Many people believe that a larger sample is always better Wh

Many people believe that a larger sample is always better. What do you think? Explain.

Solution

Larger samples are better than smaller samples (all other things being equal) because larger samples tend to minimize the probability of errors, maximize the accuracy of population estimates, and increase the generalizability of the results. Unfortunately, there are few sample size guidelines for researchers using EFA or PCA, and many of these have minimal empirical evidence.

   This is problematic because statistical procedures that create optimized linear combinations of variables (such as multiple regression, canonical correlation, and EFA\\PCA) tend to \"overfit\" the data. This means that these procedures optimize the fit of the model the given data; yet no sample is perfectly reflective of the population. Thus, this overfitting can result in erroneous conclusions if models fit to one data set are applied to others. In multiple regression this manifests itself as inflated R² (shrinkage) and mis-estimated variable regression coefficients. In EFA or PCA this “overfitting” can result in erroneous conclusions in several ways, including the extraction of erroneous factors or mis-assignment of items to factors.

The ultimate concern is error. At the end of the analysis, if one has too small a sample, errors of inference can easily occur, particularly with techniques such as EFA or PCA.