Please read N. H. Anderson (1965). This homework uses MATLAB files:

• NHA65CW.m. The partial replication of the experiment.
• NHA65mergedata.m. A program that merges individual data files into a master file.
• NHA65stats.m. A program that performs descriptive and inferential statistics on the master data file.
• NHA65averagingModel.m. The averaging model.

For all of the questions below, hand in (on the due date) the relevant snippets of output from MATLAB, such as command-window output or graphical output or M-file code. Please do not waste trees by printing pages and pages of irrelevant output.

1. Study the ethics of administering experiments to human participants. The goal of this exercise is for you to be aware of ethical considerations when creating and running experiments.
   • Read The Belmont Report. Very briefly summarize the three main points in the Applications section.
   • Read the I.U. web pages regarding protection of human subjects: STUDENT RESEARCH and Student Research Policy and Non-Research. What are the three criteria by which student projects do not require HSC approval?

2. Explore the replication of the experiment. The goals of this exercise are to understand how to program an experiment in Matlab and to generate data for analysis and modeling. RUN THE EXPERIMENT AS SOON AS POSSIBLE SO THAT THE DATA FILES CAN BE POSTED. You get credit for this exercise when you e-mail your data file to Prof. Kruschke. Load NHA65CW.m into your directory and run it, following the directions.

   After running the program, for your own edification, notice the sections of the program. These sections will be ordered much the same way in most experiments, including the one you will eventually program for your own project. Notice the way, in Matlab, that information is gathered from the user and the way data are stored. There are many subtleties in numeric and string and cell formatting; get used to reading the Matlab help files!

3. Data analysis. The goal of this exercise is for you to explore aspects of data analysis in Matlab, and to see whether our replication data match the 1965 data.
   • Get the 2005 class data files from this link. Do this only after at least 15 people (in 2005) have contributed data. Copy each one into your own directory, being sure that there are no extra blank lines inserted between rows. (This might be a little tedious, but it only takes a few minutes.) The program, NHA65mergedata.m, merges individual data files into a master file. Study this program so that you are familiar with how files are read. Merge the data files using this program. In your projects, you will have to do something like this, i.e., merge the data, as individuals e-mail you their data.
   • The program, NHA65stats.m, performs descriptive and inferential statistics on the master data file. Run the program.
     A. On the boxplot, mark any non-monotonicities of the medians. Also, mark any outliers (e.g., circle or highlight them).
     B. Look at the program and extend the t-test section to include the two additional tests indicated. Show the output of the tests.
     C. Consider the results of the t-tests. Are the predictions of the averaging model confirmed?

4. Fit the averaging model to the data. The goal of this exercise is to explore the model and its ability to fit the data. Copy the averaging model into your directory. Read the comment section at the top of that file. In particular, read about the extension of the model to make it probabilistic, for which an extra parameter (n) is needed.

   Notation: V_H is the underlying psychological value of a high trait. H is the overt rating given to a high trait.

   • Anderson (1965) seems to claim that, if V_H > V_Mp and that V_L < V_Mm, then the (deterministic) averaging model predicts H > H.Mp and L < L.Mm. Is that always true? That is, are there parameter values for which that is not true? If so, give an example of such parameter values. (Hint: Pick some constant values for V_H > V_Mp > V_I. Then compute the predicted ratings for H and H.Mp as a function of the value of the averaging weight, w. Again, this is for the deterministic model; don't include the noise term.)
   • Try fitting the model to (mean) data that are actually generated by the (deterministic) model. (When doing your fit, make sure that the number of iterations in fminsearch is set high enough that it converges. In the output, 'exitflag' should not be 0.) Specifically, let V_L=0, V_Mm=20, V_Mp=75, V_H=95, V_I=65 and w=0.7. Compute the predicted ratings for the 10 conditions (which you can easily do by scavenging snippets of code from the averaging model and putting into a new Matlab program). Now use those predicted ratings as data to be fit by the model. Initialize fminsearch at [ 0 25 75 100 50 0.5 10 ]. Does fminsearch settle onto the parameter values that generated the data? Try initializing the search with the correct parameter values. Does fminsearch stay there or stray away?
   • Now fit the model to the mean of the class data. (When doing your fit, make sure that the number of iterations in fminsearch is set high enough that it converges. In the output, 'exitflag' should not be 0.) Report the results for the following initial parameter vectors:
     [ 0 25 75 100 50 0.7 20 ]
     [ 0 25 75 100 50 0.1 20 ] What is the effect of small w?
     [ -10 20 80 110 50 0.7 20 ] Is it okay to have values <0 or >100?
     [ 0 25 75 100 80 0.7 20 ] What is the effect of large I?
   • The previous part found the maximal likelihood estimates of the parameters. If we were instead taking a Bayesian approach to parameter estimation, what would we do? Don't actually do the Bayesian approach; just briefly describe the steps involved if we were to apply it to the averaging model.