## 5.5 Lab Report Instructions

Read “Is 7 Really Magical? A Simple Test of Miller’s Law,” which is a manuscript containing an introduction and method section. For this lab, you will be conducting the analyses described in the analytic strategy (part of the method) and reporting the results in APA style. You will submit the following: (a) an R script for conducting the analyses described in the analytic strategy, (b) a Word document with your results reported in APA style, and (c) short answer responses to the discussion questions.

### 5.5.1 R Script

Do the following in R:

- Use
`t.test()`

to conduct a one-sample*t*test of the null hypothesis that the average digit span in the population is less than or equal to 7. Use`<-`

to assign a name to the output of your call to`t.test()`

. - Compute Cohen’s
*d*_{z}, either by using the formula \((M - \mu)/SD\) or by converting from the*t*with`psych::t2d()`

.^{2} - Use
`ggplot2`

to produce a histogram of the distribution of digit spans. - Use
`shapiro.test()`

to conduct a Shapiro–Wilk test on the distribution of digit spans. - Calculate
*M*,*SD*, skewness, and kurtosis of the digit span variable. Calculate*M*,*SD*, and range of participant ages:`psych::describe()`

will calculate all of these values in one go.`QuantPsyc::norm()`

will calculate skew and kurtosis for one variable and will provide significance tests for each (not provided with`psych::describe()`

). It will not provide*M*,*SD*, or range.

### 5.5.2 Results

Your results section should include the following:

- 1 sentence presenting the results of the one-sample
*t*test. - 1 sentence presenting the results of the Shapiro–Wilk test.
- 1–3 sentences describing the distribution of scores. Reference the results of the Shapiro–Wilk test, the histogram (i.e., Figure 1 in your manuscript), and skew and kurtosis values.
- A histogram showing the distribution of digit spans in the sample. Follow the rules for figures in the
*APA Publication Manual*.

### 5.5.3 Discussion

Answer each of the following questions in complete sentences.

- Do your results support your hypothesis? Your answer should include a
*plain-language*description of the results and hypothesis. - How do your results compare with Miller’s work arguing that memory span is equal to seven? Provide an explanation for why your results agree or disagree.
- How do the characteristics of the sample affect your interpretation of these results?
- What is one implication of your findings for future research, programs, or policy?

Sometimes the output of

`psych::t2d()`

will be a vector named “t”. This is okay. We will explain why this happens when we go over the assignment. If you are concerned that you might have the wrong value for*d*_{z}, check that you are getting the same result with`psych::t2d()`

and by using the formula.↩︎