Difference between Multivariate analysis, Correlation, Regression etc

[Clariman]

I want to analyse some data to see if I can uncover potential relationships or patterns between variables. Although numerate (by my own definition!) I am not a statistician and online descriptions show formulae that I no longer have the mathematical background to fully understand.

The key terms I would like to understand are in bold below. Are these terms related to each other, are some subsets of the other?

I read an academic article on my subject where the author said that the next stage would be to undertake multivariate analysis. In my own layman's terms, I am looking for something that would help me identify correlations between variables, but this seems to have a more specific meaning. Finally, when I emailed a lecturer to say what I wanted to do (in layman's terms) he suggested that I probably wanted to use regression techniques.

Are regression and correlation both types of multivariate analysis or is multivariate analysis something else? Regression and correlation seem very similar but regression has the concept of one variable being dependent on others, whereas correlation does not have that notion.

I have access to SPSS software to help with the analysis if I go down this route.

Thanks
C

[dspp]

Essentially it is the same thing.

The more variables you are trying to determine the effects of, the larger the database of statistical observations you will require. And if you need to do this to any sort of statistical confidence test (so that you can be certain that it is not a random outcome) then your need for data will explode. If some of them are non-linear then things get really hairy really quickly. And if some of the variables are not fully independent then it gets sticky.

Regression analysis (https://en.wikipedia.org/wiki/Regression_analysis) is the main branch you need to be reading about.

Multivariate analysis (https://en.wikipedia.org/wiki/Multivariate_statistics) is getting into more complex stuff. If you are going there you need help.

regards,
dspp

[modellingman]

Multivariate analysis is a broad term which covers a range of different statistical analysis techniques involving multivariate data.

Multivariate data simply means that each "observation" in a data set is described by more than one variable. For example, measuring the height and weight of each person in a group of provides observations comprising the height and weight pair for each person. Further variables such as age and gender might be used to increase the number of variables for each observation.

Regression is one technique available for analysing multivariate data so it is a type of multivariate analysis. Other types of multivariate analysis exist, see, for example, https://www.decisionanalyst.com/whitepa ... tivariate/ which lists and briefly describes 11 different types of multivariate analysis.

Correlation is a measure of linear association between a given pair of variables used within a multivariate data set. For example, the correlation between height and weight or the correlation between age and weight. Correlation (or Pearson's Correlation Coefficient to use the full title) varies between -1 and +1. Values of +1 and -1 both indicate a perfect linear relationship between the two variables, the difference being that +1 means both variables change in the same direction (if one increases the other also increases) whilst -1 means that they change in opposite directions (if one increases the other decreases). A value of 0 means the two variables have no discernible linear relationship between them.

If your data set uses n variables then, potentially, you have n*(n-1)/2 distinct pairs of variables for which correlations can be calculated. Not all pairings can be used. In particular, any pair involving a categorical variable cannot have a correlation calculated for it unless the categories are mapped to numerical values.

Calculation of all possible correlations can be a useful form of descriptive analysis in much the same way that calculating the mean and standard deviation of a univariate data set is a useful form of descriptive analysis.

There is, as far as I am aware, no universally recognised list of statistical analyses that fall under the heading of multivariate analysis. Personally, I would be reluctant to describe the calculation of correlation as a type of multivariate analysis, though I wouldn't get too hung up about it. The type of analysis you use should really be determined by what you are trying to achieve, the views (hypotheses) that you have about the possible relationships within your data (and descriptive analyses can help to formulate these views) and the nature of the data that you have available (or can generate) to feed into your analysis process.


Is the original post related to this thread - viewtopic.php?f=9&t=14959 - by any chance?

[Clariman]

Is the original post related to this thread - viewtopic.php?f=9&t=14959 - by any chance?

Many thanks dspp and modellingman. Yes, modellingman, this is related. I missed your reply to the earlier thread so thanks for bringing it to my attention.

C

[modellingman]

Is the original post related to this thread - viewtopic.php?f=9&t=14959 - by any chance?

Many thanks dspp and modellingman. Yes, modellingman, this is related. I missed your reply to the earlier thread so thanks for bringing it to my attention.

C

Towards the end of the final post of the earlier thread, I discussed the use of a chi-squared test with a contingency table to determine whether two attributes of the artefacts were independent of each other. The attributes are simply variables and in my simplified example I used two variables (attributes): one was marking type (taking 3 possible values) and the other was geography (taking 2 possible values). These are both categorical variables ie the possible values are category labels rather than numerical values. Consequently, neither can be used directly to determine their correlation with any other of the attributes (variables) of your artefacts.

However, one of the main purposes of calculating a correlation coefficient is to determine whether two variables are related to each other. Statistical theory tells us that if two variables are independent then they will have a correlation of zero.