Assignment II for Biostats Course VHM 801 at AVC - Fall semester 2018

The assignment is worth 15% of the final course mark. Please be aware that by handing in the home assignment you implicitly acknowledge to have read and accepted the instructions for home assignments as described on the VHM 801 homepage.

The assignment is based on data from a trial to investigate whether intellectual performance can be affected (improved) by the ambience under which the work is carried out. For simplicity we will refer to a an environment designed to possibly improve performance as an ``enhanced environment'', contrasting a ``neutral environment'' where the specific stimuli under study have been omitted. We have data consisting of recordings for 20 subjects selected for the study. Each subject completed a certain type of visual puzzles within both environments, and the completion times for those puzzles were taken as performance measures. The subjects completed the two puzzles within the same environment immediately after each other, whereas a longer time separation existed between the trials in the two different environments. Half of the subjects started their trials in the enhanced environment, the others starting with the neutral environment. The data contain for each subject, the completion times for all four puzzles, the order of completion and some basic demographic information.

• id: subject id (without any meaning for how the study was conducted),
• sex: sex of subject (M=male, F=female),
• age: age of subject (years),
• order: order of environments (EN=enhanced followed by neutral, NE=neutral followed by enhanced),
• etime1: first completion time in the enhanced environment (seconds),
• etime2: second completion time in the enhanced environment (seconds),
• ntime1: first completion time in the neutral environment (seconds),
• ntime2: second completion time in the neutral environment (seconds).

The home assignment has four questions (a)-(d) which should all be answered.

1. Characterize the experimental design (e.g., one-sample or another type), and describe whether randomization and blinding might have been applied to the study, and if so, outline briefly how. Discuss also briefly whether the study seems to have a reasonable balance with respect to the demographic variables. (Hint: You will need to determine which feature(s) of the study design an (im)balance could apply to.)

2. As one of the questions of interest, the researchers would look at whether people tend to complete the puzzles faster in the enhanced than the neutral environment. From the four completion times (per subject), construct a single variable that describes the overall difference between completion times recorded in enhanced and neutral settings. (Hint: The construction should involve both averaging and subtraction. It may help you to think about it in two steps where in the first step, one variable is created to summarize the enhanced trials and another variable is created to summarize the neutral trials.) Use graphical and numerical descriptive statistics to illustrate whether the data for this constructed variable point towards faster or slower completion times in the enhanced setting. Supplement the descriptive analysis with an (inferential) assessment of whether there is any evidence in the data of a difference between the two environments. (Hint: An inferential assessment may e.g. involve a confidence interval or a statistical test. Also, for this question you should disregard all concerns arising from the following questions.)

3. Use graphical and numerical procedures to determine how the order of the two environments affects the variable you constructed in (b). Again, supplement with an (inferential) assessment of whether any noted effect could be attributed to chance alone, and draw conclusions. Additionally, discuss whether the results raise any concerns for the previous analysis regarding the difference between environments.

4. This question has two parts, i. and ii. below, of which you are only required to answer one correctly to achieve a full score. Although not recommended, it is allowed to answer both parts, and in that case your score for (d) will be the best of the scores obtained for the two parts.
   1. Continue the analysis of completion times from the previous questions by constructing for each subject a new variable describing the overall difference in completion times in the first and second environments each subject was exposed to, where first and second refer to the order in which the trials were conducted. For this new variable, carry out a similar analysis as in parts (b) and (c), and draw conclusions. Think carefully about the interpretation of estimates and/or tests, and write a combined conclusion summarizing all the results obtained in parts (b)-(d).

   2. Another question of interest to the researchers of the study was whether the enhanced environment affects a person's ability to learn. In order to explore this, we will need a single variable computed for each subject and environment that expresses the speed of learning. That is, we need to construct a new variable from the two completion times within the same environment to quantify the improvement in completion time from the first to the second trial. As a way to control for differences in subjects' initial speed, it would be meaningful to express the improvement as a percentage relative to the initial speed. After having constructed such a new variable, carry out an analysis to compare the learning speed in the two environments, similar to the analysis for completion time in parts (b) and (c), and draw conclusions for this research question.