## Sample size: minimum R2 method

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WanderSea
PLS Junior User
Posts: 2
Joined: Thu Nov 29, 2018 7:57 pm
Real name and title: Filippo Marino

### Sample size: minimum R2 method

Hi everyone!

I'm conducting for the first time a PLS-SEM analysis and I'm following the Hair Jr. et al. (2014) primer's guidelines. I already read other threads about the sample size determination on the forum and I've also conducted a power analysis using G*power.

However, I wanted to ask you for clarification about the example in the sample size section of Hair's book:
"For instance, independent variables in the measurement and structural models is five, one would need 70 observations to achieve a statistical power of 80% for detecting R2 values of at least 0.25 (with a 5% probability of error)."
Does this mean that by failing to reach the 70 observations the model would be reliable only to measure higher R2 values (eg 0.25<R2<0.5) since those require smaller sample sizes?

Thank you,
Filippo

cringle
SmartPLS Developer
Posts: 805
Joined: Tue Sep 20, 2005 9:13 am
Real name and title: Prof. Dr. Christian M. Ringle
Location: Hamburg (Germany)
Contact:

### Re: Sample size: minimum R2 method

In principle, you are on the right track. In the second edition of the book, the explications have been slightly modified. Here, one looks at an effect size level and the required sample size.

The attached pictures provide further explications.

Please note that these are technical considerations. Reaching the minimum sample size does not necessarily mean that your data is good for the analysis. You need a representative sample and - with regards to the analyzed population - this should be easily several hundred and thousands of observations and/or require the use of a weighting variable to ensure the representativeness of your results (see weighted PLS: https://www.smartpls.com/documentation/ ... ighted-pls).

Best
Christian
Attachments
G*Power 2
Minimum Sample Size_Seite_3.jpg (98.03 KiB) Viewed 159 times
G*Power 1
Minimum Sample Size_Seite_2.jpg (81.15 KiB) Viewed 159 times
Minimum Sample Size in PLS-SEM
Minimum Sample Size_Seite_1.jpg (120.76 KiB) Viewed 159 times

WanderSea
PLS Junior User
Posts: 2
Joined: Thu Nov 29, 2018 7:57 pm
Real name and title: Filippo Marino

### Re: Sample size: minimum R2 method

Dear Dr Ringle,

For my study, I was following the 1st version of your primer book, therefore for a statistical power of 80%, α=5%, and 7 independent variables leading to a dependent variable, I considered to reach at least 166 observations (or 228 for α=1%).
I collected 249 observations, which accordingly to your latest explications - based on f2 - still meet the required minimum sample size.

Now I have a second question. For my research, I also wanted to check for heterogeneity, since the respondents' data was from two close but different natural protected areas. From the MGA I found 3 significantly different path coefficients. This suggests that I should analyse the two groups separately.
However, their sizes are quite different: 173 and 76.
Therefore, if I want to make a comparison and draw conclusions about the subsamples differences, does it mean that the smallest sample would limit my analysis to an effect size of f2=0.15 (min sample size of 55, for α=5% and stat power of 80%)?

Thank you again for your help,
Filippo

jmbecker
SmartPLS Developer
Posts: 950
Joined: Tue Mar 28, 2006 11:09 am
Real name and title: Dr. Jan-Michael Becker

### Re: Sample size: minimum R2 method

Yes, you have to consider the minimum sample size requirements for each group if you want to do a MGA.
Dr. Jan-Michael Becker, University of Cologne, SmartPLS Developer
Researchgate: https://www.researchgate.net/profile/Ja ... v=hdr_xprf