What Is Bootstrapping in SmartPLS and SPSS
What Is Bootstrapping
Bootstrapping is a resampling technique that repeatedly draws samples from the original dataset to estimate how stable a statistical result is. In each repetition, the software randomly selects observations from the original data with replacement, then recalculates the coefficient being tested. After thousands of repetitions, the software produces an empirical distribution of that coefficient.
In SmartPLS, bootstrapping is commonly used to test the path coefficient, outer loading, total indirect effect, specific indirect effect, and total effect. You are assessing whether a coefficient differs from 0, rather than looking only at the original coefficient estimate. The output is usually read through Original Sample (O), Sample Mean (M), Standard Deviation (STDEV), T Statistics, and P Values.
You can think of the process this way: the original data generate many simulated samples, each sample produces an estimate, and SmartPLS uses the collection of estimates to calculate the standard error, t-value, and confidence interval. Bootstrapping therefore does not automatically improve the model and does not replace checking the scale, sample size, or logic of the hypotheses.
If you are distinguishing PLS-SEM from other branches of SEM, you can also read What is PLS-SEM, What is SEM, and SEM models. These concepts help you identify whether bootstrapping is being used for the measurement model or the structural model.
The Meaning of Bootstrapping in Quantitative Research
Bootstrapping answers a practical thesis question: is there enough statistical evidence to conclude that the observed effect differs from 0. For example, hypothesis H1 may state that Service Quality has a positive effect on Satisfaction. After running the model, you have a positive path coefficient. Bootstrapping helps you assess whether that positive coefficient remains stable across the resampled datasets or appears only because of sampling fluctuation.
For a direct effect, read the path row between the independent and dependent variables. For a mediation effect, read Specific Indirect Effects or Total Indirect Effects. A mediator can produce a significant indirect effect even when each individual path still needs to be considered in the context of the full model.
In SmartPLS, bootstrapping is generally set up during structural model assessment after you have checked the measurement model. Under the current PLS-SEM procedure, you can use 5,000 bootstrap subsamples when reporting the results (Hair et al., 2022). When writing Chapter 4, state the number of subsamples, whether you used a one-tailed or two-tailed test, the significance level, and the confidence interval selected.
Bootstrapping also helps you avoid a common mistake: accepting a hypothesis simply because the coefficient is positive or negative. The sign of the coefficient shows the direction of the effect. P Values, T Statistics, and the confidence interval show the statistical evidence for that effect. You need to read these two groups of information together.
If you use SmartPLS, the SmartPLS topic page can help you connect bootstrapping with outer loading, AVE, HTMT, VIF, and R². These indicators belong to different stages of the analysis and should not be collapsed into one criterion.
How Many Bootstrap Samples Are Acceptable
The search phrase “how many bootstrap samples are good” can be misleading. Bootstrapping does not have one threshold where a larger number automatically means an acceptable result. You need to assess the number of subsamples in the settings and statistical significance in the output.
| Item to read | Rule or interpretation | Source |
|---|---|---|
| Number of bootstrap subsamples | You can use 5,000 subsamples when reporting PLS-SEM | (Hair et al., 2022) |
| P Values | Compare them with the selected significance level, which should be stated clearly in the methods section | (Hair et al., 2022) |
| Confidence interval for an indirect effect | The effect is significant when the bootstrap confidence interval does not contain 0 | (Preacher and Hayes, 2008) |
| VIF before reading the paths | VIF below 5 is a commonly reported threshold | (Hair et al., 2019) |
| R² of an endogenous variable | 0.75 can be considered substantial, 0.50 moderate, and 0.25 weak | (Hair et al., 2011) |
| f² | 0.02 is small, 0.15 medium, and 0.35 large | (Cohen, 1988) |
| Q² | Q² greater than 0 indicates predictive relevance | (Stone, 1974) |
The criteria in the table are related, but they cannot replace one another. For example, you may run 5,000 subsamples while the P Values for a path remain larger than the significance level. The number of repetitions is sufficient for the procedure, but the hypothesis still lacks enough evidence for acceptance.
For a direct effect, many theses use a 5% significance level, corresponding to P Values below 0.05 in a two-tailed test. State this convention in the methods chapter instead of writing only “p below 0.05 is acceptable” in the results chapter. If you use a one-tailed test, define the hypothesis direction and the reason for choosing a one-tailed test in advance.
