Scientists and Technologists, chapter 7, pages 52-62, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4615-8615-9_7
    DOI: 10.1007/978-1-4615-8615-9_7
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-1-4615-8615-9_7. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.