Bootstrapping is a nonparametric resampling procedure used to test the statistical significance of CB-SEM results, such as path coefficients. Because CB-SEM parameter estimates do not always follow a known sampling distribution, bootstrapping provides an empirical way to obtain standard errors, confidence intervals, and p values without relying on strict distributional assumptions. Researchers typically apply it after estimating a CB-SEM model to determine whether structural relationships are statistically significant; see also the tutorial article on CB-SEM using SmartPLS by Hair et al. (2025).

SmartPLS offers several settings to configure the bootstrapping procedure for CB-SEM.

Bootstrapping randomly generates (with replacement) subsamples from the original data set. The number of observations per subsample is equal to that of the original data set. To ensure sufficient approximation of the sampling distribution, the number of subsamples should be large. For a first evaluation, one may use a smaller number of bootstrap subsamples (e.g., 500). However, for the final results one should use a large number of bootstrap subsamples (e.g., 5,000 or 10,000). Note that larger numbers of bootstrap subsamples increase calculation time.

This setting specifies the bootstrapping method used to estimate nonparametric confidence intervals. The following procedures are available: percentile (default), studentized, and bias-corrected and accelerated (BCa).

This setting indicates whether significance is based on a one-sided or two-sided test. The choice has two effects: (1) it affects the width of the confidence interval, and (2) it affects the calculation of p values. For instance, the default specification of a 5% significance level corresponds to a 95% confidence interval, with a 2.5% probability of error at the left tail (the lower bound) and at the right tail (the upper bound).

This setting specifies the desired significance level for parameter tests and has two effects: (1) it determines the width of the confidence interval (e.g., the default specification of a 5% significance level corresponds to a 95% confidence interval), and (2) it affects the highlighting of the p values in the results report (i.e., values below the specified significance level are displayed in green, while those above appear in red).

The algorithm randomly generates subsamples from the original data set, which requires a seed value for the random number generator. You have the option to choose between a random seed and a fixed seed.

CB-SEM parameter estimates such as path coefficients do not always follow a known sampling distribution. Bootstrapping is a nonparametric resampling procedure that estimates standard errors, confidence intervals, and p values empirically, without relying on strict distributional assumptions.

Use a smaller number, such as 500, for an initial evaluation. For final results, use a large number of subsamples, such as 5,000 or 10,000, to ensure a sufficient approximation of the sampling distribution. Keep in mind that larger numbers of subsamples increase calculation time.

A random seed produces different results every time the bootstrapping algorithm is run. A fixed seed uses a pre-specified value that stays the same across executions, producing identical results for the same number of subsamples and supporting the replicability of research findings.

SmartPLS defaults to the percentile method. Studentized and bias-corrected and accelerated (BCa) methods are also available and may be preferred in specific situations, for example when the sampling distribution is expected to be skewed.

The significance level determines the width of the confidence interval and controls how p values are highlighted in the results report. Values below the specified significance level (e.g., the default 5%) are shown in green, while values above it are shown in red.

The choice between a one-sided and two-sided test depends on the hypothesis being tested. It affects both the width of the confidence interval and the calculation of p values, so the test type should match how the corresponding hypothesis was formulated.

Hair, J. F., Babin, B. J., Ringle, C. M., Sarstedt, M., & Becker, J.-M. (2025). Covariance-based structural equation modeling (CB-SEM): A SmartPLS 4 software tutorial. Journal of Marketing Analytics, forthcoming.