Hi,
I am doing my dissertation of whether one can predict one's level of empathy based on their personality type (BFI). I am analysing this using a linear regression but can't seem to figure out how to calculate the minimum sample size required?
Many thanks,
Dominique
Hi Dominique,
I agree with the preceding answer. If you'd like a discussion of the mathematical aspects of determining sample size, then here's a link for you -- starting on page 176.
https://books.google.com/books?id=MpAAnXiBTW4C&printsec=frontcover&dq=business+research+methods&hl=en&sa=X&ved=0ahUKEwiZqJfp_ovaAhUOR6wKHdU1DmsQuwUIMzAB#v=onepage&q=sample%20size&f=false
Good luck!
--Adrian
Dominique,
To answer that question, you'll need to know:
(a) the statistical significance criterion (alpha level) you plan to use;
(b) the degree of relationship that you deem minimally noteworthy (e.g., the effect size. In linear regression, this can be R-squared, or Cohen's f-squared, which is R-squared / (1 - R-squared));
(c) the number of predictor or independent variables in the model;
(d) the desired statistical power (e.g., the likelihood of detecting the target effect size with your data, assuming it exists in the population).
From these, the determination of needed sample size is pretty straightforward, and is made easy by the free software package, G*Power (http://www.gpower.hhu.de/en.html)
Good luck with your work!
Hi Dominique,
I agree with the preceding answer. If you'd like a discussion of the mathematical aspects of determining sample size, then here's a link for you -- starting on page 176.
https://books.google.com/books?id=MpAAnXiBTW4C&printsec=frontcover&dq=business+research+methods&hl=en&sa=X&ved=0ahUKEwiZqJfp_ovaAhUOR6wKHdU1DmsQuwUIMzAB#v=onepage&q=sample%20size&f=false
Good luck!
--Adrian
David's answer is great! I have found the free software 'Optimal Design' to be really useful: http://hlmsoft.net/od/
Wouldn't it make more sense, for a linear regression, to use the slope as the effect size measure?* I don't think that it is a useful information what proportion of the total variance I like the model to explain (R²); if I do a linear regression I want to know that I will be able to interpret the direction of the slope. Actually, at least that. I would prefer to estimate the slope parameter with some desired precision. This requires, theoretically, a Bayesian approach (as this is about the uncertainy associated with a parameter, not with the data), but one might use a CI as an approximation.
* that needs specifying explicitely the range and distribution of x-values at which the y-values are sampled, at least the variance of the x-values needs to be known/given/guessed.
Dominique,
A combination of both David’s (power) and Jochen’s (linear regressio/slope) answers will serve you well. You will need to be able to speak to your initial sample size selection and then you will need to be able to articulate the information that Jochen provided.
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