As we learned in Chapter 5, sample size can greatly affect the results of an EFA. Small samples can lead to the identification of incorrect factor structures and item loadings (both direction and magnitude). They also limit our ability to check the replicability of our results through internal replication. (See Chapter 6.) Thus, small samples can affect your results and limit your ability to discern how they might affect them!

Now the best solution to the small sample dilemma is to get more data. More subjects or observations can be added to a sample to improve the potential replicability of the results. However, if this is not a possibility (we all have limited resources and funds!), an alternative solution is to explore the replicability of the results through bootstrap resampling techniques. Bootstrap resampling is a subsampling and averaging procedure that can be used to produce confidence intervals for any and all of the statistics that we choose. We can get confidence intervals (CIs) around eigenvalues, communalities, factor loadings, and more. These CIs can then inform us about the precision of each estimate and the range in the estimates that we might see among other samples. This information provides another means through which to examine the replicability of our results.

The benefits of bootstrap resampling are not limited to small samples. If we consider what bootstrap resampling can tell us —the potential error in our estimates and generalizability to other samples —we can quickly see the benefit of this practice to any analysis. Although it is true that large samples are more likely to yield replicable results, this hypothesis can be tested through bootstrap analysis. These methods help inform us about the replicability and generalizability of our results.