Calculating significance for indepent samples

Hello to you all. I would be very happy if anyone would mind helping me with a little problem I have encountered whilst doing some research.

I am looking at my local hospitals MRI scanner (machine for taking fancy picutures). My first sample is with the new scanner. My second sample is with the old scanner.

The results are being compared with arthroscopy (keyhole surgery) which is the gold standard. I want to compare both samples which are independent to see whether the new scanner is actually any better.

In sample one the raw data and calculated sensitivity was

ACL Arth +ve Arth -ve Sensitivity 100%
MRI +ve 12 6
MRI -ve 0 46

In sample two the raw data was

ACL Arth +ve Arth -ve Sensitvity 85.71%
MRI +ve 24 23
MRI -ve 4 105

I have been told by the local biostatistician to use Chi-square tables but he has gone on holiday and did not tell me which figures I should be putting in to which box on the 2x2 table.

Can someone please help as I am STUCK???? Greatly appreciated and thank-you for your time and effort.
For the chi-squared test for independence to be used, the observed frequency must be a random sample and each expected frequency must be greater than 5.

The expected frequencies are calculated on the assumption that the two variables are independent. If the variables are independent, then you can expect little difference between observed frequencies and expected frequencies. When they are close together, the differences between O and E will be small and the chi-square test will be close to 0. Therefore, the null hypothesis is unlikely to be rejected.

Our hypotheses may be:

H_0: The scanners are independent
H_a: The scanners dependent
Thank-you Galactus for your reply. I sort of understand those concepts. What I really need is help with actually where do I put the figures into the 2x2 table and what data do I use?

This is what the statistician quoted me:

The sensitivity is a ratio of x/y. If you want to compare two sensitivities create a two by two table and do a chi-sq test.

so you get: x1 x2
y1 y2
tot1 tot2

Where sensitivity 1 is x1/tot1 and sensitivity 2 is x2/tot2. A chisq on x1 x2/ y1 y2 will tell you whether they are different or not.

I need to know what x 1 and 2 are and also what y1 and y2 are?

Can you or anyone else help? (Please refer to my first thread for the raw data)