Under what conditions can you claim that you have found a cause and effect relationship between variables?

The answer to this question involves two issues: (a) the level of the study, and (b) the "causality requirements," as I'll call them. My source is Oleckno, William A., Essential Epidemiology: Principles and Applications (2002), Long Grove, Illinois, Waveland Press, Inc. Although Oleckno wrote about epidemiology, the same principles hold for any statistical analysis related to a phenomenon among people. In other words, epidemiology can be understood quite broadly.

A. The Level of the Study

Here is a ranked list of the major types of studies in descending order of likelihood that the results might demonstrate a causal association:

1. Randomized Controlled Trial 
2. Randomized Community Trial 
3. Prospective Cohort Study 
4. Retrospective Cohort Study 
5. Case-Control Study 
6. Cross-sectional Study 
7. Ecological Study 
8. Descriptive Study 

The higher up your study type is on the list, the more likely it is that the relationship you have found will later prove to be a cause-effect relationship: later meaning after you have met the causality requirements described below.

B. Causality Requirements: Criteria for Assessing Causation 

All of the following criteria must be met before you can write about your variables have a causal relationship: 

1. Correct temporal sequence (exposure to the independent variable must precede incidence of or change to the dependent variable) 
2. Strength of association (high relative risk or rate ratio, high r or tau). 
3. Consistency of association (requires followup studies or studies performed by other researchers that show the same or similar results) 
4. Dose-response relationship (more exposure to the independent variable leads to greater incidence, relative risk, or odds ratio for the dependent variable) 
5. Biological plausibility (Does the association make sense? Biological includes psychological) 
6. Experimental evidence (For instance, if experiments have shown that microwaves affect living tissue, then you have a stronger chance of proving that microwaves caused some sort of physical outcome among your study participants should you find one) 

Consider both A and B when you begin to write that people should change their behavior based on your study results. You can still make recommendations, but it will be important that you note that you have not proven a cause-effect relationship unless your study (a) is a high-level test and (b) met all of the above causality requirements.