Let me try... If you expect there to be no relationships between two variables that characterise some aspect of some population, then drawing samples should indicate that there is no relationship between these two variables. If, upon drawing samples from this unknown population, you find that there is a strong relationship, then you can infer that the magnitude of this relationship is directly proportional to the likelihood that these two variables are truly related. The strength of the relationship is therefore somehow tied into your beliefs in the significance of the relationship.
So, suppose your null hypothesis was that these two variables in the population have NO relationship, the deviation from this null hypothesis would indicate the significance of your findings that INDEED there IS a relationship. This "deviation from the null" is significance of your findings, and you would expect this to correlate with the "strength" of the correlation between the two variables" which is the statistic you are testing, for which the null is zero correlation. I think this is what this paragraph is trying to say... please correct me if i'm wrong. ----- Original Message ----- From: "Will" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Sent: Thursday, March 04, 2004 8:04 AM Subject: [edstat] is this meaningful or nonsense > I don't understand this. Can anyone say this in another way, perhaps a > more mathematical way? > > "Why stronger relations between variables are more significant. > Assuming that there is no relation between the respective variables in > the population, the most likely outcome would be also finding no > relation between those variables in the research sample. Thus, the > stronger the relation found in the sample, the less likely it is that > there is no corresponding relation in the population. As you see, the > magnitude and significance of a relation appear to be closely related, > and we could calculate the significance from the magnitude and > vice-versa; however, this is true only if the sample size is kept > constant, because the relation of a given strength could be either > highly significant or not significant at all, depending on the sample > size (see the next paragraph)." > . > . > ================================================================= > Instructions for joining and leaving this list, remarks about the > problem of INAPPROPRIATE MESSAGES, and archives are available at: > . http://jse.stat.ncsu.edu/ . > ================================================================= > . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
