For Questions 11-15, use SPSS or some other program to analyze data in the “Gamer-NongamerRTs” file posted to the 9/25 module. The data in that file refer to a study similar to the one in the Caffeine study that was just described 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 “reaction times” in this paradigm. The potential difference to be tested here is between a sample of "gamers" (i.e., people who routinely play video games) versus "nongamers" (i.e., people who rarely or never play video games).

Q11: What is the estimated standard error of the difference in means for these reaction times?

Question

For Questions 11-15, use SPSS or some other program to analyze data in the “Gamer-NongamerRTs” file posted to the 9/25 module.  The data in that file refer to a study similar to the one in the Caffeine study that was just described 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 “reaction times” in this paradigm. The potential difference to be tested here is between a sample of "gamers" (i.e., people who routinely play video games) versus "nongamers" (i.e., people who rarely or never play video games).

Q11: What is the estimated standard error of the difference in means for these reaction times?

BlackTom AI · Accepted Answer

The provided item is a numerical question asking for the estimated standard error of the difference in means between two groups (gamers vs nongamers) based on reaction time data. However, the actual dataset values are not included here, so we cannot independently verify a numeric value like 6.636. Instead, here is how you would determine the SE of the difference in means from the data if you were analyzing it in SPSS or a similar program.

- Step 1: Separate the data into two groups. Identify which participants are categorized as gamers and which as nongamers, and record the sample size in each group (n1 for gamers, n2 for nongamers).
- Step 2: For each group, compute the descriptive statistics: the group mean (M1, M2) and the group variance or standard deviation (s1^2, s2^2). The standard errors for each group are not directly used for the difference in means, but the variances are.
- Step 3: Determine which standard error formula to use. If you assume equal variances across groups and you plan to pool the variances, you would compute the pooled variance sp^2 and then the standard error of the difference as SE_diff = sqrt( sp^2 * (1/n1 + 1/n2) ). The pooled variance is sp^2 = ((n1 - 1)s1^2 + (n2 - 1)s2^2) / (n1 + n2 - 2).
- Step 4: Alternatively, if you do not assume equal variances (the Welch approach), you would compute SE_diff = sqrt( s1^2/n1 + s2^2/n2 ), which does not pool variances. This yields a different standard error and uses the individual group variances.
- Step 5: In SPSS, you can obtain the standard error of the difference in means directly from an independent-samples t-test output. Look for the row corresponding to the comparison between Gamers and Nongamers and use the value labeled as the standard error of the difference (often labeled SE or Std. Err. of the Difference). Depending on which model you specify (equal variances assumed vs. not assumed), you may see two SE values.
- Step 6: Verify the inputs. Ensure reaction times are clean (no outliers or incorrect entries) and that the group labels are accurate. If the data are not balanced (unmatched sample sizes), the SE will reflect the n1 and n2 values accordingly.

Why the stated numeric value could be incorrect without the data: the number 6.636 could only be confirmed by plugging the actual group variances and sample sizes into the chosen formula (pooled or unpooled) and performing the calculation. Since s1^2, s2^2, n1, and n2 are not provided in the prompt, any single numeric answer here is not verifiable from the information given. If you have access to the dataset, apply the steps above (preferably via SPSS or an equivalent tool) to obtain the correct SE_diff and compare it to 6.636.

Contextual notes:
- If reaction times are measured in milliseconds, the SE will have the same units as reaction time. A value around 6.6 ms could be plausible depending on variability and sample sizes, but this is purely speculative without the data.
- When reporting results, it is good practice to state which SE formula was used (pooled vs. unpooled) and to report n1, n2, s1, s2 alongside the SE and t-statistic for the difference in means.

PSYCH 3321 SP2025 (28481) Homework 6

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