A few Notes on Chi-Square Test.

General vs Specific Case.

The difference between the specific case (1 degree of  freedom) and the general case (2 or more degrees of freedom) is a technical one.  Using the specific case for problems involving 1 degree of freedom (two phenotypic classes) is the most conservative method. (formulas)

Level of significance.

The meaning of the outcome of any statistical test is evaluated according to the criterion set up by the experimenter.  This may reflect variables peculier to the experiment itself.  Very often the outcome is evaluated according to what is common practice in the scientific community.

The level of significance or p value reflects the experimenter's willingness to reject an experimental result that is actually correct.

Example: I carry out the cross Aa x Aa 100 times.  That is, I do the same experiment each time and I test the Null hypothesis that I will get a 3:1 ratio in each cross.  Some c² values will be quite small and others will be quite large.  If I set my level of significant at .05, on average I will reject the results of 5 out of 100 of my replicate experiments because the c² value will exceed my critical value of 3.84 (1 df). If I set my level of significant at .01, on average I will reject 1 out of 100 of my replicate experiments because the c² value will exceed my critical value of 5.99 (1 df).  These two values are generally accepted by the academic community.

If I set my level of significance too low (some type of scientific zero tolerance), for example, p = .90 I would, on average,  90 out of 100 of my replicate experiments because the c² value will exceed my critical value of .02 (1 df). If on the other hand, I set my level of significance really high (for example at the .0001 level ), I would almost never reject any results.  On the other hand I might accidentally accept results which are actually wrong.

A Chi-Square Table