I have a sample of 20 years, I want to perform multiple regression analysis to estimate economic growth. I have 9 independent variables, but because my sample is small i get insignificant results. I do not have data to maken it a sample of 100 years or anything near that. What can I do? Can I incorporate the sample size into my problem? How do I enter a sample size in SPSS?
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$\begingroup$ What kind of data is is that you have? I.e. what are the variables and how are they measured? $\endgroup$– KOECommented Jan 31, 2014 at 17:08
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$\begingroup$ "but because my sample is small i get insignificant results." This is serendipitiously correct, since given a large enough sample size, you would find statistically significant effects, even if they weren't significant significant. This is an issue of power. With $n=20$, you don't have enough power to detect even significant significant effect sizes. $\endgroup$– AdamOCommented Jan 31, 2014 at 17:25
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2 Answers
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In principle, you cannot make your results significant when the amount of your data is limited. The calculation of your p-value has taken into account your sample size n. One thing you can try is model selection, in which you assume you don't need all 9 independent variables .A small portion of them will explain the majority of the variability in your response. It is the kind of techniques used when n << p i.e when the number of observations < the number of covariates. There are different type of model selection methods such as Lasso and Elastic Net, which are implemented in recent version of SPSS.
http://en.wikipedia.org/wiki/Least_squares#Lasso_method http://en.wikipedia.org/wiki/Elastic_net_regularization
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you don't enter sample size into SPSS, it'll know it when you enter you data: it's the number of observations.
with N=20, and 9 variables you need to estimate 9+intercept+error variance=11 parameters. you can barely have one parameter in the model. often the rule of thumb is 20 observations per parameter. unless you're dealing with a very stable physical phenomenon, there's no way you're going to get help from statistics alone in such a model.
example of a very stable physical model: you got 20 packs of eggs, each with 10 eggs. your dependent variable is the weight of a egg pack, 10 independent variables are weights of each egg starting from the one on top left corner. i bet that if you run this experiment all betas will be $beta_i=1$, they'll be significant, as well as the intercept too. So, the intercept would be the weight of the packaging.
So, the hope is not lost if you're not in social sciences, but in manufacturing or natural sciences.
