Confidence Intervals &
A Quick & Dirty Approach
Confidence intervals and hypothesis tasting are
the key elements of "Inferential statistics." A confidence interval
question "Based on sample data, what numbers would & would not be a
guess for the mean of the population from which the sample came?"
The concept of a reasonable guess requires some
definition. Often in business we only need to guess an upper or lower
bound on a number:
"the mean operating cost is under ˆ500 per day" or "the mean pages
per ink cartridge is over 5000." Sometimes we need to guess both; this
is what statisticians call a two sided interval: "the mean productivity
between 7 and 9 widgets per hour."
These types of guesses, called confidence intervals, quality as "reasonable" if they are calculated from sample
data using a procedure which, despite the inevitable uncertainty of
generalizing from a sample to its parent population, is nevertheless
to be correct in a specified proportions of applications, usually 90%
We use sample data to determine what guessesoabout
the population mean are reasonable by calculating a "confidence
based on a "margin of error" above and/or below the population mean. A
about the population mean is reasonable in the iight of the data if it
"close" to the sample mean; specially, if the difference between the
and the sample mean is less than the margin of error.
The margin of error depends on two characteristics of the sample and
judgment call. The two characteristics of the sample are the number of
and how much those observations vary from one another. Small samples
heterogeneous observations require a big margin of error, which means
much power to exclude unreasonable guesses.
The judgment call is known as the "confidence level." In practice, the
level chosen is almost always 95%. Choosing a confidence level of 90%
a more lenient standard of what is a "reasonable guess." The margin of
for 90% confidence is larger, so fewer guesses can be ruled out.
choosing a confidence level of 99% means a smaller margin of error and
stricter standard for a "reasonable guess."
For technical reasons statisticians refuse to
specified proportion the "probability" that the unknown population mean
is in the calculated interval, preferring the phrase "confidence
but for most practical purposes the difference is inconsequential.
Calculating Quick & Dirty Confidence Intervels with Excel
Quick & Dirty Hypothesis Testing