Download the SPSS file from here: https://drive.google.com/file/d/0ByCGHAhT6gpJN

Question

Download the SPSS file from here: https://drive.google.com/file/d/0ByCGHAhT6gpJNkQxVXNRM1VqemM/view

Using our class data set "sociability.sav", perform exploratory factor analysis with the social anxiety scale (sa1, sa2, sa3, sa4r, sa5, sa6). Use principal component to extract the common factors and rotate the factor solutions by varimax. a. Are the variables appropriate for running an exploratory factor analysis? Why? b. How many factors should be extracted? Why? c. Interpret and label the common factors). d. How good is the factor solution? A Five-item ability test was administered to a group of 100 students. The items were in multiple-choice format with five options and among them, one is the correct choice and four are distractors. Subjects' overall performances were then classified into one of the three ability groups. Specifically, the high group (H) consisted of the top 30 students whereas the low group (L) consisted of the bottom 30 students. The remaining were in the middle group (M). The table below shows the counts of correct response on each item by the three performance groups: a. For each item, compute the difficulty index, the difficulty index controlled for guessing, and the discriminability index. b. Make a D-D (difficulty vs. discriminability) plot and decide which items should be retained.

Explanation / Answer

Part-a

From following results KMOW>0.70 and Bartlett test is signficant and also correlations are all significant so variables are appropriate for factor analysis

   KMO and Bartlett's Test
Kaiser-Meyer-Olkin Measure of Sampling Adequacy.       .782
Bartlett's Test of Sphericity   Approx. Chi-Square   666.764
   df   15
   Sig.   .000

           Correlations
       Social Anxiety 1   Social Anxiety 2   Social Anxiety 3   Social Anxiety 4 (reverse item)   Social Anxiety 5   Social Anxiety 6
Social Anxiety 1   Pearson Correlation   1   .291**   .434**   .406**   .392**   .389**
   Sig. (2-tailed)       .000   .000   .000   .000   .000
   N   526   526   526   525   526   526
Social Anxiety 2   Pearson Correlation   .291**   1   .364**   .132**   .302**   .266**
   Sig. (2-tailed)   .000       .000   .002   .000   .000
   N   526   526   526   525   526   526
Social Anxiety 3   Pearson Correlation   .434**   .364**   1   .289**   .359**   .401**
   Sig. (2-tailed)   .000   .000       .000   .000   .000
   N   526   526   526   525   526   526
Social Anxiety 4 (reverse item)   Pearson Correlation   .406**   .132**   .289**   1   .194**   .198**
   Sig. (2-tailed)   .000   .002   .000       .000   .000
   N   525   525   525   525   525   525
Social Anxiety 5   Pearson Correlation   .392**   .302**   .359**   .194**   1   .550**
   Sig. (2-tailed)   .000   .000   .000   .000       .000
   N   526   526   526   525   526   526
Social Anxiety 6   Pearson Correlation   .389**   .266**   .401**   .198**   .550**   1
   Sig. (2-tailed)   .000   .000   .000   .000   .000  
   N   526   526   526   525   526   526
**. Correlation is significant at the 0.01 level (2-tailed).

Part-b From following table we observe only one factor is sufficient as only one factor has eigen value>!

           Total Variance Explained
Component           Initial Eigenvalues           Extraction Sums of Squared Loadings
       Total   % of Variance   Cumulative %   Total   % of Variance   Cumulative %
   1   2.693   44.878   44.878   2.693   44.878   44.878
   2   .952   15.865   60.743          
dimension0   3   .809   13.476   74.219          
   4   .587   9.778   83.997          
   5   .521   8.683   92.680          
   6   .439   7.320   100.000          
Extraction Method: Principal Component Analysis.

Part-c:

We label the single factor as social anxeity

Part-d

Factor solution does not seem to be good as from following table we observe that some of factor loadings are less than 0.70

Component Matrix(a)
   Component
   1
Social Anxiety 1   .739
Social Anxiety 2   .565
Social Anxiety 3   .723
Social Anxiety 4 (reverse item)   .512
Social Anxiety 5   .720
Social Anxiety 6   .724
Extraction Method: Principal Component Analysis.
a. 1 components extracted.

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