Comparing two designs (or anything else!) using independent sample T-tests - Improving the User Experience through Practical Data Analytics - page 56

repeating: the sample means of the two samples above are almost surely 1 not equal
to the respective “true means.” That is, before we do the analysis, we are not sure
whether the difference in the sample means (4.22 − 3.40 = 0.82) is indicative of a
real difference in the true means if we could magically collect data from all clients
of Mademoiselle La La (current and future!). After all, if the true means are indeed
equal, the means of the two samples will still very likely be different! 2
Thus, we're left with the question of whether the difference of 0.82, given the
variability among the values within each group/column and the sample sizes of 18
and 20, is a large enough difference to believe in H1—that there is a real difference!!
This is exactly what an independent samples t-test will determine. We will irst per-
form the test in Excel, then in SPSS.
2.5.1 EXCEL
First, you go to the “data” tab on the Excel ribbon and click on “Data Analysis”
(not shown under the data tab, but on the extreme right at the top, as we saw
in Chapter 1)—which you have, indeed, activated as discussed in Chapter 1.
Then highlight “t-Test: Two-Sample Assuming Equal Variances.” (See arrow in
Figure 2.3 .) This command in Excel implies the t-test is for independent samples.
Then 3 you click on the highlighted command and consider the dialog box that
comes up. Fill in the location of each “variable”—i.e., tell Excel where each column
of data you wish to use is located.
From Figure 2.4 , you can see that the irst design's data (“variable 1”) is b2-b19,
while the data from the second design (“variable 2”) is located in c2-c21. Experi-
enced Excel users may ind other, perhaps more eficient, ways to enter the location
of the data.
It can also be seen in Figure 2.4 that we have requested that the output be put on
a new worksheet (i.e., page!!) that we named “jared”—see the bottom, vertical arrow.
Finally, you click on “OK” in the upper right corner (see “thick arrow” in Figure 2.4 ).
This will provide the output on the “jared” worksheet shown in Figure 2.5 .
1 We wish to thank Dr. Robert Virzi for several comments about this chapter and pointing out that the
means could possibly be equal, even though it might be extremely unlikely. If we were describing a true
normal distribution, in which each data value is theoretically carried to an ininite number of decimal
places (assuming, theoretically, there is a measuring device that could do this!!), then the sample mean
and true mean would have zero chance of being equal. However, in a case in which the value of a data
point is an integer from 1 to 5, there is a chance, likely very small—depending on the sample size and
population size—that the two means would be equal. However, the essential thought expressed is still
a valid one for all practical purposes.
2 The same issue arises with this sentence. And, again, the probability that the two sample means are
equal is not literally zero. If each sample has n = 2, the probability the two sample means are equal is
about 13%. It will decrease as the n 's increase.
3 Note that there is another command right underneath the highlighted one that says “t-Test: Two-Sample
Assuming Unequal Variances,” which is misnamed in Excel (!) and should be “t-Test: Two-Sample
Not Assuming Equal Variances.” This usually gives a fractionally different result from the test we are
doing, one that is rarely materially different, and we shall illustrate this command later in this section.