24.3 Two independent means: Notation

Since two groups are being compared, distinguishing between the statistics for the two groups (say, Group A and Group B) is important. One way is to use subscripts (Table 24.1).

TABLE 24.1: Notation used to distinguish between the two independent groups

	Group A	Group B
Population means:	μA	μB
Sample means:	ˉxA	ˉxB
Standard deviations:	sA	sB
Standard errors:	s.e.(ˉxA)=sA√nA	s.e.(ˉxB)=sB√nB
Sample sizes:	nA	nB

Using this notation, the difference between population means, the parameter of interest, is μA−μB. As usual, the population values are unknown, so this parameter is estimated using the statistic ˉxA−ˉxB.

Notice that Table 24.1 does not include a standard deviation or a sample size for the difference between means; they make no sense in this context.

For example, if Group A has 15 individuals, and Group B has 45 individuals, and we wish to study the difference ˉxA−ˉxB. what is the sample size be? Certain not 15−45=−30.

On the other hand, the standard error of the difference between the means does make sense: it measures how much the value of ˉxA−ˉxB varies from sample to sample.

For the reaction-time data, we will use the subscripts P for phone-users group, and C for the control group. That means that the two sample means would be denoted as ˉxP and ˉxC, and the difference between them as ˉxP−ˉxC.