For Questions 6-10, use SPSS or some other program to analyze data in the “Caffeinated RT” file posted to the 9/25 module. The data in that file refer to a study in which participants respond to a number of stimuli to identify when a “test stimulus” appears on screen among an array of different stimuli. The first column of data simply contains an arbitrary subject number for each participant. The second column lists participants’ average of their “normal reaction times” in this paradigm. The third column lists the same participants’ average of their reaction times in this paradigm 45 minutes after they have consumed a caffeinated energy drink (enough time for the caffeine to be absorbed).

Q6: What is the estimated standard error of the mean of the differences between the "normal" and "caffeinated" reaction times?

Question

For Questions 6-10, use SPSS or some other program to analyze data in the “Caffeinated RT” file posted to the 9/25 module.  The data in that file refer to a study in which participants respond to a number of stimuli to identify when a “test stimulus” appears on screen among an array of different stimuli.  The first column of data simply contains an arbitrary subject number for each participant.  The second column lists participants’ average of their “normal reaction times” in this paradigm. The third column lists the same participants’ average of their reaction times in this paradigm 45 minutes after they have consumed a caffeinated energy drink (enough time for the caffeine to be absorbed).

Q6: What is the estimated standard error of the mean of the differences between the "normal" and "caffeinated" reaction times?

BlackTom AI · Accepted Answer

The question asks for the estimated standard error of the mean of the differences between the 'normal' and 'caffeinated' reaction times.

First, restate what you would need from the data: for each participant i, you have two measurements — the normal RT (let's denote as RT_normal_i) and the caffeinated RT (RT_caffeinated_i). The natural quantity to analyze for a paired design is the difference for each participant:
  d_i = RT_caffeinated_i − RT_normal_i  (or RT_normal_i − RT_caffeinated_i, depending on the convention you choose).

Next, you compute the mean difference across all participants:
  mean_d = (1/n) * sum(d_i)

Then, determine the variability of these differences using the standard deviation of the differences:
  s_d = sqrt( sum( (d_i − mean_d)^2 ) / (n − 1) )

Finally, the standard error of the mean of the differences (SEM) is:
  SEM_d = s_d / sqrt(n)

Notes and potential pitfalls:
- n is the number of participants (the number of paired observations), which you obtain from the first column that lists a subject number for each participant.
- If you compute differences as RT_normal_i − RT_caffeinated_i, mean_d will have the opposite sign compared to RT_caffeinated_i − RT_normal_i, but the SEM will be the same since it depends on the dispersion around mean_d, not the direction of subtraction.
- In a practical SPSS workflow, you would compute a difference variable (e.g., DIFF = caffeinated − normal) for all cases, run a Descriptives or Explore to obtain mean and standard deviation of DIFF, and then compute SEM as (SD of DIFF) / sqrt(n). If SPSS provides SE for the mean directly in an output table, you could use that value as SEM_d.

What you cannot determine from the question alone:
- The numeric SEM value (e.g., the specific 5.417 you might see) cannot be obtained without the actual data (the n participants and the paired RT values or the per-subject differences d_i).
- Without the data or a precomputed list of d_i values, you cannot verify the result, check assumptions, or reproduce the SEM calculation.

In practice, to answer Q6, you would:
- compute d_i = RT_caffeinated_i − RT_normal_i for each participant i,
- determine n (the number of participants),
- calculate mean_d and s_d from the d_i values,
- then compute SEM_d = s_d / sqrt(n),
- report SEM_d as the estimated standard error of the mean of the differences.

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