Statistical Methods

  Question 1 (24 marks) A human-computer interaction (HCI) researcher was interested in examining whether humans are better able to use a joystick or a mouse to point a computer cursor. She therefore constructed an experiment in which participants used either a joystick (joystick condition) or a mouse (mouse condition) to point a cursor to a target displayed on a computer monitor. She measured the time (seconds) that it took to place the cursor over the target (dependent variable referred to as time, where a higher time score indicates poorer performance). To determine whether potential benefits of using the joystick or mouse generalized to difficult HCI scenarios, the target was either stationary (static condition) or moved slowly across the computer screen at a constant velocity (motion condition). Participants were randomly and uniquely assigned to 1 of 4 conditions in the interface (levels: joystick, mouse) × target type (levels: static, motion) experimental design. Given the data collected by the researcher (see Table 1 below), what can she conclude about how easily humans interact these HCI interfaces and how are these HCI interfaces influenced by target type? Include a line graph of the means. 3 Table 1. Target localization times in the interface × target type conditions. Subject Interface Target Time 1 Joystick Static 2.53 2 Joystick Static 2.24 3 Joystick Static 3.16 4 Joystick Static 1.50 5 Joystick Static 3.06 6 Joystick Static 2.76 7 Joystick Static 2.57 8 Joystick Static 4.03 9 Joystick Static 1.70 10 Joystick Static 0.70 11 Joystick Motion 2.00 12 Joystick Motion 2.54 13 Joystick Motion 2.23 14 Joystick Motion 0.10 15 Joystick Motion 0.75 16 Joystick Motion 1.30 17 Joystick Motion 2.11 18 Joystick Motion 2.60 19 Joystick Motion 1.05 20 Joystick Motion 2.05 21 Mouse Static 1.39 22 Mouse Static 0.67 23 Mouse Static 1.62 24 Mouse Static 1.69 25 Mouse Static 0.29 26 Mouse Static 2.29 27 Mouse Static 0.93 28 Mouse Static 1.32 29 Mouse Static 0.33 30 Mouse Static 1.67 31 Mouse Motion 1.35 32 Mouse Motion 1.29 33 Mouse Motion 1.31 34 Mouse Motion 2.48 35 Mouse Motion 1.83 36 Mouse Motion 1.03 37 Mouse Motion 2.18 38 Mouse Motion 2.01 39 Mouse Motion 1.79 40 Mouse Motion 1.87 4 Question 2 (11 marks) A marketing team wants to determine which of two prospective product lines consumers might prefer. They randomly select subjects to participate in a quantitative focus group in which half of the participants were given product A, while the other half of participants were given product B. Participants completed a questionnaire that probed their affinity for the product they inspected during the focus group. Questionnaires items were collapsed into a continuous-valued composite index of product affinity. In a preliminary analysis, the marketing team ensured that the assumption of homogeneity of variance was met: 𝐹𝑚𝑎𝑥 = 𝑠𝑙𝑎𝑟𝑔𝑒𝑠𝑡 2 𝑠𝑠𝑚𝑎𝑙𝑙𝑒𝑠𝑡 2 = 5.59 4.33 = 1.29, 𝐹𝑚𝑎𝑥.𝑐𝑟𝑖𝑡 = 4.04 . Given the product affinity data they collected (see Table 2 below), which product are consumers more likely to prefer? Show all relevant descriptive statistics. Table 2. Product affinity scores for Product A and product B. Subject Product Scores 1 A 3.27 2 A 2.52 3 A 4.83 4 A 0.68 5 A 4.59 6 A 3.84 7 A 3.35 8 A 7.00 9 A 1.19 10 A –1.32 11 B 2.69 12 B 4.04 13 B 3.26 14 B –2.08 15 B –0.44 16 B 0.93 17 B 2.97 18 B 4.17 19 B 0.30 20 B 2.80 5 Question 3 (18 marks) Sociologists investigated whether there is an association between salary and life enjoyment. They administered questionnaires to randomly selected participants who reported their salary in thousands of dollars (salary) and a battery of questionnaire items that probe life enjoyment. The life enjoyment items were collapsed into a continuousvalued composite index of life enjoyment (LE). Given their data (see Table 3 below), is there an association between salary and life enjoyment? If so, how does a change in salary quantitatively relate to a change in life enjoyment? Include a scatterplot of the data and the line of best fit. Table 3. Salary in thousands of dollars (salary) and life enjoyment composite index (LE). Subject salary LE 1 29 24 2 25 13 3 37 30 4 16 21 5 35 13 6 32 36 7 29 18 8 48 32 9 18 5 10 6 16 11 28 14 12 35 16 13 31 14 14 5 16 15 13 12 16 20 5 17 30 25 18 36 26 19 17 13 20 29 20 6 Question 4 (10 marks) Cognitive psychologists are examining the effect of visuospatial cueing on perceptual processing speed. They designed an experiment in which a square randomly appeared on either the left or right side of a computer monitor and participants were required to push a button as soon as they detected the square. Each participant repeated this action hundreds of times. On half of the trials, a quick flash of light preceded the appearance of the square and it always appeared on the same side of the computer monitor as the square (Cued condition). On the other half of the trials, no such flash occurred (Control condition). The researchers measured the average time it took participants to detect the square on trials in both the Cued and Control conditions (see Table 4 below). What can the researchers