Sample size calculation using G*power Analysis

 PLS Junior User
 Posts: 2
 Joined: Mon Sep 21, 2015 12:54 pm
 Real name and title: Shiaw Tong Ha
Sample size calculation using G*power Analysis
Dear all,
My model contains 4 independent variables, 1 moderator, and 2 dependent variables.
I plan to use g*power analysis to calculate the sample size. May I know which test should I use?
I appreciate any feedback. Thanks.
My model contains 4 independent variables, 1 moderator, and 2 dependent variables.
I plan to use g*power analysis to calculate the sample size. May I know which test should I use?
I appreciate any feedback. Thanks.
Re: Sample size calculation using G*power Analysis
You may use the table in page 21 of the book "A Primer on Partial Least Squares Structural Equation Modeling (PLSSEM)" which calculate sample size based on power of analysis.
References
Hair, J. F., Hult, G. T. M., Ringle, C. M., & Sarstedt, M. (2013). A Primer on Partial Least Squares Structural Equation Modeling (PLSSEM). Thousand Oaks: Sage.
References
Hair, J. F., Hult, G. T. M., Ringle, C. M., & Sarstedt, M. (2013). A Primer on Partial Least Squares Structural Equation Modeling (PLSSEM). Thousand Oaks: Sage.
Re: Sample size calculation using G*power Analysis
However, if you want to use Gpower you could get sample size of 138 respondent as the following (please correct me if I'm mistaken)
F tests  Linear multiple regression: Fixed model, R² increase
Analysis: A priori: Compute required sample size
Input: Effect size f² = 0.15
α err prob = 0.05
Power (1β err prob) = 0.95
Number of tested predictors = 5
Total number of predictors = 5
Output: Noncentrality parameter λ = 20.7000000
Critical F = 2.2828562
Numerator df = 5
Denominator df = 132
Total sample size = 138
Actual power = 0.9507643
F tests  Linear multiple regression: Fixed model, R² increase
Analysis: A priori: Compute required sample size
Input: Effect size f² = 0.15
α err prob = 0.05
Power (1β err prob) = 0.95
Number of tested predictors = 5
Total number of predictors = 5
Output: Noncentrality parameter λ = 20.7000000
Critical F = 2.2828562
Numerator df = 5
Denominator df = 132
Total sample size = 138
Actual power = 0.9507643
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 SmartPLS Developer
 Posts: 1046
 Joined: Tue Mar 28, 2006 11:09 am
 Real name and title: Dr. JanMichael Becker
Re: Sample size calculation using G*power Analysis
The questions is, which test is the one you are interested in.
The test above is for the F test of a regression. It assesses the significance of the R² at the given effect size level (e.g., effects size 0.15 = R²). Hence, with 138 cases you will find a model with an R² of 0.15 significant at 95% of the time.
Many researchers are more interested in the significance of single effects instead of the variance explained by the overall regression equation. Hence, you might want to choose the "Linear multiple regression: Fixed model, single regression coefficient" as the method in G*Power.
There you have to set the effect size f², which is the same effect size that is reported in SmartPLS under f². It is the contribution to the R² by the predictor (R²inlcuded  R²excluded) / (1  R²included).
Unfortunately, this effect size is not very straightforward to determine. The default of 0.15 is relatively high. It would require a standardized coefficient of roughly 0.275 if your overall R² is at about 0.5 and a standardized coefficient of 0.336 if your overall R² is at 0.25.
If you have an expectation for the standardized coefficient of 0.2 and an overall R² of 0.25, you would get an effect size f² of 0.053. With five predictors, this would require you to have a sample size of 248 for a power of 95% to find the 0.2 coefficient significant.
The test above is for the F test of a regression. It assesses the significance of the R² at the given effect size level (e.g., effects size 0.15 = R²). Hence, with 138 cases you will find a model with an R² of 0.15 significant at 95% of the time.
Many researchers are more interested in the significance of single effects instead of the variance explained by the overall regression equation. Hence, you might want to choose the "Linear multiple regression: Fixed model, single regression coefficient" as the method in G*Power.
There you have to set the effect size f², which is the same effect size that is reported in SmartPLS under f². It is the contribution to the R² by the predictor (R²inlcuded  R²excluded) / (1  R²included).
Unfortunately, this effect size is not very straightforward to determine. The default of 0.15 is relatively high. It would require a standardized coefficient of roughly 0.275 if your overall R² is at about 0.5 and a standardized coefficient of 0.336 if your overall R² is at 0.25.
If you have an expectation for the standardized coefficient of 0.2 and an overall R² of 0.25, you would get an effect size f² of 0.053. With five predictors, this would require you to have a sample size of 248 for a power of 95% to find the 0.2 coefficient significant.
Dr. JanMichael Becker, University of Cologne, SmartPLS Developer
Researchgate: https://www.researchgate.net/profile/Jan_Michael_Becker
GoogleScholar: http://scholar.google.de/citations?user ... AAAJ&hl=de
Researchgate: https://www.researchgate.net/profile/Jan_Michael_Becker
GoogleScholar: http://scholar.google.de/citations?user ... AAAJ&hl=de

