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I have data on the entirety of a certian population (not a sample). I would like to conduct a multivariate analysis for this data. The data consists of an interval dependent variable and interval and binary explanatory variables.

many colleagues of mine suggested to analyze this with regression model. Given that the analysis subjects are the whole population, what value is there for significance? Is there a better way to conduct a multivariate analysis than a regression model in this case?

thanks.

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  • $\begingroup$ What is your research question and your variables! How are they measured? These questions are detrimental to the type of statistical test used. $\endgroup$ – Yuval Spiegler Nov 27 '16 at 8:26
  • $\begingroup$ I am not aloud to reveal the subject or variables, but the gole of the analysis is to analyse the relationships between several (approx. 10) variables $\endgroup$ – tzipy Nov 27 '16 at 8:59
  • $\begingroup$ Even so, what types of data are these variables? Is the dependent variable in an interval, ordinal or nominal scales? If unordered, is it binary? What about the explanatory variables? Does the data meet parametric assumptions? $\endgroup$ – Yuval Spiegler Nov 27 '16 at 9:04
  • $\begingroup$ the data does meet parametric assumptions. the dependent variable is interval and we have dummy variables and intervals as independents. $\endgroup$ – tzipy Nov 27 '16 at 9:22
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In a case where you have the entire population and the data is full, and meats parametric assumptions, than yes - you can perform a linear regression. The significance levels of the coefficients will naturally be pointless. A significance level is a measure of the likelihood that the coefficient $\beta_i$ was taken from a population which has a $\beta_i=0$. Since the model has no idea of what part of the population we are using, it does not know that we use the entire population as such, the coefficient in the regression will equal the coefficient in the population and the significance test loses all meaning.

Usually, the coefficient is just an averaged relation between $y$ and $x$ in the sample data, and even when highly significant, does not equal the actual relationship in the population (which can be estimated with confidence intervals). When using the population, even a non significant coefficient is "significant", but more so, represent the actual relationship.

One last thing, the fact that we can measure the entire population does not mean we can assume to talk about causation. At his needs to be carefully done checking for cofounders and using theory etc...

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