Can we call alpha the percentage/value of uncertainty in the confidence interval concept?
Since alpha is the measurement of the outer range value of the confidence interval limit. for example 95% confidence interval means we are confident that 95% of the population parameter will fall in a certain confidence interval range where 5% will not fall which we interpret as the uncertainty
Hey Kalyan,
That's almost right, but let me clarify a bit about confidence intervals and the role of alpha (α) in this context:
Confidence Interval (CI): A confidence interval gives a range of values that is likely to contain a population parameter, like a mean or proportion. The confidence level (like 95%) tells us how confident we can be that the interval includes the true parameter.
Alpha (α): The confidence level is usually expressed as 1−(1−α). For a 95% confidence interval, α is 0.05 (or 5%). This α represents the proportion of all possible samples for which the confidence interval will not contain the population parameter. In simpler terms, there's a 5% chance that the true parameter will not be in our confidence interval.
So, when you say a 95% confidence interval, it means you're 95% confident that the interval contains the true population parameter, and there's a 5% chance it does not. This 5% (the α) is split on both ends of the interval, implying that 2.5% of the time, the parameter could be below the interval, and 2.5% of the time, it could be above the interval.
In summary, alpha is the level of uncertainty we accept in our estimate. For a 95% CI, we're accepting a 5% level of uncertainty, where there's a 5% chance that the true population parameter lies outside our calculated interval.
Best,
Ned