Education 257 FINAL PROBLEMS, Winter 2003, March 13, 2003 Solutions for these problems are to be submitted in hard-copy form. Given that these problems are untimed, some care should be taken in presentation, clarity, format. Especially important is to give full and clear answers to questions, not just to submit unannotated computer output, although relevant output should be included. You may use any inanimate resources--no collaboration. This work is done under Stanford's Honor Code. Please read the questions carefully and answer the question that is asked. Papers will be scored into 3 categories: "Excellent" indicates successful completion of all parts of all questions (within perhaps one or two very trivial arithmetic errors); "Satisfactory" indicates a good attempt was made at all parts of all problems, but there were some serious errors or omissions; "Incomplete" indicates inadequate effort or performance. Place completed hard copy in Rogosa's Cubberley mailbox by 5PM Friday 3/21 As usual for data sets path is /afs/ir.stanford.edu/class/ed257/HW or /usr/class/ed257/HW ] By student request duplicates of these data sets are provided through http links You should note that this turns out to be a very very easy set of problems, so my expectations are high........ =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= 1. Why Worry? Doctoral research from one Pamela S Clute appearing in the Journal for Research in Mathematics Education (1984) investigated the level between anxiety and mathematics achievement. The outcome ("score") is the score on the exam for a College-level mathematics survey course. The design was 2 x 3 x 2 with 7 replications per cell. Factor A ("method") was method of instruction-- a standard direct instructional method and a direct instruction discovery method (which developed the subject by a sequence of questions). Factor B ("anxiety") was the anxiety level of the student; students were assessed and placed into low, medium, high, anxiety levels. Factor C ("college") was the college at which the mathematics course was given: U.C. Riverside, CSU San Bernardino. None of the three factors can be considered random factors. Based on the summary statistics given in the report of the research, the data were recreated (approximately). In file mathanxiety.dat are score C1, method C2, anxiety C3, college C4 a. Construct useful displays of the cell means for this factorial design and comment. b. Carry out tests for the 3 main effects and interactions, controlling your overall error rate so that it does not exceed .05. What effects appear significant? c. Construct a profile plot depicting any sizable two-way or three-way interactions =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= 2. Subtlety is always lost on me. Many studies have supported the assertion that females are superior to males in decoding nonverbal cues. Robert Rosenthal, in various studies, has looked at three different types of nonverbal cues, often termed Channels: specifically, face, body, and tone of voice. The data file is nonverbal.dat. The outcome measure is skill at decoding the nonverbal cues (in C1). The design is a 2x3 with gender the row factor (C2) and nonverbal cue (Channel) the column factor (C3). (Data are recreated from summary statistics.) In our version of this study we have 4 female subjects in each level of Channel (C2 = 1) and 2 male subjects in each level of Channel (C2 = 2). a. examine cell means and comment on apparent main effects and interactions. b. Carry out test for main effects and interactions, controlling your overall Type I error rate. Describe your results. =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= 3. This problem and adapted data are taken from a text by an illustrious educational researcher. Research Setting: The general concern is with childhood aggressive behavior (and especially its persistence into adult violent behavior and other negative outcomes). Hudley&Graham (Child Development, 1993) conducted a study (based on attribution theory) which had as one of its outcome measures an assessment of negative intent. The rationale for this measure being that a boy's aggressive behavior might be a consequence of their misattributing the intent of others ("actors")in ambiguous situations. Thus, an intervention that taught these boys to interpret actors' intent as something other than negative in ambiguous situations should ultimately lessen their aggressive behavior. Data: In the Hudley&Graham study African American boys. average age about 10.5 years, were assigned at random to one of three experimental groups: (1) a 12 session intervention to infer non-hostile intent in ambiguous situations; (2) attention training (a lesser program to deal with effects of participating in a study); (3) control group (no intervention or training). Data on 36 subjects are in file aggress.dat . c1 has Negative Intent Rating and c2 contains membership in the three experimental groups (intervention = 1; attention = 2; control = 3). a) Write a statistical model for this single classification data structure b) carry out an anova for this one-way classification and test the omnibus null hypothesis of no differences between the group means for Negative Intent using Type I error rate .05. c) carry out a post-hoc pairwise comparison procedure using the Tukey Method in order to construct interval estimates for all pairwise comparisons with family-wise confidence coeff .95. d) in planning a follow-up study which will have equal numbers of subjects in each group, how many subjects should there be in each group so that the interval estimate for these pairwise comparisons will have width of 1.5 units (using experimentwise error rate .01, i.e. confidence coefficient .99)? =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= 4. [Instructors note: I don't cotton to the aroma therapy nonsense, but I have to acknowledge the following story. In the last version of Ed257 one day Andrew Ho came to class attempting to consume a late lunch consisting of some of the "food" from the basement emporium. To my amazement, the pungent smell from Andrew's plate prevented me from being able to complete a paragraph, and after repeated attempts, I had to ask Andrew to eat in the hallway so I could continue class.] Can pleasant aromas help a student learn better? Hirsch and Johnston, of the Smell & Taste Treatment and Research Foundation, believe that the presence of a floral scent can improve a person's learning ability in certain situations. In their experiment, 22 people worked through a set of two pencil and paper mazes six times, three times while wearing a floral-scented mask and three times wearing an unscented mask. Individuals were randomly assigned to wear the floral mask on either their first three tries or their last three tries. Participants put on their masks one minute before starting the first trial in each group to minimize any distracting effect. Subjects recorded whether they found the scent inherently positive, inherently negative, or if they were indifferent to it. Testers measured the length of time it took subjects to complete each of the six trials. In file scent.dat C1 ID: C2 Sex: M=male, F=female C3 Age: Age in years C4 Smoker: Y if subject smoked, N if did not C5 Opinion: "pos" if subject found the odor inherently positive, "indiff" if indifferent, "neg" if inherently negative C6 Order: 1 if did unscented trials first, 2 if did scented trials first C7 U-Trial 1: length of time required for first unscented trial C8 U-Trial 2 : length of time required for second unscented trial C9 U-Trial 3: length of time required for third unscented trial C10 S-Trial 1 : length of time required for first scented trial C11 S-Trial 2 : length of time required for second scented trial C12 S-Trial 3: length of time required for third scented trial There are various structures of these data to investigate in understanding the possible effect of aroma. Work hard to find a good analysis for these (repeated measures) data. One way to use the outcome measures is to look at improvement, which could be expressed as the percentage change in speed of completion from the first trial to the third trial for each maze. Are there better approaches? =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= 5. PART I Average salary paid to teachers and expenditures per pupil are two commonly used measures of the amount of money spent on education. Data on these two measures are provided by state, and states are classified by region of the country. (Data from the 1980's) What can be learned from this state-level data? Are these variables associated? How do you interpret that? Are there regional differences? Description:file edspend.dat Average salary paid to teachers and expenditures per pupil on education in the 50 states and the District of Columbia. Number of cases: 51 Variable Names C1. State: State C2. Region: Region C3. Pay: Amount of pay in thousands C4. Spend: Average amount spent per student in thousands Part II In course example file grow.dat are data from the Berkeley Growth Study (Nancy Bailey). These data are for Child #8 in the BGS study with age in months in C2 (ranging from 1 to 60) and intellectual performance (outcome) in C1. Try out methods for straightening the C1 on C2 scatterplot by transformations of C1. Obtain a prediction equation for intellectual performance as a function of age. Give the fit and an interval estimate for intellectual performance at 10 months of age. Repeat for 60 months of age. =-=-=-=-=-=-=-=-=-= END