Generic recipe for data analysis with general linear model

Courtesy of David Schneider

1. State population, and conditions for taking sample.

2. Construct the model:
   
   (a) state the response variable;
   
   (b) state the explanatory variable(s);
   
   (c) state type of measurement scale for each of these;
   
   (d) write model relating response to explanatory variable.

3. State HA/H0 about terms in model, (and about parameters in model if appropriate). State α, the tolerance for Type 1 error.

4. Execute analysis: place data in model format, code model statement, obtain fitted values and residuals.

5. If regression line is used, examine plot of residuals against fitted values. If bowl or arch is evident, revise the form of the model (back to step 2).

6. Partition df and SS = df * var (Response) according to model, table SS, df, MS, F (by computer usually).

7. Calculate Type 1 error (the p value) from density function (F or t distribution, etc.).

8. Check assumption for use of p-value from density function.
   
   (a) Residuals independent? (plot residuals versus residuals at lag 1)
   
   (b) Residuals homogeneous? (residual versus fit plot)
   
   (c) Residuals normal? (histogram of residuals, quantile plot or normal score).

9. If assumption are met then step 10. If not, decide whether to recompute pvalue. Recompute better p-value by randomization or bootstrap if sample small (n < 30), or p near α.

10. Declare decision about model terms: if p <α then reject H0 and accept HA, if p > α then hold H0 and reject HA. Report conclusion with evidence: F-ratio, df1,df2, and p-value (not α) for each term.

11. Examine parameters of interest. Report conclusions with parameter estimates(means, slopes) and one measure of uncertainty (st. error, st. dev., or conf. intervals) .