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Confidence Levels in confidence intervals
Hi, I'm Dr Nic In this video I am
going to talk about confidence intervals, and particularly the level of confidence.
First, you may like to watch the videos, Understanding Confidence Intervals,
and Calculating a confidence interval for a mean using a formula.
Also look in the description below for other videos about confidence intervals.
When we state a confidence interval for a mean or some other population parameter
we usually state the level of confidence.
The most commonly used levels of confidence are 90%, 95% or 99%
A confidence interval expresses
a range of values within which we are pretty sure the population parameter, such as the mean, lies.
The confidence level expresses how sure we are. So if we have a 95% confidence interval for
the mean weight of apples in an orchard we are pretty sure that the mean is within that range.
The level of confidence affects the size of the confidence interval.
This is an area where people can get confused.
The more confident we wish to be that we have included the unknown population value in our confidence interval, the wider the confidence interval needs to be.
It is as if we were trying to catch the parameter in a net.
The bigger the net is, the more likely we will be to catch the parameter.
Let us explore the formula for a confidence interval for a mean.
We use the sample mean, which is the best estimate of the population mean,
for the middle of the interval.
Then we find the standard error,
which is a combination of the sample standard deviation, s,
and the sample size - or more specifically, the square root of the sample size.
The effect of a change in sample standard deviation.
The bigger the standard deviation is, the greater is the standard error - a measure of how spread
out the sample means would be.
The confidence intervals are wider with a more varied population.
The effect of a change in sample size.
As the sample size gets bigger, we have more information, so the standard error gets smaller,
as larger samples decrease the spread of the sample means.
The confidence intervals are narrower, with a larger sample.
The formula uses a value from a t distribution or Z distribution to know how many standard
errors make up the margin of error.
The effect of a change in confidence level.
With a small sample of 15, we use a t distribution with 15-1 = 14 degrees of freedom.
for 90% the t value is 1.76 for 95% the t value is 2.14
for 99% the t value is 2.98
As we increase the level of confidence we wish to have about the interval,
the interval width increases.
So what does a 90% confidence interval mean?
It means that for every one hundred confidence intervals we calculate from sample data,
about 90 of them will contain the population parameter, and 10 will not.
In the description below are links to further videos around confidence intervals and other statistical concepts such as sampling error.
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