On the Minimum Sample Size Requirement in PLS-SEM

On the Minimum Sample Size Requirement in PLS-SEM

The minimum sample size required for conducting Partial Least Squares Structural Equation Modeling (PLS-SEM) is influenced by several factors. These factors include the complexity of the research model, the number of latent variables and indicators utilized, the magnitude of relationships between the latent variables, the desired level of statistical power, and the desired level of significance.

Recently, Kock & Hadaya (2018) developed two formulas for determining the minimum sample size in PLS-SEM: the inverse square root method and the gamma exponential method. In these two formulas, the minimum sample size requirement in PLS-SEM depends on the minimum absolute significant path coefficient in the model, statistical power, and level of significant. In practice, researchers want to determine the minimum sample size before the data analysis and/or after the data analysis.

A. Minimum sample size before data analysis

According to Kock & Hadaya (2018), if one does not know in advance the value of the path coefficient with the minimum absolute magnitude, a reasonable minimum sample size is 160 based on the inverse square root method or 146 based on the gamma exponential method. I recommend that researchers use the inverse square root method as it is more conservative compared to the gamma exponential method.

By applying the inverse square root method, the recommended minimum sample size of 160 can be confirmed using the WarpPLS 8.0 software. The WarpPLS output (Figure A) demonstrates that the minimum sample size of 160 is sufficient when the following conditions are met: the minimum absolute significant path coefficient in the model is 0.197, the statistical power is set to 0.80, and the level of significance is 0.05.  Please refer to the red font in Table A as well.

Figure A: An output generated by WarpPLS 8.0

However, in the actual implementation of PLS-SEM, it is possible for the minimum absolute statistically significant path coefficients to be smaller than 0.197 (e.g., 0.180, 0.150, 0.120), and researchers may consider these smaller coefficients to be practically significant or meaningful. In such cases, larger sample sizes are required. Table A (blue font values) illustrates various sample sizes (fourth column) that researchers can utilize based on the statistical power, level of significance, and minimum absolute significant path coefficients. For instance, using Table A, if the minimum absolute significant path coefficient is 0.150 and the desired statistical power and level of significance are 80% and 5%, respectively, a sample size of 275 can be employed.

Table A: Minimum sample size requirement in PLS-SEM before data analysis 

Statistical Power	Level of Significance	minimum absolute significant path coefficients	Sample size using the inverse square root method
80%	5%	.200	155
80%	5%	.197	160
80%	5%	.180	191
80%	5%	.150	275
80%	5%	.120	430
80%	5%	.100	619
85%	5%	.200	180
85%	5%	.197	186
85%	5%	.180	222
85%	5%	.150	320
85%	5%	.120	500
85%	5%	.100	719

Source: Values in the 4th column, i.e., sample sizes based on the inverse square root method are my computation using the WarpPLS 8.0 software with different values in terms of statistical power, level of significance, and minimum absolute significant path coefficients.

 

B. Minimum sample size after the data analysis

After performing the PLS-SEM analysis using WarpPLS 8.0 software, it is recommended to assess the adequacy of the sample size through a post hoc statistical power analysis using the inverse square root method. To perform this analysis in the software, input the following: the actual minimum absolute significant path coefficient obtained from the PLS-SEM, a statistical power of 0.80, and a significance level of 0.05.

Let's consider an example where the researcher initially had a sample size of 275 before conducting the data analysis. After the analysis, the researcher discovers that the minimum absolute significant path coefficient in their model is 0.214. To evaluate the adequacy of the actual sample size (n=275) for the current study, taking into account a minimum absolute significant path coefficient of 0.214, a statistical power of 0.80, and a significance level of 0.05, the researcher can follow the two steps below to validate the adequacy of the sample size using WarpPLS 8.0

Step 1: In the main menu, click Explore and then choose Explore statistical power and minimum sample size requirements.  See Figures B and C.

Figure B: WarpPLS showing the Explore menu and the Explore statistical power and minimum sample size requirements option.

 

Figure C: WarpPLS Screenshot showing the dialog box after clicking the Explore statistical power and minimum sample size requirements option.

Step 2: Referring to Figure C above, the default minimum absolute significant path coefficient in the model is currently set at 0.197. To reflect the updated value of 0.214, simply replace the value with 0.214 and press enter. By utilizing the Inverse Square Root Method, the minimum sample size required is determined to be 135, as shown in Figure D. This result implies that the actual sample size of 275 is more than sufficient, considering that the post hoc statistical power analysis revealed a minimum sample size requirement of only 135.

Figure D. WarpPLS screenshot showing the minimum sample size required is only 135

Reference

Kock, N., & Hadaya, P. (2018). Minimum sample size estimation in PLS‐SEM: The inverse square root and gamma‐exponential methods. Information Systems Journal, 28(1), 227–261.

Kock, N. (2022). WarpPLS User Manual: Version 8.0. Laredo, TX: ScriptWarp Systems.

Kock, N. (2018). Minimum sample size estimation in PLS-SEM: an application in tourism and hospitality research. In Applying partial least squares in tourism and hospitality research. Emerald Publishing Limited.