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I want find statistical support that dependence is inversely proportional to power. To do so, I have

  • ~260 cases,
  • with four questions about dependence, and
  • one question about power

The questions about dependence are on a continuous scale, whereas the question about power only allows three ordered answers (I am powerful, equilibrium, the other one is powerful).

To support the inverse proportionality of power and dependence (in this application), is the right way to do a ordinal logistic regression?

I have plotted grouped error bars for the data (error.bars.by()) and they show the case I want to prove quite clearly; however I suppose I need the right figures on top of that as well.

Thanks for any suggestions and advice.

I had a look at some threads on Cross validated (1,2,3) about similar questions, and as far as I understand there is not a clear answer to how the above described mutual inverse correlation/proportionality could be tested. Correct me if I'm wrong.

Thanks for answers and comments so far. As far as I understand ordinal logistic regression helps me to find support for a relation of power with dependence, if I use dependence as predictor and power as dependent variable.

mdewey
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Roman
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  • You have to decide which is the dependent variable and which is the predictor. – Peter Flom Aug 07 '13 at 12:15
  • Thanks for your comment Peter. I noticed that when I tried it in R. But since the variables are supposed to be inverse proportional, I should really use a method which reflects that. If this is not possible, I will just use dependence (continuous) as a predictor for power (ordinal). – Roman Aug 07 '13 at 13:16
  • I am guessing that "datasets" here means observations (cases, records). – Nick Cox Aug 08 '13 at 08:45
  • @Nick: They do indeed. I will rectify that. – Roman Aug 08 '13 at 08:58

2 Answers2

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As so often happens, we need to fix terminology.

Inverse proportionality in a mathematical sense can only mean that variables have constant product, e.g. $x$ and $y$ are such that $xy =$ some constant ($c$, say). With no other information it is then mathematically arbitrary whether you decide to describe that with $y = c/x$ or $x = c/y$, as the two forms are equivalent. Throughout we assume non-zero values.

As one of your variables is ordinal, however, the idea of inverse proportionality cannot apply to your data. The whole point is that whatever numerical codes you might assign are just arbitrary, so long as they are in the right order. So you might choose 1,2,3 or 42, 53, 64 or even -1,0,1: it makes no difference. Ordinal "measurement" is too weak to allow algebraic statements that depend on ratio scale measurement.

In short, what you are imagining is better called inverse relationship or association. As one variable goes up, the other goes down, and no more than that.

Another point of usage here is that the word "prove" is too strong. In statistics there are no proofs outside mathematical statistics. In applied statistics or data analysis, we can test hypotheses and sometimes find that evidence supports them or that evidence fails to support them. But write of "proof" in (say) a submission to an English-language journal in your field, and almost certainly some reviewer will say something like this: use a different word.

All that said, the important part of your question cannot really be answered by us. As @Peter Flom said "You have to decide which is the dependent variable and which is the predictor". If you think there is a case for both kinds of relationships, you could try two kinds of models, but power as a function of dependence must be an ordinal model, and dependence as a function of power is much more likely to be a classical regression model, as far as we can tell without seeing any of your data.

I don't understand how MANOVA can be considered an alternative to an ordinal model.

Nick Cox
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  • Thanks for your extensive answer Nick. I think, apart from choosing my words more wisely, I have to get more familiar with ordinal logistic regression. After looking at several websites I still struggle to fully comprehend which approach I should choose for my problem. It would be nice if anyone had a link to a website, ebook or a title of a book which explains ordinal logistic regression to a statistics beginner. – Roman Aug 08 '13 at 14:48
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    I would check out the books by Alan Agresti. His introductory book at categorical data analysis sounds most suited to your request. www.amazon.com will guide you so I won't give the details here. – Nick Cox Aug 09 '13 at 17:35
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I solved the problem by using the Kruskal-Wallis test. After reading (again) the process for ordinal logistic regression on this and this website I considered ANOVA, due to probable violation of the normal assumption I decided based on this answer on CrossValidated that a Kruskal-Wallis test does the job just right.

Hereby I use the following command in R:

kruskal.test(formula, data, subset, na.action, ...)

Formula is defined in the manual as:

a formula of the form lhs ~ rhs where lhs gives the data values and rhs the corresponding groups.

My lhs is the continuous data (average of all four questions measuring dependence), rhs is my ordered data.

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