On the Construction of Hypotheses

I’ve been asked to clarify how to specify non-directional and directional Hypotheses of Difference and Association – an essential part of your second Business Statistics Forum (BSF2).  You've already learned a few rules, to this end: When X is nominal (or whenever you're using an experimental research design), then you're going to develop a Hypothesis of Difference.  When X (and Y) are measured at no less than the ordinal level, then you're going to construct a Hypothesis of Association.  

In terms of how best to structure (word) each of these hypotheses, consider the following hypothetical examples (parenthetical information is added to clarify the level of measurement of X and Y and should not appear in your hypotheses):
 

Null Hypothesis of Difference:

There's no difference between Male and Female (SEX is a nominal level X) Attitudes Toward Management Scores (an interval level Y)

Research Hypothesis of Difference (Non-Directional):

There is a difference between Male and Female Attitudes Toward Management Scores

Research Hypothesis of Difference (Directional):

Males will have higher Attitudes Toward Management Scores than Females

Null Hypothesis of Association:

There's no association between Age (an I/R level X) and Attitudes Toward Management Scores (an interval level Y)

Research Hypothesis of Association (Non-Directional):

There is an association between Age and Attitudes Toward Management Scores

Research Hypothesis of Association (Directional):

As Age increases, Attitudes Toward Management Scores will decrease

As you have already learned this semester, directional hypotheses involve specification of how X and Y are related.  For a Hypothesis of Difference, you specify how a category of X (e.g., males or females, those exposed to X or those not exposed to X, etc.) will differ from the other category or categories in their responses to Y (see the example above).  For a Hypothesis of Association, you specify whether a positive or negative association will exist between X and Y (see the example above).  What's the difference between a "positive" and "negative" association?  For old time's sake:

Positive:  "As X increases, Y increases" or "As X decreases, Y decreases" (Be sure the direction of X and Y is the same)

Negative:  "As X increases, Y decreases" or "As X decreases, Y increases" (Be sure the direction of X and Y are inverse or the opposite)

Finally, you should recall that, as a researcher, you determine if the relationship between X and Y is positive or negative based on your understanding of prior research.

I hope this helps!

Professor Ziner