Optimized scorings for ordinal data for the general linear model
There are a number of possible statistical procedures that can be used for analyzing ordinal categorical data collected in a designed experiment. In this paper we present an approach which allows us to do a preliminary examination of the data set to see whether or not the statistical results are sensitive to the choice of procedure. In our approach we start by considering analyzing ordinal categorical data collected in a designed experiment considered in the context of a general linear model with scores assigned to the ordinal categories. The standard F-statistics for testing linear hypotheses concerning model parameters are considered. Since the increasing scores can be chosen arbitarily, two sets of scores may potentially lead to opposing analytical and statistical conclusions. To deal with such concerns we optimize the F-statistics as functions of the scores assigned to the categories. For reference purpose we suggest using the F-distribution, although there is the usual caution if sample sizes are small. In two cases, namely, when the maximized F is nonsignificant, or when the minimized F is significant, all scores lead to the same conclusions, respectively, either rejecting or accepting H0. For example, in a one way lay-out with C treatments and K categories a nonsignificant maximum F indicates that there would be no significant treatment effect no matter what scores are used. Methods for computing the maximum and the minimum F-statistics are presented. The methods suggested in the paper are exemplified. The relationship between the F-statistics used for testing the treatment effect in one-way design and certain monotone correlations is also established.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 27 (1996)
Issue (Month): 3 (April)
|Contact details of provider:|| Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description|
|Order Information:|| Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional|
When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:27:y:1996:i:3:p:231-239. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Shamier, Wendy)
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.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with 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 profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.