conclude about the effect of visuospatial cueing on perceptual processing speed? Show all relevant descriptive statistics. Table 4. Mean subject reaction times (milliseconds) in the Cued and Control conditions. Condition Subject Cued Control 1 204 218 2 200 225 3 212 221 4 191 195 5 210 203 6 207 210 7 204 220 8 223 226 9 193 207 10 181 219 7 Question 5 (7 marks) A pharmaceutical company is interested in examining the efficacy of a new experimental drug to reduce allergic reactions and therefore recruited subjects to participate in a randomized clinical trial. The researchers exposed participants to a benign allergen to elicit allergic reactions. Half of the participants were assigned to an experimental drug treatment condition in which they were administered the new experimental drug (Drug condition), while the remaining half of participants were placed in a placebo condition in which they received a sham pharmacological treatment (Placebo condition). They measured a continuous-valued, composite index of allergic reaction symptomology to examine whether those who received the experimental drug treatment showed a reduction in allergic reaction symptomology (see Table 5 below). Upon preliminary analysis, the researchers discovered that the assumption of homogeneity of variance was violated: 𝐹𝑚𝑎𝑥 = 𝑠𝑙𝑎𝑟𝑔𝑒𝑠𝑡 2 𝑠𝑠𝑚𝑎𝑙𝑙𝑒𝑠𝑡 2 = 6.79 1.67 = 4.07, 𝐹𝑚𝑎𝑥.𝑐𝑟𝑖𝑡 = 4.04 . Furthermore, they realized that the dependent variable was not normally distributed, as scores were heavily positively skewed. Given these observations, using a parametric analysis of the mean difference between conditions is not appropriate. What can the researchers conclude about the efficacy of the drug using a non-parametric analysis? Show all relevant descriptive statistics. Table 5. Composite allergic reaction symptomology scores in the Drug and Control conditions. Subject Condition Scores 1 Drug 1.05 2 Drug 0.70 3 Drug 2.10 4 Drug 0.20 5 Drug 1.91 6 Drug 1.38 7 Drug 1.09 8 Drug 4.41 9 Drug 0.29 10 Drug 0.02 11 Placebo 5.73 12 Placebo 8.21 13 Placebo 6.70 14 Placebo 1.00 15 Placebo 2.02 16 Placebo 3.33 17 Placebo 6.19 18 Placebo 8.47 19 Placebo 2.67 20 Placebo 5.92 8 Short Answer (30 marks) For these questions, you are given brief summaries of research scenarios and specific hypotheses. You need to choose which statistical test is appropriate to analyze the hypothesis given the context of the research scenario. Each scenario is worth 5 marks. 1 mark is for correctly identifying the appropriate statistical test. An additional 4 marks are awarded for justifying your answer with respect to 1. The type of data collected by researchers (i.e., continuous, ordinal, or nominal) 2. Whether researchers are investigating an association/relationship between at least two variables or are instead investigating differences between conditions using the same variable 3. If applicable, the number of conditions and/or factors 4. If applicable, the independence/dependence of observations between conditions You may format your answers as either short paragraphs or bullet lists. Question 1 (5 marks) A vision scientist was examining whether human depth perception relies on contextual visual information (i.e., depth cues). He constructed an experiment in which participants viewed an object in virtual reality and had to estimate how far away the object was. Participants repeated this many times and the researcher computed how accurately participants were able to infer the depth of the object. Accuracy was operationalized as the difference between participant estimates of object distance and the true distance of the object. On half of the trials, the object appeared in a long hallway with realistic décor, thus providing contextual depth cues. On the other half of trials, the object appeared in a white void of empty space. Participants experienced both trial types in randomized order and their accuracy was compared between the hallway and void conditions. If depth is inferred from visual cues, accuracy should be lower in the void condition than in the hallway condition. What analysis should the vision scientist perform to examine whether subjects we less able to infer depth when deprived of depth cues? Question 2 (5 marks) A zoologist was interested in investigating whether non-human primates (NHPs) experience attentional “pop-out”; that is, when you are visually searching for something in a cluttered environment, the object you are looking for can either be difficult to find or is immediately obvious—it “pops out”. Therefore, they constructed an experiment in which NHPs were trained to locate an object amongst clutter and he measured how long it took the NHPs to locate the object. In the baseline condition, the object was presented alone. The researcher also included 2 additional conditions in which the object was presented amongst low-levels of clutter or high-levels of clutter. The NHPs completed each condition in randomized order. If NHPs experience “pop-out”, locating the object should take equally as long in in the baseline condition as it does in both cluttered conditions. Which analysis should the zoologist perform?