Chat with AIExam 15: Factor Analysis and Reliability Analysis: Data Reduction Techniques
What are three of the criteria that researchers can use to determine how many factors should be retained from an EFA?
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VerifiedEigenvalues, percentage of variance explained, and theory. A general rule of thumb is that factors should have eigenvalues over 1.0 and explain at least 10% of the variance of all of the items in the factor analysis in order to be retained. In addition, the factors should make sense conceptually and theoretically. Just because items load together onto a factor, if it does not make sense for the items to be combined into a single factor then the factor should perhaps not be retained.
What does it mean to say that an item is "cross-loaded" on two factors?
(30) VerifiedThis means that the item, or measured variable, loads meaningfully (e.g., greater than .30) on more than one factor. This is problematic because it means that this item is not a particularly strong indicator of either factor and does not do a good job of distinguishing between the factors.
Suppose that I performed a reliability analysis to determine whether high school students' grades in four different subjects (English, Math, Science, Social Studies) formed a reliable scale with a high Cronbach's alpha. I performed the analysis and got the results presented in the two tables below.
Reliab ility Statistics Cronbach's Alpha N of Items .892 4 Scale Mean if Item Deleted Scale Variance if Item Deleted Corrected Item-Total Correlation Cronbach's Alpha if Item Deleted English grade 21.9358 111.296 .769 .859 Math grade 23.1301 109.392 .700 .886 Science grade 22.1658 105.074 .801 .847 Social studies grade 21.5330 110.514 .787 .853 a. What is the reliability of this scale, as indicated by the Cronbach's alpha. Is this a high or low level of reliability?
b. Which item seems to be contributing the least to the overall Cronbach's alpha?
c. Which item, if any, would you recommend removing from this scale?
(31) Verifieda. The Cronbach's alpha for these four items is .892, which is quite high. This indicates that these four items form a scale with strong internal reliability.
b. All four of the items seem to be good indicators of the scale. In the far right column of the second table, under the heading "Cronbach's alpha if item deleted," you can see that the alpha would go down slightly if any of these items were deleted. However, it would go down the least if the item "Math grade" were deleted, from .892 to .886. This suggests that the Math grade item is contributing the least to the overall alpha.
c. None, as the alpha is highest when all four of the items are included in the scale.
What is the purpose of conducting an exploratory factor analysis (EFA)?
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