ISCAM

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Section 1 (9-10am)Section 2(10-11am)
Goals: In this lab, you will
- Produce and summarize numerical and graphical summaries comparing two groups on a quantitative reponse
- Use a randomization test to compare two randomly assigned treatments on a quantitative reponse
Background

Researchers have established that sleep deprivation has a harmful effect on visual learning (the subject does not consolidate information to improve on the task). Stickgold, James, and Hobson (2000) investigated whether subjects could “make up” for sleep deprivation by getting a full night’s sleep in subsequent nights. This study involved randomly assigning 21 subjects (volunteers between the ages of 18 and 25) to one of two groups: one group was deprived of sleep on the night following training with a visual discrimination task, and the other group was permitted unrestricted sleep on that first night. Both groups were allowed unrestricted sleep on the following two nights, and then were re-tested on the third day. Subjects’ performance on the test was recorded as the minimum time (in milliseconds) between stimuli appearing on a computer screen for which they could accurately report what they had seen on the screen. Previous studies had shown that subjects deprived of sleep performed significantly worse the following day, but it was not clear how long these negative effects would last.

Study Design
The researchers expected participants in both groups to improve on the visual discrimination task the second time around (i.e., have faster reaction times), but they hypothesized that the unrestricted sleep group would have more improvement than the restricted sleep group (on average), assuming trying to "catch up" on sleep does not work for visual learning.

Sleep deprivation group (n = 11): −10.7, 4.5, 2.2, 21.3, −14.7, −10.7, 9.6, 2.4, 21.8, 7.2, 10.0
Unrestricted sleep group (n = 10): 25.2, 14.5, −7.0, 12.6, 34.5, 45.6, 11.6, 18.6, 12.1, 30.5
(a) Summarize the study design
What is the observational unit? blank
What is the explanatory variable? blank
What is the response variable? blank
What is the sample sizes for each group? blank
(b) Is this an experimental study or an observational study? Briefly justify.
(c) Write out the null and alternative hypotheses, in words, for this research study. [Hint: No association ...]
(d) Is the alternative hypothesis one-sided or two-sided?

one-sidedtwo-sided
Do the researchers expect to see positive or negative values for the response? For the difference in mean response (unrestricted - deprived)?

positive; positivepositive; negativenegative; positivenegative; negative

Descriptive Statistics

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

Clear the data window
Type SleepDeprivation.txt in the data window. Press Use Data to preview the data.
Press Use Data again to load in the data.
Use the Separate by menu to select the explanatory variable.
Check the boxes to display the Actual means and standard deviations and skewness values.
Check the box to Add Boxplots as well.

Note: These data are in stacked format, each variable is a different column.

Include a screen capture of the graph and numerical summaries output (only)

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

Choice of Statistic
There are several ways we could choose to measure the tendency observed in (e). A common choice of statistic is of course the difference in group means. Calculate this statistic by subtracting the “deprived” group’s value from the “unrestricted” group’s value.
(f) x̄_unres - x̄_deprived = (Report to 2 decimal places))
(g) Is it possible that the differences seen here could have occurred just by chance variation, due to the random assignment of subjects to groups, even if there were really no effect of the sleep condition on improvement?

possiblenot possible
(h) As usual, we want to know how PLAUSIBLE it is for us to obtain a difference in sample means at least as extreme as 15.92 by chance alone. What is the source of “chance” in this study?

random samplingrandom assignmenthypothetical
(i) Outline the steps of a simulation analysis that would explore the “could have been” outcomes under the null hypothesis by modelling the randomness described in (h). (Hint: What if I gave you some index cards?)

	Let the instructor or TA review your answer to (i) before continuing.

Simulation

The data for this study are pre-loaded into the Comparing Groups (Quantitative) applet.

Verify that the two dotplots and the observed difference in group means agree with our data.
Then check the Show Shuffle Options box and scroll to the right.
Select the Plot display.
Then press the Shuffle Responses button once and watch the dots. The values will be pooled together and then redistributed back to newly assigned groups.
What value did you get for the simulated difference in group means?
Press the Shuffle Responses button four more times. Do you get the same difference in means each time?
Change the Number of repetitions from 1 to 995 (to produce a total of 1,000 repetitions). Press Shuffle Responses.

Include a screen capture of your null distribution of simulated differences in group means.

File Upload

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(p) Describe the shape, mean, and standard deviation of the resulting null distribution.
Explain what is represented by this standard deviation value you just reported.
Now enter the observed difference in group means from the research study into the Count Samples box, use the Greater Than option (to match our alternative hypothesis), and press the Count button.
(q) What does the applet report for the "empirical" (simulation-based) p-value?
(r) Provide an INTERPRETATION of this p-value in context (make sure you address the statistic, the source of the randomness in the study, and what you mean by “more extreme”).
(s) Approximate a 95% confidence interval by taking the observed statistic and adding/subtracting 2 SDs (Hint: What are you using for the SD of the statistic?)

Conclusions
(t) SIGNIFICANCE: What conclusion would you draw from this simulation analysis regarding the question of whether the learning improvements in the sleep deprived group are statistically significantly lower (on average) than those in the unrestricted sleep group? Also explain the reasoning process by which your conclusion follows from the simulation results.
(u) ESTIMATION: Provide a one-sentence interpretation of the 2SD confidence interval you found above, in context.
(v) CAUSATION: Does the design of this study allow you to conclude that the reduction in improvement scores is caused by the sleep deprivation? Explain.
(w) GENERALIZABILITY: To what “population” is it reasonable to generalize these results?
For this lab, after you submit Jotform will send you an email with a pdf attachment. Upload this pdf file into Canvas.

If you worked with a partner on this lab, both of you need to join a Investigation 7 group before submitting.
Should be Empty:

Background

Study Design

Descriptive Statistics

Choice of Statistic

Simulation

Conclusions