combining certanties

[Dak]

basic question:

 

1/ on day one, 45% of people are in favour of x

 

2/ on day two, 50% of people are in favour of x

 

assume a margin of error of [math]{\pm}[/math]0% and a certainty of 95% (i.e., 5% chance of each statement being false).

 

so, what's the certainty of the conclusion 'therefore, support for x has grown between days 1 and 2'?

 

I suppose that if there's a 5% chance of each precept being wrong, and two precepts (i.e., 2 chances for a precept to be wrong), then there'd be a 10% chance of... what? the conclusion being not neccesarily true?

 

The certainty of the conclusion seems as if it'd be 10%, but that feels a tad wrong. e.g., precept 2 could be wrong, but in actual fact on day 2 support could have been 60%, thus the conclusion would still be correct.

 

so, yeah, basically how do the certainty intervals combine in this case to give a certainty for the conclusion?

 

(for bonus points: how would that work with confidence intervals instead of certainty?)

[NeonBlack]

I'm not an expert on statistics and probability, but I don't think this question is well-formed.

 

For example, what does it mean for the statement "on day one, 45% of people are in favour of x" to be "false"?

[Dak]

my appologies.

 

I meant if the statement was false, then z% of people would be in favour of x on day 1, where z is not 45.

 

i've mostly seen statements of certainty (as opposed to confidence intervals) on public oppinion polls, hence why i worded my example like that.

 

(think estimates of parent-population mean based on sample mean: you usually end up being able to say 'there is x % chance that the parent population mean is between y and z' iirc)

[Josy]

Since the proportion of the population that supports x is a continuous quantity, it's not simply a question of true or false; presumably you'd model the proportion of the parent population as a normal distribution with a mean of 45% (or 50% on Day 2) and a s.d. of something or other, then move forward from there. It's a while since I did any stats as well, so I can't really be much use on this.