Question 1

What are three of the criteria that researchers can use to determine how many factors should be retained from an EFA?

Accepted Answer

Eigenvalues, 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.

Question 2

What does it mean to say that an item is "cross-loaded" on two factors?

Accepted Answer

This 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.

Question 3

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.
 $\begin{array}{c}
\text { Reliab ility Statistics }\
\begin{array}{|r|r|}
\hline \begin{array}{c}
\text { Cronbach's } \
\text { Alpha }
\end{array} & \text { N of Items } \
\hline .892 & 4 \
\hline
\end{array}
\end{array}$ $\begin{array}{|l|c|r|r|r|}
\hline & \begin{array}{c}
\text { Scale Mean } \
\text { if Item } \
\text { Deleted }
\end{array} & \begin{array}{c}
\text { Scale } \
\text { Variance if } \
\text { Item Deleted }
\end{array} & \begin{array}{c}
\text { Corrected } \
\text { Item-Total } \
\text { Correlation }
\end{array} & \begin{array}{c}
\text { Cronbach's } \
\text { Alpha if Item } \
\text { Deleted }
\end{array} \
\hline \text { English grade } & 21.9358 & 111.296 & .769 & .859 \
\text { Math grade } & 23.1301 & 109.392 & .700 & .886 \
\text { Science grade } & 22.1658 & 105.074 & .801 & .847 \
\text { Social studies grade } & 21.5330 & 110.514 & .787 & .853 \
\hline
\end{array}$ 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?

Accepted Answer

a. 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.

Question 4

What kinds of variables are appropriate to use in a factor analysis?

Accepted Answer

The answer of What kinds of variables are appropriate to...

Question 5

How does an EFA differ from a confirmatory factor analysis (CFA)?

Accepted Answer

The answer of How does an EFA differ from a...

Question 6

What is the purpose of conducting an exploratory factor analysis (EFA)?

Accepted Answer

The answer of What is the purpose of conducting an...

Exam 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?

What does it mean to say that an item is "cross-loaded" on two factors?

What kinds of variables are appropriate to use in a factor analysis?

How does an EFA differ from a confirmatory factor analysis (CFA)?

What is the purpose of conducting an exploratory factor analysis (EFA)?