1. ## factor analysis

i have a set of 30 questions and want to factorize them. after performing factor analysis with spss (both non-rotated and rotated), still i can not group the questions into the 9 factors suggested. what should i do?

thanks!

2. hello.
why 9? how many can you group them into?

3. after 'data reduction", 9 components were found.

thanks!

btw, how to test the normality of my data? subjects scored each question from 1-5. is that i have to pool all the answers together and see how the scores are distributed? how can i do it with spss?

thanks again!

4. well..i'm not really sure what your data is...and you could take a second opinion on this...
but usually you check the distribution of data within each variable that you will use in the analysis

your variables will be...questions? so you will have to check the distribution of the various answers (1-5) for each question..

It is quite straightforward in SPSS:
1. As a first step you can draw the histograms and look at the normality curve. Graph>Histogram>select variable (question)>check 'display normal curve'>ok
2. You can also look at normality tests in Analyze>Descriptive statistics>Explore command>select the variable>Both stats & plots>in plots: check normality plots with tests
3. Graphs>P,P>select variable>Test distribution: Normal

here is a link for exploratory data analysis http://www.microbiologybytes.com/maths/spss2.html

I hope that's some help

5. thank you madhatter. from the "test of normality", the p-values are all .000 in both kolmogorov-smirnov and shapiro-wilk. is that imply that my data is not normally distributed?

in my dataset, i have 300 patients completed a questionnaire with 30 questions. the answer to each question is 1 to 5. i tried "data reduction" in spss to factorize the data and 10 (not 9) components were resulted (all with eigenvalue >1). From the "component matrix", rotated and non-rotated, there was no clear cut in grouping the questions. any comments?

thanks!

6. i have a set of 30 questions and want to factorize them. after performing factor analysis with spss (both non-rotated and rotated), still i can not group the questions into the 9 factors suggested. what should i do?

Are the 30 questions from an established/published instrument that has been used (factor analysed) previously? Is this why you think you should be getting 9 factors?

If you identify 10 factors based on your eigenvalues (i.e. above 1.0), and previous research has identified 9, what is the eigenvalue of your 10th factor (is it close to 1.0)? What does the scree plot indicate?

If you have developed the 30 questions yourself, why are you expecting 9 factors? Nine factors from a set of 30 questions seems like a lot. Do the factors make sense? i.e. can you recognise why the particular items have loaded together?

btw, how to test the normality of my data?

For large sample sizes (300 isnt super large but its getting up there) i think the normality test is too sensitive. I generally go off skewness and kurtosis indices. Look for variables above +-1.0.

Hope this helps.

7. The default in SPSS is to extract all factors with eigenvalues over 1 (Kaiser's stopping rule). This isn't really sufficient in order to determine an interpretable and useful factor structure - it's just a very basic guideline that will in many cases extract more factors than necessary. Remember that a factor with an eigenvalue of 1 explains only as much variance as a single item.

I'd suggest you find a multivariate text (e.g. Tabachnick and Fidell) and read up about factor analysis - the technique involves a lot of semi-subjective decisions that need to be made carefully, it's not really one where you can just plug numbers into SPSS and come out with an answer, sadly!

In terms of deciding how many factors to extract, I prefer using a scree test and looking for a 'break' in the eigenvalues, but there are other criteria in use - e.g. selecting factors that explain more than 5% of the explained variance.

8. thanks all. the output is like this:

9. Looks like a one factor solution to me. See how the first factor explains far more of the variance than any of the others - which all have steadily decreasing returns? There's a huge gap between the first and second eigenvalues, and then very small, similarly sized gaps from then on. You could run a confirmatory analysis if you're keen on structural equation modelling, but it really does look like a simple unitary factor structure.

10. thanks a lot CowboyBear! so in this situation, i can just conclude that all questions can be grouped into 1 factor and give a general interpretation to the factor?

regarding test of normality, the output is here. is that the data is not normally distributed?

many thanks!

11. Yep, a one factor solution seems warranted - the next step is probably scale/reliability analysis, to see how internally consistent the items are and whether the removal of any items would improve the consistency (Cronbach's alpha, the usual measure of internal consistency, assumes a one-factor structure, loosely speaking).

The test results indicate that the null hypothesis of normally distributed items doesn't hold (p values under 0.05), but given your large-ish sample there'd almost inevitably be evidence to reject the null hypothesis. The more important issue is how badly the normality assumption is violated - the skewness/kurtosis values of q30 that you show are fairly small, indicating the assumption isn't breached too badly. Google/google scholar "skewness kurtosis rules of thumb" to get an idea what cutoffs are in use. Small to moderate breaches of normality in the factor analysis context aren't too big a problem, the technique's reasonably robust.

12. You might also look closely at your rotated component matrix. While .30 (I think) is the recommended min level (check Tabachnick & Fidell or other MV stats text) for practical significance you might adopt a higher value? You also have a number of items that cross-load on different factors. It might be that you have one or two items that are having a big impact on they way all other items are loading.

Run your factor analysis again without these items that are cross-loading and see if the total variance explained is improved.

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