Comparing Averages of Two Paired Samples

There are two types of mean comparisons allowed by this type of data:

Independent Samples: If we compare food company versus computer company prices (for example 31.16 versus 25.91), this is called a comparison of means betweenindependent samples. The confidence interval procedure for is given by either ( 7.7) or ( 7.8).

Paired Samples: If we compare Jan. 2002 prices versus Jan.2003 prices (for example 31.16 versus 28.07), this is called a comparison of means betweenpaired samples. The confidence interval for is discussed below.

The best way to tell whether you have independent or paired samples is to ask: do I have "two samples" (independent) or "one sample measured twice" ( i.e. paired)? The statistical treatment is different because paired samples involve sampling luck just once. This gives paired-samples better statistical properties than independent samples. For independent samples, luck-of-the-draw occurs two times.

The correct procedure for estimating the difference between means of paired columns is as follows: subtract the two measurements, and use a one-sample confidence interval ( 7.4) or ( 7.5) on the differences.

For the food service companies, the calculations are given in Table 7.2:

Using ( 7.5), a 95% confidence interval for the difference in means is given by

or (-2.93, 9.11).

For the independent sample comparison of food versus computer companies (for 2002),
the calculation is as follows:

Therefore, , , and the difference between means is estimated as

where the second term is the standard error. For a 95% confidence interval, the critical value from the

or (-4.01, 14.51).