The sadistic Question 4 from the second paper of 2003 invided the candidates to "compare and contrast the use of the Chisquared test, Fisher’s Exact Test and logistic regression when analysing data". This was a terrible idea, and the pass rate was 17%. Such questions have never been repeated since.
Additional reading can be done, if one wishes to actually understand these concepts.
I recommend the following free online resources:
Additionally, I invite everybody to visit this page, where the author Steve Simon (presumably, somebody qualified in statistics) responds to an email he received which asked him to comment on the differences between a Chisquare test, Fisher's Exact test, and logistic regression.
Qualitiative data types
 Categorical measurements based on descriptions, rather than numerical values.
 Qualitative data comes in two flavours:
 Ordinal data: numerical data assigned to subjective observations, which are ordered (eg. GCS scores)
 Nominal data: Variables described in terms of quality, eg. colour of hair.
 These are tested using the Chisquare and Fisher's Exact Test
A statistical test commonly used to compare observed data with data we would expect to obtain according to a specific hypothesis. The chisquare test can be used to test for the "goodness to fit" between observed and expected data.
 chisquare is the sum of the squared difference between
observed (o) and the expected (e) data: χ>^{2}= χ(oe)^{2}/e
 May be inappropriate if the sample numbers are small.
 Cannot be calculated if the expected value in any category is less than 5.
Another test like the Chisquare test, to compare observed data with expected data.
 Used for small data sets (where Chisquare is useless)
 Only applicable in a 2x2 contingency table
 Method of predicting a binary variable (eg. dead or alive) on the basis of numerous predictive factors, to compare observed and predicted data.
 ICU mortality is predicted using logistic regression analysis
 Regression coefficients allow the contribution of different predictor variables to be analysed.
 Goodness of fit can be estimated using a variety of mathematic methods.
Chi Square, Fisher's Exact Test and Logistic Regression
A Comparison of Methods

Chi Square 
Fisher's Exact Test 
Logistic regression 
Application 
"give a representation of the likelihood that a given spread of data occurs by chance" 
Specific uses 
Nominal data: large samples

Nominal data: small samples

Binary variables 
Advantages 
 Able to analyse multiple tables and rows of data

 Better suited to small data sets (sample size less than 20)
 "Exact": does not rely on approximation

 Useful to predict an outcome variable which is binary and categorical from predictor variables that are continuous
 Used because having a categorical outcome variable violates the assumption of linearity in normal regression.

Limitations 
 Ineficient in handling ordinal data.
 Cannot be calculated if the expected value in any category is less than 5.

 Only suited to small data sets (sample size less than 20)
 Computationally intense: calculations needed for this test increase rapidly as the sample size increases
 Cannot adjust for possible confounding variables

 Assumes an independence of errors
 Assumes no outliers