 PLS Junior User
 Posts: 2
 Joined: Mon Sep 21, 2015 12:54 pm
 Real name and title: Shiaw Tong Ha
Re: Sample size calculation using G*power Analysis
Thank you very much for your valuable information and support. I really appreciated.
Re: Sample size calculation using G*power Analysis
Dear All,
My model consists of 9 independent variables, 2 dependent variables, 2 moderating variables and 3 control variables.
I also want to use gpower analysis in order calculate the sample size. Could you pls enlighten me on how to tackle this ?
Thank you
My model consists of 9 independent variables, 2 dependent variables, 2 moderating variables and 3 control variables.
I also want to use gpower analysis in order calculate the sample size. Could you pls enlighten me on how to tackle this ?
Thank you

 PLS Junior User
 Posts: 7
 Joined: Tue Nov 22, 2016 10:39 am
 Real name and title: Peter Bergwall, Doctoral student
Re: Sample size calculation using G*power Analysis
Hi everyone!
Great to see that there is a thread on G*power here already.
I have a problem relating to the statistical power and critical t boundaries for f square values (effect size).
My dataset has 98 respondents and I have 7 constructs predicting one specific dependent variable.
I am interested in the statistical power of the predictors' effects on the dependent variable.
I use the following settings in G*Power 3.1.9.2:
Test family: t tests
Statistical test: Linear multiple regression: Fixed model, single regression coefficient
Type of power analysis: Sensitivity: Compute required effect size  given alpha, power, and sample size
Tail(s): Two
Alpha err prob: 0.05
Power (1  beta err prob): 0.80
Total sample size: 98
Number of predictors: 7
Hence, the output parameters are:
Noncentrality parameter (delta): 2.83
Critical t: 1.99
Df: 90
Effect size (f square): 0.082
Running the PLS algorithm in SmartPLS v.3.2.6 results in four paths with f square values above 0.082 (namely, 0.27, 0.25, 0.23, and 0.10). Based on the previous G*power calculation, I interpret these results as statistically significant and with sufficient statistical power based on the criteria I've specified.
However, when I bootstrap the f square values in SmartPLS (500 subsamples), the t statistics are not even close to the critical t boundary. The one largest effect (f square = 0.27) displays a tstatistic of 1.563 and a pvalue of 0.119.
Can anybody tell me how to interpret these differences between G*power and SmartPLS? Is the t statistic (in relation to the critical t value) more "important" than the G*power calculation of the power of the effect sizes?
/ Peter
Great to see that there is a thread on G*power here already.
I have a problem relating to the statistical power and critical t boundaries for f square values (effect size).
My dataset has 98 respondents and I have 7 constructs predicting one specific dependent variable.
I am interested in the statistical power of the predictors' effects on the dependent variable.
I use the following settings in G*Power 3.1.9.2:
Test family: t tests
Statistical test: Linear multiple regression: Fixed model, single regression coefficient
Type of power analysis: Sensitivity: Compute required effect size  given alpha, power, and sample size
Tail(s): Two
Alpha err prob: 0.05
Power (1  beta err prob): 0.80
Total sample size: 98
Number of predictors: 7
Hence, the output parameters are:
Noncentrality parameter (delta): 2.83
Critical t: 1.99
Df: 90
Effect size (f square): 0.082
Running the PLS algorithm in SmartPLS v.3.2.6 results in four paths with f square values above 0.082 (namely, 0.27, 0.25, 0.23, and 0.10). Based on the previous G*power calculation, I interpret these results as statistically significant and with sufficient statistical power based on the criteria I've specified.
However, when I bootstrap the f square values in SmartPLS (500 subsamples), the t statistics are not even close to the critical t boundary. The one largest effect (f square = 0.27) displays a tstatistic of 1.563 and a pvalue of 0.119.
Can anybody tell me how to interpret these differences between G*power and SmartPLS? Is the t statistic (in relation to the critical t value) more "important" than the G*power calculation of the power of the effect sizes?
/ Peter

