A researcher is interested in the effects of a psychedelic drugin treating post-traumatic stress disorder (PTSD). To assess if thepsychedelic may be effective in attenuating the severity of PTSDsymptoms, she performs a pilot experiment to compare the effects ofthe psychedelic to the commonly?prescribed selective serotoninreuptake inhibitor (SSRI) Sertraline in individuals diagnosed withPTSD. The amount of the psychedelic was selected based on an onlineforum in which recreational drug users describe their drug-takingexperiences. Previous research has indicated that 100 mg Sertralineis an effective amount for the general population in clinicalsettings. Individuals with PTSD were randomly assigned to one oftwo treatment conditions: Psychedelic or Sertraline. The dependentvariable is a score on the PTSD Checklist (PCL); a lower scorecorresponds to fewer PTSD symptoms. The scores are presented in thetable below.
Psychedelic Group (25 mg) | Sertraline Group (100 mg) |
Subject | PCL scores | Subject | PCL scores |
1 | 5 | 12 | 27 |
2 | 4 | 13 | 18 |
3 | 5 | 14 | 13 |
4 | 7 | 15 | 13 |
5 | 8 | 16 | 12 |
6 | 10 | 17 | 11 |
7 | 6 | 18 | 7 |
8 | 7 | 19 | 23 |
9 | 7 | 20 | 10 |
10 | 8 | 21 | 8 |
11 | 5 | 22 | 8 |
- State the H0for the experimentabove. Please use appropriate notation
- Perform the Unpaired t-test on excel. Treat the Sertralinegroup scores as “Variable 1” and the Psychedelic group scores as“Variable 2”. Report the results of the statistical analysis below.Be sure to include the df, the obtained statistic, and thep-value in your answer. Please round all answers to twodecimal places.
- t(_____) = _____, p = _____.
- What do you conclude based on these results?
- For Excel: subtract each Sertraline score fromthe Psychedelic score and compute the mean of thesedifferences. Calculate standard deviation ofdifferences using Excel function: =stdev.s. Calculate themargin of error in the confidence interval using the Excelfunction: =confidence.t(alpha, standard deviation, number ofdifference scores). Add and subtract the margin of error toand from the mean of the differences to obtain the upper and lowerlimits, respectively. Report the 95% confidence intervalfor the difference between means here: (____, ____). Are yourconclusions about the 95% confidence interval consistent with theresults you reported in question 2b above, and, ifso, why?
- Report the 95% confidence interval for the psychedelicgroup here: (____, ____).
Report the 95% confidence interval for the sertralinegroup here: (____, ____).
Excel: use the =confidence.t(alpha, SDof the group, sample size) function to determine theconfidence interval for each group: this will give you the marginof error. Also, compute the means of each group. Next, add andsubtract the margin of error to the mean of each group to get theset of confidence limits. Inspect the confidence intervals anddetermine if there is a statistically significant differencebetween the two groups. Are these results consistent with theresults you reported in question 3 above?
- Compute the “Difference between means” in Excel by subtractingthe mean of the psychedelic group from the mean of the sertralinegroup and p-value from the statistical test. Fill thespaces below to define the meaning of the obtainedp-value and include the “Differencebetween means” value in your answer.
There is a ___________ probability of obtaining a meandifference at least as large as ________________ units under thecondition that the null hypothesis is true.
- According to the quick plot of the data, determine if thereenough evidence/reason to claim heterogenous variances. Name thetest that could be performed in the case of unequal variances._______________________
Now imagine that this was a one-group, pretest-posttest design.The severity of the volunteers’ PTSD symptoms was measured usingthe PCL before psychedelic administration (pretest) and thenafterwards (posttest). Those scores are presented below.
Subject | Pretest | Posttest |
1 | 25 | 15 |
2 | 24 | 18 |
3 | 25 | 13 |
4 | 27 | 13 |
5 | 28 | 12 |
6 | 30 | 11 |
7 | 26 | 7 |
8 | 27 | 23 |
9 | 27 | 25 |
10 | 28 | 18 |
11 | 25 | 22 |
- Perform paired t-test on excel. Try to achieve positive valuesin your results by selecting “Report differences as: by treatingPretest as “Variable 1” and Posttest as “Variable 2”. Report theresults of the statistical analysis below. Be sure toinclude the df, the obtained statistic, and the p-value inyour answer. Please round all answers to two decimalplaces.
- t(_____) = _____, p = _____.
- What do you conclude based on these results?
- For Excel/other software users; subtract eachposttest score from the pretest score and compute the mean of thesedifferences. Use the standard deviation and confidenceinterval formulas above to complete this problem. Reportthe 95% confidence interval for the mean of differences here:(____, ____). Note: the center of this interval should bethe mean of the difference. Are your conclusions about the95% confidence interval consistent with the results you reported inquestion 8d above, and, if so, why?
- Someone in the research team advises the researcher to comparethe 95% confidence interval for the pretest scores to the 95%confidence interval for the posttest scores. Why is this analysisincorrect for these data? Hint: think about what is analyzed in apaired t-test.
