Null Hypothesis

An Example Experiment

In the simplest sort of experimental design, one measures the effect of a single independent variable, such as the amount of information held in short-term memory on a single dependent variable and the reaction time to scan through this information. To pick a somewhat arbitrary example from cognitive psychology, consider what is known as a Sternberg experiment, in which a short sequence of memory digits (e.g., “34291”) is read to an observer who must then decide whether a single, subsequently presented test digit was part of the sequence. Thus for instance, given the memory digits above, the correct answer would be “yes” for a test digit of “2” but “no” for a test digit of “8.” The independent variable of “amount of information held in short-term memory” can be implemented by varying set size, which is the number of memory digits presented: In different conditions, the set size might be, say, 1, 3, 5 (as in the example), or 8 presented memory digits. The number of different set sizes (here 4) is more generally referred to as the number of levels of the independent variable. The dependent variable is the reaction time measured from the appearance of the test digit to the observer's response. Of interest in general is the degree to which the magnitude of the dependent variable (here, reaction time) depends on the level of the independent variable (here set size).

Sample and Population Means

Typically, the principal dependent variable takes the form of a mean. In this example, the mean reaction time for a given set size could be computed across observers. Such a computed mean is called a sample mean, referring to its having been computed across an observed sample of numbers. [Page 939]A sample mean is construed as an estimate of a corresponding population mean, which is what the mean value of the dependent variable would be if all observers in the relevant population were to participate in a given condition of the experiment. Generally, conclusions from experiments are meant to apply to population means. Therefore, the measured sample means are only interesting insofar as they are estimates of the corresponding population means.

Notationally, the sample means are referred to as the Mjs, whereas the population means are referred to as the μjs. For both sample and population means, the subscript “j” indexes the level of the independent variable; thus, in our example, M2 would refer to the observed mean reaction time of the second set-size level (i.e., set size = 3) and likewise, μ2 would refer to the corresponding, unobservable population mean reaction time corresponding to set size = 3.

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