 PLS Junior User
 Posts: 7
 Joined: Tue Nov 22, 2016 10:39 am
 Real name and title: Peter Bergwall, Doctoral student
Re: Sample size calculation using G*power Analysis
Okay, after sleeping on it I realized a possible way to go about the problem described above.
Commonly, the relation between type 1/alpha errors ("false positives") and type 2/beta errors ("false negatives") is viewed as a tradeoff. If you accept a more liberal boundary for the one you should take on a more conservative approach for the other. At least, that's my understanding of power analysis.
In general, 0.05/0.80 (Alpha err prob/1Beta err prob) are used as conventional criteria in the social sciences. Consequently, if I change my settings in G*power to, say:
Alpha err prob: 0.20
1Beta err prob: 0.99
then my results makes more sense, compared to the bootstrapping results in SmartPLS:
Noncentrality parameter (delta): 3.62
Critical t: 1.291
Df: 90
Effect size (f square): 0.13
So, there is a 20% probability that I will erroneously reject the null hypothesis (=no effect) for effects as low as f square=0.13. On the other hand, there is a 1% probability that I will fail to detect an effect as low as f square=0.13, if the effect is indeed present.
Going back to the t statistics generated by the bootstrapping procedure. Applying these adjusted specifications, the three predictors showing the largest f square values now have acceptable t values and p values (t values above 1.291 and p values below 0.20). However, the predictor displaying a f square value of around 0.10 still displays insignificant t and p values.
I attribute the higher alpha error probability to the small sample size (n=98). But since it is a pilot study, I still think there are some interesting findings that are worth looking into with a larger sample size (the full scale study).
Commonly, the relation between type 1/alpha errors ("false positives") and type 2/beta errors ("false negatives") is viewed as a tradeoff. If you accept a more liberal boundary for the one you should take on a more conservative approach for the other. At least, that's my understanding of power analysis.
In general, 0.05/0.80 (Alpha err prob/1Beta err prob) are used as conventional criteria in the social sciences. Consequently, if I change my settings in G*power to, say:
Alpha err prob: 0.20
1Beta err prob: 0.99
then my results makes more sense, compared to the bootstrapping results in SmartPLS:
Noncentrality parameter (delta): 3.62
Critical t: 1.291
Df: 90
Effect size (f square): 0.13
So, there is a 20% probability that I will erroneously reject the null hypothesis (=no effect) for effects as low as f square=0.13. On the other hand, there is a 1% probability that I will fail to detect an effect as low as f square=0.13, if the effect is indeed present.
Going back to the t statistics generated by the bootstrapping procedure. Applying these adjusted specifications, the three predictors showing the largest f square values now have acceptable t values and p values (t values above 1.291 and p values below 0.20). However, the predictor displaying a f square value of around 0.10 still displays insignificant t and p values.
I attribute the higher alpha error probability to the small sample size (n=98). But since it is a pilot study, I still think there are some interesting findings that are worth looking into with a larger sample size (the full scale study).

