I was reading a Wikipedia article on the birthday paradox and stumbled upon the following statement:
...the pairings in a group of 23 people are not statistically equivalent to 253 pairs chosen independently...
Could you explain what does it mean and why does it matter in this case?
Here is the quotation in its original context:
Although the pairings in a group of 23 people are not statistically equivalent to 253 pairs chosen independently, the birthday paradox becomes less surprising if a group is thought of in terms of the number of possible pairs, rather than as the number of individuals.