## Step 3: Explore the data

First we will examine the distributions of the improvement scores for the two explanatory variable groups.

(b) Use the Descriptive Statistics applet to produce graphical and numerical summaries comparing the responses (improvement scores) of the two explanatory variable groups. Reminder, a negative improvement score indicates the subject did worse on the second (Day 4) testing.

 With the data file open, select all contents on the page (e.g., ctrl-a).  Then copy (e.g., ctrl-c) the contents to your clipboard.    In the applet, check the stacked box and then press the Clear button. Then click inside the Sample data window. Paste the data (e.g., ctrl-V). Notice the group variable is the first column and there are no spaces within variable names. Press Use Data. Check the boxes to display the Actual means and standard deviations. Check the box to display Boxplots as well.

### Take a screen capture of your output and paste into your lab report.

(c) Compare the distributions of the improvement scores (as best you can with so few observations) between these two groups. There may not be an obvious overall pattern but give your reader a sense of the visual images you are looking at. Make sure you discuss (supporting with appropriate statistics) shape, center, variability, outliers, and other unusual observations. Also include the sample sizes. Everything should be written in the context of this study.

Keep in mind that there is a difference between "improved" and "improved more" and to talk in terms of a "tendency to improve."
[Again, you may want to come back to this question later.]

(d) Also address the following questions:

• Calculate (by hand) and report the difference in the mean improvement scores between these two groups (unrestricted - deprived).
• Is this difference a parameter or a statistic? Explain.
• Does it appear that sleep-deprived subjects who were then given the chance to "catch up" on sleep were subsequently able to perform about as well as subjects getting unrestricted sleep on this visual discrimination task or did the sleep deprivation on the first night appear to still have a detrimental effect 3 days later? Clearly explain how you are deciding.
• Conjecture whether you expect this difference will turn out to be "statistically significant" and state why you think so or why not based on what you have seen in the sample data so far.