Q5 Knowledge Base One-Sample t-test

Knowledge-Base -- One-sample t-test

 Variable configuration for t-tests

             Metric Dependent Variable            Nominal independent Variable

One-sample t-test:                 Scores                           Location             

sample or population     

Independent-sample t-test: Scores                           Treatment           

level 1 or level 2   

Paired-sample t-test:              Scores                          Time Before or After 

When testing a theory that expresses an interaction between an independent variable and a dependent variable, one of two things are typically studied:

 (1) The relationship between a metric dependent variable and a metric independent variable

(2) The differences on a metric dependent variable between levels of nominal independent variable 

 The null says: There is no relationship between variables, or there is no difference between groups. In other words, the results obtained actually occurred by chance. 

 A sample theory for a relationship study might be: Add cops to the beat, crimes go down. 

A sample theory for a differences study might be: The average score on the SAT exam for students at XYZ University is higher than the average SAT score for college students nationwide. (There is a higher caliper of student at XYZ University when using SAT as a measure).

 To test the theory, we formulate the null hypothesis: There is not a statistically significant difference in SAT score between the students at XYZ University and university students nation wide. 

Therefore, there are actually three types of null hypotheses, one for each possible data-type combination.

Relationship null: "There is not a statistically significant relationship between the (dependent variable) and the (independent variable)"

Differences null: "There is not a statistically significant difference in the (dependent variable) between (levels of the independent variable)"

Non-parametric null:  “There is not a statistically significant difference in the (count of the dependent variable) among (the levels of the independent variable) between the observed count and the count that would be expected by chance alone.”