What do you think of this experiment?

I think it'd be an interesting experiment. Here's a few variables I would try to maintain or watch out for:

1. Maintain same recording conditions of the speeches (volume/clarity of the recording)
2. no visual clues or cues.
3. randomize the order which the recordings of 4 speakers are presented to the listener.
4. speakers use the same exact words with no more or no less emphasis of the words.
5. make the rating scales as objective as possible. Careful to inject no bias or leading the student towards any conclusion addibng any tester's questionnaire bias.
6. predetermine the nationality of the test taker. It would be wise to chose no one who/whom might be of that same nationality as the 4 nationalities/accent.

thx Ragman that was the plan
I am asking because today my tutor rejected this experiment, which would be fine if he gave me logical arguments. But he argued that:
1) this is linguisitics experiment, not psychology (?)
2) it's more in interest of sociology (?)
3) he can't see any variables here (?)

It all boils down to this: he's the boss.

The experiment is too ambitious and lacks control of speaker vs accent, or type of material.
You could use two speakers x two accents x two "news items" whose "credibility" is scored. Subjects are then assigned to at random to one of the 16 possible presentation stimuli (8x2 orderings), each speaker having given a sample of each item In this way, analysis can be made of significant differences in credibility with respect to accent rather than speaker, and with respect to baseline scores of credibility for each news item. You need a lot of subjects !

thx for reply fresco. At least your argument makes more sense to me, now I see the flaws!

But I don't quite understand - why 16 possible presentation stimuli? I can only see 8 (each speaker having a sample of each accent and each material).

And it would mean that I need speakers who speak both - perfect English and one of the accents..

You're right. Its not 16!
And minimlly you don't need speakers of two accents (there's n0 such thing as "perfect English" RP is just another accent,) 2 accented speakers A,B , 2 news items p,q and reverse orders
ApAq, BpBq, ApBq, BqAp, AqAp, BqBp, BpAq, AqBp= 8stimuli groups.

thx again fresco
The good news is I got an email from my tutor today. He asked me to send the pdf's of accent papers and he will have a think about it.
It's a group project and people had different ideas but only one experiment can be carried out and I guess he has the last say.

I was thinking how to disguise the participants:

To make them blind to the aim of study while listening to the recordings they will look at the screen with changing colours/patterns. They will be told that we are interested how the colours/patterns affect cognition and perception of lecture. They could also be told that they will listen to genuine recordings of our University lectures. The questionnaire, along with the traits ratings, will contain "filler questions" regarding "cognition processes" to disguise the participants.

Any possible flaws? Do you think visual "quasi-stimuli" could affect the dependent variable?

The idea of "credibility of news item" disguises the intent of the experiment and attempts to make "subject matter" neutral.
I'm not sure why you want to use actual lecturers. That seems far too personal. Surely the independent variable is "accent" which must be separated from other social factors like "familiarity" over which you have no control, In that way you don't need "quasi-stimuli".

Try researching sociolinguistic literature for "accent and credibility" for a background hypothesis. Note that zeitgeist could be important...i.e. acceptability of accent is subject to "fashion",