For an indirect effect, do not look only at the p-value. Open the confidence interval table and check the lower and upper bounds. If the confidence interval contains 0, the conclusion about the indirect effect is not sufficiently robust under the bootstrap confidence interval rule (Preacher and Hayes, 2008).
How to Read Bootstrapping in the Output
In SmartPLS 4, run the model first and then select the Bootstrapping function. In the dialog box, choose the number of subsamples, the test type, and the confidence interval. Button names may vary slightly between versions, so check the correct Calculate window and the Bootstrapping results section instead of mechanically following a screenshot from SmartPLS 3.
The table below is illustrative output, not the result of a real study. The columns follow a format commonly found in SmartPLS output.
| Path Coefficients | Original Sample (O) | Sample Mean (M) | Standard Deviation (STDEV) | T Statistics | P Values |
|---|---|---|---|---|---|
| CLDV -> HAILONG | 0.418 | 0.421 | 0.071 | 5.887 | 0.000 |
| GIACA -> HAILONG | 0.126 | 0.129 | 0.082 | 1.537 | 0.124 |
| HAILONG -> TRUNGT HÀNH | 0.356 | 0.353 | 0.069 | 5.159 | 0.000 |
In the CLDV -> HAILONG row, Original Sample (O) is 0.418, meaning that the effect coefficient estimated from the original sample is positive. T Statistics is 5.887 and P Values is 0.000 as displayed by the software. In the thesis, you should usually write this as p < 0.001, rather than writing p as exactly 0. At the 5% significance level, the illustrative data provide evidence supporting the hypothesis of a positive effect.
In the GIACA -> HAILONG row, the coefficient is still positive, but P Values is 0.124. You should not write that price has a positive effect simply because O is greater than 0. The appropriate conclusion is that there is not enough statistical evidence to confirm the effect at the selected significance level.
Sample Mean (M) shows the average coefficient across the bootstrap samples. Comparing M with O can help you identify a notable difference, but do not set your own difference threshold without an appropriate methodological basis. STDEV is the standard deviation of the bootstrap distribution and is used when forming the t-value.
For a mediation effect, open Specific Indirect Effects. For example, if the table contains the row CHATLUONG -> HAILONG -> YDINH, read Original Sample, T Statistics, P Values, and the confidence interval bounds. The indirect effect may be positive, negative, or close to 0. The conclusion must be based on both the direction of the effect and the confidence interval.
What to Do When Bootstrapping Does Not Meet the Criterion
First, identify which part you mean by “does not meet the criterion.” If you have not run enough subsamples, run the analysis again using the settings stated in the methods section. If the P Values of a path are large, the issue concerns the evidence for the hypothesis, not a SmartPLS error.
Check the Measurement Model Again
Review Outer Loadings, Composite Reliability, AVE, and HTMT. An outer loading from 0.7 upward is commonly used in PLS-SEM (Chin, 1998). CR from 0.7 and AVE from 0.5 upward are commonly cited benchmarks (Fornell and Larcker, 1981). HTMT should be below 0.85, or below 0.90 for closely related concepts (Henseler et al., 2015).
If the scale does not meet the criterion, review the theoretical meaning of each indicator and the history of item deletion. Do not delete items in bulk simply to make the hypothesis p-value look better. Each deleted item needs a methodological reason, and you need to recheck the model after deletion.
Check Multicollinearity and the Data
Review Inner VIF Values or Outer VIF Values. A high VIF can reduce the stability of the coefficients and make paths less likely to reach significance. Also check variable coding, missing values, duplicate response rows, and low-quality cases.
If the data have a problem, clean them according to rules defined in advance. Changing the data after seeing that a hypothesis failed, solely to produce a smaller p-value, creates a serious risk at the thesis defense.
Keep the Unsupported Result and Explain It Correctly
After you check the model, scale, and data, a hypothesis may still remain unsupported. Report the coefficient, t-value, p-value, and conclusion based on the data. You can discuss that the effect lacks statistical evidence in the context and sample of the study, but do not turn an unsupported result into a supported one by changing the threshold after viewing the output.
Distinguishing Bootstrapping from the p-value and Monte Carlo Simulation
Bootstrapping is the process of creating resampled datasets and an empirical distribution. A P Value is an indicator calculated from a statistical test and used to assess the evidence against the null hypothesis. The two concepts appear next to each other in the output, but they are not synonymous.
