Men, Women, and Multivariate AnalysisHey buddy, c'mere—I wanna tell you something.  D'you know there's some real big differences between men and women?  

What do you mean, "Obviously"?  Hey, I'm not just talking physical differences, pal—I'm talking personalities! And if you want to get clinical about it, we're talking about stuff you can't even see unless you bust out some multivariate analysis. 

Hey, I don't care whether you're analyzing data for a Lean Six Sigma project or psychological research—this multivariate analysis is something you ought to know about.  

Word on the street is that looking at gender differences one aggregated personality trait at a time—you know, univariate analysis—just doesn't cut it. Turns out, if you really want to see just how different the personalities of men and women are, it's a lot better to take the multivariate approach to analyzing the data. 

A recent paper by some researchers at the University of Turin in Italy and the University of Manchester in the United Kingdom lays it all out in graphic detail. If you're into data, it's a sweet read.  

See, many psychological scientists have long maintained that sex differences in personality, and most other psychological attributes, are comparatively small. They called it "The Gender Similarities Hypothesis," and they performed analyses and hypothesis tests that supported that idea.

But in The Distance Between Mars and Venus: Measuring Global Sex Differences in Personality, Marco Del Giudice, Tom Booth and Paul Irwing get all multivariate on those earlier univariate analyses. They re-analyze the data used in earlier studies with a different methodology, and arrive at very different conclusions.

From a data analysis perspective, here's the sentence that broadly lays out their approach: 

When groups differ along many variables at once, the overall between-group difference is not accurately represented by the average of univariate effect sizes; in order to properly aggregate differences across variables while keeping correlation patterns into account, it is necessary to compute a multivariate effect size.

  
After some more detailed discussion, they drop the bomb, conclusion-wise: 

...when univariate effect sizes were estimated on latent variables and aggregated in a multivariate index (the strongest methodology), sex differences increased about tenfold and became extremely large.

 
So, earlier research underestimated gender differences in personality because the analysis oversimplified some factors, while not adequately accounting for correlation between multiple factors.  Analyzing the exact same data with a multivariate mindset revealed that the differences between men and women were far more significant. 

Now, at this point, people who've been in relationships with members of the opposite sex may feel free to roll their eyes and say, "Duh!"  

But for anyone who needs to analyze data, this study provides a valuable lesson about the importance of selecting the right factors to analyze, and identifying the right approach to analyze the data you've collected. 

In Minitab Statistical Software, you can use tools available in Stat > Multivariate to analyze your data's covariance structure, assign observations to groups, explore relationships among categorical variables, and more.

And quality practitioners can use Minitab's multivariate control charts (Stat > Control Charts > Multivariate Charts) to investigate how correlated or dependent variables influence a process or outcome together--for instance, to investigate if temperature and pressure are jointly in control in producing plastic parts.

Have you ever had a data set that yielded different outcomes depending on how you approached the analysis? 

 

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