Edgar Degas: The Absinthe Drinker (1875-76).



Definition

1. An hypothesis is a stated relationship between two variables.
2. Hypotheses must be falsifiable.
3. Operational definitions must be provided for all the variables in an hypothesis.
4. Hypotheses stating causal relationships should indicate direction of causality.

Suggestions for Formatting of Hypotheses:

• for continuous level measures: the greater the x, the greater/less the y
  • example: the greater the education, the greater the income
  • example: among Protestants, the greater the education, the greater the income
  • null form for one-tailed test: among Protestants, an increase in education will not lead to greater income.
  • null form for two-tailed test: among Protestants, there is no relationship between education and income.
  
  Test statistic: t-test of the correlation or regression estimate.
  
  
• for one categorical and one continuous measure: category x1 will have a higher/lower score on y than category x2
  • example: males will have higher educational attainment than females
    
  • null: males will not have higher educational attainment than females.
  
  Test statistic: t-test of difference in means.
  
  
• For two categorical measures: category x1 will be more likely to have characteristic y1 than category x2
  • example: males are more likely to have a 4-year college degree than females
  • null form: males are not more likely to have a 4-year college degree than females.
  
  Test statistic: chi-square test of goodness of fit.
  
  
• Hypotheses stating non-causal relationships or no relationships:
  • There is an association between x and y
    
  • There is no relationship between x and y.
    
    
  • example: There is an association between self-esteem and locus of control (where your theory states a non-causal correlation between these variables).
    
  • example: There is no relationship between attitude and behavior (where your theory states no relationship between these two variables).
  
  Test statistic: t-test of the correlation.

Further suggestions for writing hypotheses can be found on Pp. 33-37 in Delbert C. Miller, Handbook of Research Design and Social Measurement, Fifth Edition.

The Research and Null Hypotheses:

Ha: theta NE 0 (there is a relationship).
Ho: theta EQ 0 (there is not a relationship).

Where, theta refers to the parameter estimate (regression weight, difference in means, correlation).

Statistical Significance and Substantive Significance

Statistical significance refers to whether a relationship between two variables is sufficiently strong that, within a margin of error of 5% (for example), one would not expect the relationship to have occurred by chance (i.e., the strength of the relationship most likely is not equal to zero). It is an artifact of statistics that the larger the sample size, the less the strength of the relationship needed to obtain statistical significance at a given level of error. Thus, for a very large sample, one might find that a very weak relationship between two variables is statistically significant.

Substantive significance refers to whether the relationship between two variables is sufficiently strong that, in the consensus opinion of the community of scholars, the relationship represents an important finding. Thus, a very weak relationship that is statistically significant (because of a very large sample size) might not be considered to be substantively important by the community of scholars.

Errors in Testing Hypotheses:

Type I error: reject Ho even though it is true [mistakenly think you have a relationship; "false knowledge"].
Type II error: do not reject Ho even though it is false [mistakenly think you do not have a relationship; "unrecognized relationship"]