The one-sample t-test is used as a tool of inferential parametric statistics, which allows using the findings of the sample analysis for comparison with the general population. The essence of this test is to evaluate whether a given sample comes from the general population or, to put it another way, to compare known sample and population averages to examine the significance of differences between them (LS, 2021). For example, if we know that the average score of American students in a statistics course is 80 and our class has an average score of 85, we can use a one-sample t-test to evaluate whether there are differences in the mean values and whether our class sample comes from the general population of American students. This test requires that the dependent variable be measured at a continuous level; that is, it must be measured either as an interval or as a ratio. It is also necessary to have the value of the population mean to which the sample mean will be compared: in general, this is sufficient to perform a one-sample t-test.
Since this test deals with a single sample, no splitting into intra-sample cohorts is allowed, as it violates the logic of a particular analysis. Accordingly, the number of dependent variables should be equal to one. There is no independent variable as such in this case because there is nothing to manipulate in the inferential test. However, the absence of an independent variable is only formal; in reality, an independent factor always exists. In the class grade point average example above, the conditional independent variable might be the degree of student achievement that the researcher uses to generate a sample of students. They can sample high- and low-achieving students without differentiating them into cohorts only formally. Meanwhile, in a one-sample test, it is essential that the observations are independent; that is, they do not arise from each other, and that the distribution of the dependent variable is close to normal.
To further understand the nature of this test, we can consider an example related to health care. For example, it may be known that for medical employees, working more than 80 hours per week can be disruptive to overall productivity, create adverse effects on work motivation, and increase the number of errors committed. Accordingly, it makes sense to conduct a one-tailed study in a particular clinical setting to assess whether employees, on average, work above this threshold. To do this, a sample of clinical staff at the institution must be collected that is large enough to ensure that bias is minimized. For each respondent, the amount of time they spend per week on work tasks is examined, followed by an inferential analysis. If the resulting p-value is above a critical level (e.g.,.05), it follows that the null hypothesis must be accepted, and it is postulated that the average time spent on work tasks turns out to be greater than or equal to 80. In other words, the employees of a particular clinic are overworked, resulting in a disruption of the institution’s productivity.
References
LS. (2021). One-sample t-test using SPSS Statistics. Laerd Statistics.