In the form of a curvilinear relationship. A curvilinear relationship is easy to spot: First, the relationship goes in one direction, then in the other. A well-established curvilinear relationship is the association between the ages of mothers and the rates of deaths among infants (called infant mortality). The highest infant mortality rates occur among mothers 16 years of age or younger. Rates decline with increasing age until mothers are about 40 or older; after which the rates increase sharply. Looking at the entire range of ages, we conclude that the relationship is curvilinear. Nonlinear, meaning that the relationship cannot be expressed as a straight line, is also used to describe this kind of a relationship.

In the form of no relationship. Sometimes we wish to hypothesize that two variables are not related to one another. For example, one might argue that the happiness of children is not associated with the income of their families. Another way of saying this is that the two variables are independent of one another. Thus, a hypothesis stating no relationship between variables can be expressed in several ways as well:

The income of families is not related to (or associated with) the happiness of children.

There is no relationship (or association) between the incomes of their families and the happiness of children.

The incomes of families and the happiness of children and are not related (or associated, which ever you prefer).

The income levels of families and the happiness of children are independent.

Some group (A) is different from another group (B). This form of hypothesis occurs when the purpose of research is to find out if two groups are different with respect to some variable.   Generally, however, we can go beyond just saying we expect to find some difference. Usually, a hypothesis specifies the direction of the difference by saying that the variable for one group is larger or smaller than for another group. To illustrate, we could hypothesize that:

School attendance rates are greater in urban than rural areas.

In the form of the direction of change for some variable. To illustrate:

The age at marriage among females has increased in the past 20 years.

Are hypotheses necessary?

Research does not require the use of a hypothesis. A large number of studies are conducted without one. Most fact gathering surveys do not involve hypothesis testing. If you wanted to describe the changing ratio of females to males at your university over the past ten years, a hypothesis would not be needed. You could collect and analyze enrollment data over the years, present your findings, and draw a conclusion about the rate and direction of change.

When a sound hypothesis can be derived, there are advantages in using one. A hypothesis gives a study a clear, specific focus. Data are obtained, analyzed, and interpreted in terms of the hypothesis. Also, the conclusion of the study can be easily and clearly presented by simply stating whether or not the hypothesis was supported by the data.