A single sample means test is a statistical test that can determine whether or not a population estimate (i.e., sample statistic) is significantly different from a known value.
A hypothetical example may help illustrate this. Let's say a national survey of the adult population asks how religious people are on a 10-point scale, ranging from 1 being "not at all religious" and 10 being "very religious." And let's say that the mean on this scale in the U.S. is 6.01. With our sample of genetic counselors, we can ask whether or not genetic counselors are similar to the general population in their religiosity. To do this, we use a single sample means test, which takes into consideration sampling error. Similar tests are possible for proportions (i.e., with nominal/ordinal variables), but SPSS cannot do those. How to do a single sample means test in SPSS is illustrated below.
To begin with, go to "Analyze" -> "Compare Means" -> "One-Sample T Test":
The "One-Sample T Test" window will open:
Select the variable you want to compare to a target value, then move it into the "Test Variable(s):" box:
The next part is absolutely essential and easy to overlook the first time you run this. In the "Test Value" box below the "Test Variable(s):" box you need to put the target value. In our case, we'll put 6.01:
(Note: It's not uncommon for beginners to leave the "Test Value" box blank. And, for some reason, SPSS puts a default value in the box of zero, which means the test will run if you don't put your target value in the box as SPSS will assume your target value is zero. Just make sure you put the correct target value in the "Test Value" box.)
The results will open in the Output Window:
There are two tables. The first simply describes the sample and variable included in the analysis. The N, Mean, Standard Deviation, and Standard Error of the Mean are all included. Of particular interest for the example, the mean religiosity score of genetic counselors is 4.65, which is lower than our hypothetical religiosity of the U.S. population generally. However, the question is whether or not this is due to random error or an actual affect of genetic counselors.
The second table tells us whether or not the difference between the two is likely due to chance. The first column is the t-statistic. Using a t-table, one could use this value to determine whether or not the two means are significantly different. SPSS does the calculations for you. The next column, "df," provides your degrees of freedom, which is n-1 for single sample means tests. The third column, Sig. (2-tailed), provides the p-value for this particular test, which is the probability of finding the difference between the genetic counselors' mean and the general U.S. adult population mean we found (again, this is hypothetical) simply due to random error (assuming they are actually the same). In our example, the p-value is .000, which is smaller than the standard p-value used in statistics of .05, indicating the odds of us finding this difference if the population means are the same simply due to chance is less than 1 in 1000. In this case, we would reject the null hypothesis that there is no difference and accept the alternative hypothesis that there is a difference between genetic counselors and the general population in their average religiosity.