 SmartPLS Developer
 Posts: 1046
 Joined: Tue Mar 28, 2006 11:09 am
 Real name and title: Dr. JanMichael Becker
Re: Sample size calculation using G*power Analysis
I think your analysis is ok, but I would usually run a post hoc test with the effect sizes in my model. Given your results, your lowest effect size is 0.10 and you have a sample size of 98. This results in a power of 92.8% for that effect size. You find an insignificant effect, thus you may have an effect that is really insignificant (zero) or you are in the remaining 7.2% of false negatives.
For the effect size of 0.27 you have a power of 99.9%. If this effect size is not significant it is unlikely that this is due to a lack of power. Hence, the effect is indeed not significant.
For the effect size of 0.27 you have a power of 99.9%. If this effect size is not significant it is unlikely that this is due to a lack of power. Hence, the effect is indeed not significant.
Dr. JanMichael Becker, University of Cologne, SmartPLS Developer
Researchgate: https://www.researchgate.net/profile/Jan_Michael_Becker
GoogleScholar: http://scholar.google.de/citations?user ... AAAJ&hl=de
Researchgate: https://www.researchgate.net/profile/Jan_Michael_Becker
GoogleScholar: http://scholar.google.de/citations?user ... AAAJ&hl=de

 PLS Junior User
 Posts: 1
 Joined: Fri Aug 04, 2017 11:23 am
 Real name and title: Yves Blieck (PhD student)
Re: Sample size calculation using G*power Analysis
Hello all
I want to calculate the required sample size to validate a model:
• the measurement model (wich has already been validated in a Delphi study)
• the structural model has a lot af relations (we have several models designed a priori)
• IPMA analysis to determine what latent variables and indicators are important to ‘influence’ dependent latent variable.
The model has 8 latent variables: 7 independent (1 exogenous and 6 endogenous) and 1 dependent variable (2 dimensions).
There are in total 47 variables in the measurement model (the variable with the largest number of indicators is 16). The dependent variable has 11 indicators.`
I use G*Power for the power analysis, the settings are:
• F test (linear multiple regression: fixed model. R2 deviation from zero)
• Type of power analysis " a priori" compute required sample size
• F2 = 0,35 or 0,15
• Alpha error = 0,05
• Power 0,80
• Number of predictors: ?
My question questions are:
1. Are my settings correct?
2. what should I input as number of predictors:
a. the largest number of indicators connected to a latent variable (n=16)?
b. the number variables in the measurement model (n=47)?
c. the number of indirect latent variables (n=7)?
The 10 times rule confuses me and I do not find straightforward information on this topic.
I computed all possibilities and my current sample size N=+/191 is only insufficient in the most severe scenario (F2 = 0,15 number of predictors=47).
I want to calculate the required sample size to validate a model:
• the measurement model (wich has already been validated in a Delphi study)
• the structural model has a lot af relations (we have several models designed a priori)
• IPMA analysis to determine what latent variables and indicators are important to ‘influence’ dependent latent variable.
The model has 8 latent variables: 7 independent (1 exogenous and 6 endogenous) and 1 dependent variable (2 dimensions).
There are in total 47 variables in the measurement model (the variable with the largest number of indicators is 16). The dependent variable has 11 indicators.`
I use G*Power for the power analysis, the settings are:
• F test (linear multiple regression: fixed model. R2 deviation from zero)
• Type of power analysis " a priori" compute required sample size
• F2 = 0,35 or 0,15
• Alpha error = 0,05
• Power 0,80
• Number of predictors: ?
My question questions are:
1. Are my settings correct?
2. what should I input as number of predictors:
a. the largest number of indicators connected to a latent variable (n=16)?
b. the number variables in the measurement model (n=47)?
c. the number of indirect latent variables (n=7)?
The 10 times rule confuses me and I do not find straightforward information on this topic.
I computed all possibilities and my current sample size N=+/191 is only insufficient in the most severe scenario (F2 = 0,15 number of predictors=47).

