## 5.3 The Study: Is 7 Really Magical?

The following is the Introduction and Method sections of a hypothetical study. For this lab, you will conduct the analyses described in the analytic strategy below.

Eminent psychologist George Miller is best known for his seminal paper, “The Magical Number Seven, Plus or Minus Two: Some Limits on Our Capacity for Processing Information.” “The Magical Number Seven” has been interpreted to claim that humans can hold an average of seven objects in working memory—an idea sometimes referred to as Miller’s Law. Miller’s Law proposes a remarkably simple model of working memory capacity. We tested this model of working memory in a sample of undergraduate psychology students who were in their third or later year of their program and had excelled in their coursework. Because these students had showcased academic excellence over several years of post-secondary education, we hypothesized that their memory spans would be greater than seven.

### Participants and Procedure

Participants (N = 174) were undergraduate psychology students enrolled in a research methods and statistics course designed to prepare students to conduct research and for graduate school. Entry into this course is competitive based on GPA in psychology courses. As such, these students were above average in terms of academic achievement. Participation in this study was part of the students’ coursework.

### Measures

Memory span is the longest sequence of items a person is able to correctly repeat immediately after presentation, in at least 50% of trials. We measured digit span, which is memory span for digits, using the R package MemorySpan. This package includes a program for measuring digit span by printing digits to the R console and asking participants to type those values into the console. If the correct sequence of values is entered into the console, the user is presented with a new sequence which is one unit longer than the prior sequence. If the incorrect sequence is entered into the console, the trial ends and the user’s digit span for that trial is returned. By default, the program begins with a digit span of one, but participants were instructed that they could increase this value to save time. Participants completed 10 trials. Their digit spans were defined as the longest sequence they correctly repeated in at least 5 of the 10 trials.

### Analytic Strategy

To test whether Miller’s Law applied to digit spans for this population of students, we conducted one-sample t tests against the null hypothesis that our sample was drawn from a population in which average memory span is less than or equal to seven. One-sample t tests assume that variables are drawn from a normally distributed population. We tested this assumption by visually inspecting histograms, examining skew and kurtosis values, and with Shapiro–Wilk tests.