use of 'that' in reported speech

[gureo]

Hello teachers,
I was wondering about the necessity and difference in using the word 'that' in reported speech.

For example:
John said, "The test was easy".

John said the test was easy.
vs.
John said that the test was easy.

After searching around on the web for some usage rules, I find an equal number of examples of that both include and leave out the 'that', but no explanation as to why (or when) one should include it.

Are there any rules for the use of 'that' in reported speech such as in the example above?

Thank you !

[oregeezer]

If it is "reported speech" then you should always use it if the speaker said it!

[gureo]

Thanks for the reply oregeezer!

So, is not using "that" in this example technically incorrect, then?

Leaving aside the comparison of the 2 in terms of reported speech, does using "that" somehow alter the specific meaning of the sentence in someway? I have a student who won't let up until I give her some reasoning for why or why not one would add the "that" to this type of sentence.

[gureo]

Any others with ideas about the differences of usage on 'that'? ...such as these sentences:

I heard the test was easy.
vs.
I heard that the test was easy.

Is there a 'rule' for when to use 'that' and when to leave it out? I am still fuzzy on this one...