I am pretty new to bayesian statistics or any kind of statistics for that matter. I was reading this book "Bayesian Statistical Modelling - Peter Congdon". And in the introduction I came across this paragraph in this book. It was in the section explaining advantages of bayesian methods over classical estimation methods.
The classical inference model poses certain problems of interpretation both in significance testing and interval estimation. For example, if the test is whether the sex ratio at birth is 0.5(equal numbers of male and female births) and a sample of 10 births contain 9 females, then binomial distribution tells us that the probability of this is $\cfrac{10}{1024}$. A two-sided classical significance test would however be based not on this probabilities but on the probabilities of all 10 births being female $\left(\cfrac{1}{1024}\right)$, and on the probabilities of 9 or 10 births being male; overall significance level is $\cfrac{22}{1024} = 0.02$/ So probabilities of various events that did not occur are used against null hypothesis.
I understand the part till the binomial distribution is used, however I am stumped at what this text is talking about classical significance test and how the results differ. Aren't the results supposed to be same for a phenomena irrespective of the methods used. Can someone help me understand this? Thank you!
Edit 1:
The paragraph below this is:
The classical theory of confidence intervals for parameter estimates is that in the long run with data from many samples a 95% interval (say) calculated from each sample will contain the true parameter approximately 95% of the time, for remaining samples it will exclude the true parameter value. The particular confidence interval from anyone sample may or may not contain the true parameter value. This goes counter to intuitive and often held belief that the standard confidence interval from a particular sample contains the true parameter value approximately 95% certainty.