Very often, we use data which are derived from some measurements. These measurements usually have a confidence measure associated which tells how reliable or confident we are about the measure. For example, we often see some confidence intervals associated with various polls.

I was wondering if there is a theory or algebra about combining multiple measurements and the resulting confidence measure of the aggregate. For example, if I measure X with a confidence interval +-x%, Y with confidence interval +-y%, what can I say about the confidence interval of X+Y? Similarly, what can we say about the confidence intervals for other operators?

Is there an algebra for this?

Very often, we use data which are derived from some measurements. These measurements usually have a confidence measure associated which tells how reliable the measure is, or how confident we are about the measure. For example, we often see some confidence intervals associated with various polls.

I was wondering if there is a theory or algebra about combining multiple measurements and the resulting confidence measure of the aggregate. For example, if I measure $X$ with a confidence interval $\pm x\%$, $Y$ with confidence interval $\pm y\%$, what can I say about the confidence interval of $X+Y$? Similarly, what can we say about the confidence intervals for other operators?

Is there an algebra for this?

Very often, we use data which are derived from some measurements. These measurements usually have a confidence measure associated which tells how reliable or confident we are about the measure. For example, we often see some confidence intervals associated with various polls.

I was wondering if there is a theory or algebra about combining multiple measurements and the resulting confidence measure of the aggregate. For example, if I measure X with a confidence interval +-x%, Y with confidence interval +-y%, what can I say about the confidence interval of X+Y? Similarly, what can we say about the confidence intervals for other operators.

Is there an algebra for this?

Very often, we use data which are derived from some measurements. These measurements usually have a confidence measure associated which tells how reliable or confident we are about the measure. For example, we often see some confidence intervals associated with various polls.

I was wondering if there is a theory or algebra about combining multiple measurements and the resulting confidence measure of the aggregate. For example, if I measure X with a confidence interval +-x%, Y with confidence interval +-y%, what can I say about the confidence interval of X+Y? Similarly, what can we say about the confidence intervals for other operators?

Is there an algebra for this?