T Statistics is also not bootstrapping. In the Path Coefficients table, the t-value is generally calculated by dividing the coefficient by the bootstrap standard error. The t-value is therefore a result read from the bootstrap distribution, while bootstrapping is the mechanism that creates that distribution.
Monte Carlo simulation also creates many simulated samples, but the way the samples are generated and the purpose may differ. Bootstrapping resamples observations from the real dataset with replacement. You should not use the two terms as though they referred to the same operation in SmartPLS.
Bootstrapping in SPSS can be performed through different procedures or modules, such as when testing regression, mediation, or confidence interval estimation. The interpretation still depends on the analysis type and the output table name. An SPSS result does not automatically become a PLS-SEM result, because SmartPLS also includes a measurement model, a structural model, and indicators specific to PLS.
If your study uses AMOS or CB-SEM, distinguish it from PLS-SEM before selecting the procedure. You can read What is CB-SEM to avoid placing CB-SEM fit indices such as CFI, TLI, or RMSEA in a SmartPLS analysis.
Common Errors When Reading Bootstrapping
Looking only at the p-value and ignoring the coefficient sign. A small p-value indicates evidence of an effect different from 0, but it does not show whether the effect is positive or negative. The sign of Original Sample (O) shows the direction of the effect.
Writing p = 0.000. This is the software's display limit. In the thesis, write p < 0.001 when the output displays 0.000.
Treating the number of subsamples as a model-quality threshold. 5,000 subsamples is a recommended setting in the PLS-SEM reporting procedure (Hair et al., 2022), but it does not mean that every hypothesis must be supported.
Reading Sample Mean instead of Original Sample. Each column has its own function. When presenting a path coefficient, you generally need to report O, the t-value, the p-value, and the confidence interval according to the output structure you used.
Failing to distinguish direct and indirect effects. A hypothesis about a mediator must be read from the correct row in Specific Indirect Effects. Reading the direct path row can lead to an incorrect conclusion about mediation.
Running the analysis repeatedly without recording the settings. Save the result file, number of subsamples, test type, significance level, and deleted items. If your supervisor asks why two runs produced different results, you need to identify the difference in settings or data.
How to write this in your thesis: “The bootstrapping results with [number of subsamples] repetitions show that the effect of [independent variable] on [dependent variable] has a coefficient of β = [value], t = [value], p [< or >] [significance level]. Therefore, hypothesis [H1] is [supported/not supported] in the study sample.”
Frequently asked questions
What is bootstrapping in SmartPLS?
It is a resampling procedure that repeatedly draws observations with replacement from the original data to create a distribution of the coefficients. SmartPLS uses this distribution to calculate the standard error, t-value, p-value, and confidence interval for a path, outer loading, or indirect effect.
How many bootstrap samples are good?
In PLS-SEM, you can use 5,000 bootstrap subsamples when reporting the results according to the guidance (Hair et al., 2022). However, 5,000 does not guarantee that every hypothesis will be supported. You still need to read the p-value, confidence interval, effect coefficient, and model checks.
Is bootstrapping in SPSS the same as in SmartPLS?
The resampling principle can be similar, but the procedures and model types differ. SPSS can use bootstrapping for regression or mediation analysis, while SmartPLS uses it in PLS-SEM with a measurement model and a structural model.
What bootstrapping p-value is acceptable?
You need to define the significance level before reading the results. At the 5% level with a two-tailed test, a p-value below 0.05 is commonly used as statistical evidence of an effect different from 0. Also report the sign and size of the coefficient, because the p-value does not show whether the effect is strong or weak.
What if the bootstrap confidence interval contains 0?
For an indirect effect, a confidence interval containing 0 indicates that there is not enough evidence to conclude that the effect differs from 0 under this criterion (Preacher and Hayes, 2008). Check the model, data, and mediator specification again, then report the unsupported result if there is no valid methodological reason for adjustment.
Do I need to run bootstrapping many times?
You can rerun the analysis when you change a valid setting, clean the data according to a predefined rule, or adjust the model on a theoretical basis. Do not run it repeatedly just to find one small p-value and ignore the other runs. Keep an analysis history and state clearly which result version you used in the thesis.
Open your SmartPLS file, check the correct Path Coefficients or Specific Indirect Effects table, record the number of subsamples, and compare each hypothesis with its p-value and confidence interval. If you need to run the analysis on your own .sav or .csv file, see M4 data analysis with DoThesis.