I am going to conduct one-group cross sample cross-sectional study and use multiple linear regression with objective to determine predictors of outcome variable (continous numerical data).
However, i am quite confuse with items related to sample size calculation for multiple linear regression.
1. TYPE OF TEST
There are multiple type of multiple linear regression in sample size software. What is the function for each type actually?
(a) Exact - linear multiple regression - random model
(b) F-test - linear multiple regression - Fixed model, R² deviation from zero
(c) F-test - linear multiple regression - Fixed model, R² increase
(d) t-test - linear multiple regression - Fixed model, single regression coefficient
2. TAIL(S)
How do we determine whether it is ONE-TAIL or TWO-TAILS?
3. EFFECT SIZE
(a) How do we determine effect size in sample size calculation?
(b) If there is limited info in literature, can we just take medium effect size (0.15) in sample size calculation?
(c) If we quite unsure whether it is small or medium effect size, can we take the middle value in between i.e. 0.08?
4. H1 ρ² and H0 ρ²
What are they actually?
5. PREDICTORS
(a) Can we run all independant variables as tested predictors?
(b) How do we determine controlled predictors and tested predictors, and what is the advantage of using this strategy instead of run all independant as tested predictors?
6. Power - i will set at 0.80. No issue.
7. Alpha err prob - i will set at 0.05. No issue.
Thank your.
Regards,
Fadhli
First you need to determine if your goal is the predict or explain because the model building methods are different for these two goals. Please see the attached. Best, D. Booth
Hello -
Assuming you want to 'predict' (meaning estimate with regard to a random variable), perhaps you should be more concerned with the estimated variance of the prediction errors for individual cases and for totals, depending upon your goals and the details of your project.
Graphical residual analyses and test data are important.
Sample size ultimately depends upon obtaining desired variance for desired standard errors, with bias minimized.
The population that your results are supposed to represent may be important.
Best wishes - Jim
PS - My per peeve here is that one should not forget that there is a natural tendency toward heteroscedasticity.
Have a look at this
https://stats.stackexchange.com/questions/10079/rules-of-thumb-for-minimum-sample-size-for-multiple-regression
I did. Most of those rules of thumb are pretty useless. It really depends on what you want to do and what kind of regression you want to do. Then we can figure out how close you need to be with your estimates and then make a much better estimate of sample size. An online source that some use is called G*power. you are welcome to try it. Best, David Booth
This manual - which takes a different approach based on simulation rather than approximate formulas is very good at taking you through the process step by step,
http://www.bristol.ac.uk/media-library/sites/cmm/migrated/documents/mlpowsim-manual.pdf
A key determinant which unfortunately is not generally available in Power calculation software is the degree of collinearity between the 'independent' variables - the greater the degree of correlation , the larger the sample size that is needed. The last time I used G power it did not have this capability but Nquery did
https://www.statsols.com/nquery-sample-size-calculator-for-academics
I have no financial links with this software .
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