 SmartPLS Developer
 Posts: 1046
 Joined: Tue Mar 28, 2006 11:09 am
 Real name and title: Dr. JanMichael Becker
Re: Sample size calculation using G*power Analysis
It depends!!! It actually depends on quite many decisions. For example, it depends on what you want to focus (test). If you read the prior discussions you would notice that one other common power analysis method appropriate in this case (and often the one that people actually want to use) would be under TTest the "Linear multiple regression: Fixed model, single regression coefficient".1. Are my settings correct?
It depends on what you want to test and whether you have formative or reflective measurement models. If your n=16 indicators latent variable is a formative latent variable and you are interested in testing the weights, then you should use 16 (and the above mentioned ttest method). If it is a reflective latent variable and/or you are concerned with the R² increase of the final dependent variable, you would use n=7 for the number of predictors of that variable.2. what should I input as number of predictors:
However, you would never use n=47. PLS (the name partial least squares says it already) considers only partial models and thus you are interested in powering each partial model to the required level.
Dr. JanMichael Becker, University of Cologne, SmartPLS Developer
Researchgate: https://www.researchgate.net/profile/Jan_Michael_Becker
GoogleScholar: http://scholar.google.de/citations?user ... AAAJ&hl=de
Researchgate: https://www.researchgate.net/profile/Jan_Michael_Becker
GoogleScholar: http://scholar.google.de/citations?user ... AAAJ&hl=de
Re: Sample size calculation using G*power Analysis
Dear all,
My model contains 1 independent variables, 1 mediator, and 1 dependent variables in which a moderator in between mediator and dependent variable.
I have 5 dimensions(a,b,c,d,e) for the independent variable which have (5 questions for a , 5 questions for b, 4 questions for c , 5 questions for d, and 4 questions for e).
The mediator has 6 questions. The dependent variable has 5 questions. The moderator has 4 questions. The demographic has 7 questions. There are 45 questions in total.
I plan to use g*power analysis to calculate the sample size. May I know which test should I use?
I appreciate any feedback. Thank you very much.
Regards
Tan
My model contains 1 independent variables, 1 mediator, and 1 dependent variables in which a moderator in between mediator and dependent variable.
I have 5 dimensions(a,b,c,d,e) for the independent variable which have (5 questions for a , 5 questions for b, 4 questions for c , 5 questions for d, and 4 questions for e).
The mediator has 6 questions. The dependent variable has 5 questions. The moderator has 4 questions. The demographic has 7 questions. There are 45 questions in total.
I plan to use g*power analysis to calculate the sample size. May I know which test should I use?
I appreciate any feedback. Thank you very much.
Regards
Tan
 kamellia.ch
 PLS Junior User
 Posts: 10
 Joined: Thu May 18, 2017 2:47 pm
 Real name and title: kamelia chaichi
Re: Sample size calculation using G*power Analysis
I have a question too. My model contains 9 moderators and three variable going to one construct, totally 12 paths (arrows ) to one construct, but the table in PLS book demonstrated until the number of max 10 arrows, how can I calculate sample size? can anyone guide me, please? thank you

 PLS Junior User
 Posts: 1
 Joined: Sat Sep 01, 2018 7:19 am
 Real name and title: ahmad abbasi
Re: Sample size calculation using G*power Analysis
hi
i have 3 variable ( endogenous latent variable ) and every 3 variable has 6 ( Exogenous latent variable ) .
how to use Gpower I stimate the minimuem and total size of my community?
I want to use smart pls 3 for figure out of my thesis.
i have 3 variable ( endogenous latent variable ) and every 3 variable has 6 ( Exogenous latent variable ) .
how to use Gpower I stimate the minimuem and total size of my community?
I want to use smart pls 3 for figure out of my thesis.

 SmartPLS Developer
 Posts: 1046
 Joined: Tue Mar 28, 2006 11:09 am
 Real name and title: Dr. JanMichael Becker
Re: Sample size calculation using G*power Analysis
I think the former descriptions describe the process quite well. The most important aspect is to determine the expected effect size. It is central in determining the power. The number of variables is only peripheral.
Dr. JanMichael Becker, University of Cologne, SmartPLS Developer
Researchgate: https://www.researchgate.net/profile/Jan_Michael_Becker
GoogleScholar: http://scholar.google.de/citations?user ... AAAJ&hl=de
Researchgate: https://www.researchgate.net/profile/Jan_Michael_Becker
GoogleScholar: http://scholar.google.de/citations?user ... AAAJ&hl=de