Psychology 613
Data Analysis III
Prof. Bertram Malle
Spring 2008

Assignment 3a: Item Analysis

The file assign3a.dat contains the raw data you need for this assignment. Alternatively you can use the SPSS desktop file by control-clicking or right-clicking this link to save or download the file.

The data consist of personality self-descriptions on 32 unipolar adjective scales. (A complete list of the 33 variables [subnr + 32 adjectives] and their abbreviations can be found here.)

The data were collected with the purpose of demonstrating psychological differences between those people who tend to describe themselves in socially "undesirable" terms and those who tend to describe themselves in socially "desirable" terms. To perform this comparison, however, I needed to make sure that the self-description measures really hung together as multi-item scales that stand for constructs, such as extraversion/introversion, calm/nervous, etc. Your task is to assess the internal consistency of two of those scales.

In the spirit of EDA, inspect the data before you run the main analyses. After gathering distributional information on all 32 items, comment (in a few sentences) on degree of normality and frequency of outliers across the set of 32 items. SPSS's FREQUENCIES or EXAMINE command gives you all you need for current purposes. You do not have to apply any transformations, and you do not have to include any SPSS output in your homework file, only commentary.
Begin with the set of 12 adjective scales that I have selected for RELIABILITY analysis:
```
RELIAB VAR =  ALL
 /SCALE (AGREEABLENESS) =   KIND OPPOSING APPROVIN HARSH PERSEVER
 FRIENDLY CONTRARY COOPERAT QUIET CRITICAL LAX SHY
 /STA = CORR
 /SUM = TOTAL CORR.
```
Through systematic inspection of intercorrelations and alphas, and through item deletion and recoding (if necessary), develop a reliable measure of "agreeableness." For the meaning and some constituents of this dimension of the "BigFive" personality model, take a look at this table. When I did the item analysis, the alpha of my final measure was 0.77; yours should not be lower. Turn in the output of your final run, but add a verbal description of your steps that led you to this final run, along with justifications for why you took those steps.
Now construct a scale for a second construct that should be internally consistent. Choose one of the Big Five constructs that appears to be well-represented by a subset of the adjectives and run RELIABILITY analyses until you have a scale of reasonable length, meaningful items, and a good (~ 0.70) alpha.
Write a one-page summary, briefly reporting on the initial exploratory analysis (distributions, outliers), then on the two scale constructions.
Assignment 3b: Initial Principle Components Analysis (PCA)
You can reuse your SPSS data file from part 3a of this homework. You will now practice the use of PCA to illuminate the structure of these items.
1. Conduct a principle component analysis (PCA) using the SPSS FACTOR commands. In the first run, let the program extract as many components as it wants. What is the criterion that the system uses for extraction?
  FACTOR VAR = DISTANT TO EASYGOIN /plot = eigen /format = sort /extr = pc /rota = varimax.
  Note that I used the command /format = sort in the above syntax. It orders the items in such a way as to group those together that load highest on a particular PC. This greatly improves the interpretability of the component (laoding) matrices.]
2. Inspect the scree plot and comment on the "strength" (size of eigenvalue) of the various components. Does the scree plot support the number of components that the program extracted? Why did the program extract the number of components it did?
3. Look at the unrotated factor loading ("component") matrix -- can you find approximate interpretations for each component? (See again for background information.) You don't need to adopt a particular theoretical stance here; just write a sentence or two about a good interpretation of what you see.
4. Now look at the VARIMAX-rotated loading matrix and try to interpret the components you see there. Find a label and describe the variables that hang together under that label. Is there a "simple structure" - that is, are most variables clearly linked to a single component?
5. Researchers often use the results of a PCA as a guideline for forming subscales or unidimensional "tests." If PCA is used just as a guideline for scale construction, people often don't calculate the precise component scores (linear combination of the variables loading on the component, precisely weighted by their coefficients). Rather, they select the variables that load highly on the component (because only those should be retained in a parsimonious scale) and simply average them (the items may need to be standardized first, if they are in different metrics.) This is called "unit weighting." The new scale then has a coefficient alpha describing its reliability (internal consistency).
  Your task is to create a "scale" based on the third rotated component. Select the variables that load highly on that component and compute their alpha, using SPSS's RELIABILITY procedure. In your RELIABILITY analysis, weed out any variables that seem to drag down the alpha. Use the item deletion procedure to arrive at a reliable, unidimensional scale, with a reasonably small number of items. Show your initial SPSS commands, verbally report on your selection and deletion procedure, and list the variables that were retained in this scale, along with its final alpha.
6. Write a one-page summary, reporting on the PCA results (unrotated and rotated), and the scale construction based on the third rotated principle component.