1. LECTURE 5 HYPOTHESIS TESTING EPSY 640 Texas A&M University

2. CONCEPTUAL ANALYSIS Conceptual analysis (Scriven, 1988) is a major focus for verbal hypothesis formation and critical evaluation. A verbal statement should be analyzed for its components and their relationship to each other

3. LOGICAL CONTENT Logical content of verbal statements is a basis for conceptual analysis. In simple statements these are usually reduced to –Concept A described by (list of qualifiers) –Concept A related to Concept B –Concept A causes Concept B These are then linked to a specific population or to the entire population of interest.

4. CONCEPTUAL ANALYSIS Example: Children retained in grade 1 do not achieve as well in 2 nd grade on reading as do children with similar end of grade 1 reading achievement who were promoted: Analysis of statement: retention causes lower reading achievement in grade 2; grade 1 reading achievement is not the cause of grade 2 differences Population: unknown, implicitly all grade 1 children who are retained and promoted with similar grade 1 reading achievement

5. Operational definitions Each construct is linked with a measurement that can be made. Since this is a one-to-many operation, there inevitably will be several or many operational definitions for most constructs

6. META-ANALYSIS Meta-analysis - a method for systematically describing constructs as part of a statistical approach to describing research findings. –the most comprehensive method that deals with operational definitions. The process is dynamic –a person conducting the meta-analysis » reviews each definition as encountered »characterizes it in one or more ways »as new definitions are encountered, expands the list of elements for the characterizations. These are then coded using a nominal, ordinal, or interval scale as appropriate for further analyses.

7. VISUAL HYPOTHESES The path model developed by Wright (1923) has proven extremely helpful in providing visual analogs to verbal hypotheses. not clear that all verbal hypotheses can be represented visually, but the power provided by path representations for most social science verbal hypotheses makes this form a major advance in social research

8. Causality Judea Pearl (2000). Causality. Cambridge, UK: Cambridge University Press Probability theory and causal assertions Networks and directed acyclic graphs (DAGs) “A variable X is said to have a causal influence on a variable Y if a directed path from X to Y exists in every minimal structure consistent with the data.”

9. Potential Cause Potential Cause “A variable X has a potential causal influence on another variable Y (that is inferable from P, a sample distribution) if the following conditions hold: 1.X and Y are dependent in every context. 2.There exists a variable Z and a context S such that i) X and Z are independent given S; ii) Z and Y are dependent given S

10. Genuine Cause 1. A variable X has a genuine causal influence on another variable Y if there exists a variable Z such that either i) Z is a potential cause of Y ii) Z and Y are dependent given S iii) Z and Y are independent given S or 2. X and Y are in the transitive closure of the relation defined in 1.

11. X Y X and Y dependent Z X Z is a potential cause of X Y Z Y X Z and Y are independent given X (also termed complete mediation) GENUINE CAUSE OF X ON Y

12. Cause as Mediation X is a complete mediator of the relationship between Z and Y Partial cause (Scriven, 1978): no such thing in social science research as singular cause; multiple causes exist and may complement each other –Ex. Student achievement increase may be due to change in curriculum, but may still rise even without curriculum reform due to increased attention to school scores by parents

13. Classical Hypothesis Testing 1. Parameter selection. As discussed above verbal hypotheses usually are found in three forms: descriptive, relational, or causal. Once constructs are operationalized, the researchers decides on the appropriate population parameters to assign to each construct

14. Classical Hypothesis Testing 2. Hypothesis formation. In classical hypothesis testing two mutually exclusive specific mathematical statements about the selected parameter are constructed. H 0 :  = a H 1 :  = b, where a  b decidability: in any study with a finite number of cases we will always be able to decide between the two, at least in probability

15. Classical Hypothesis Testing 3. Selection of significance level. In classical hypothesis testing the probability of error we wish to accept for the confidence interval around each hypothesized parameter value termed the significance level or alpha level. Based on the researcher’s willingness to tolerate a sample mean that will fall outside the confidence interval by chance. Common alpha levels are.05 or.01

16. Classical Hypothesis Testing 4. Selection of statistical test procedure- select an appropriate hypothesis test statistic that has a different known distribution under the null hypothesis 5. Compare sample statistic with distribution 6. Decide between hypotheses