Thank you so much for helping me with this – lots of useful feedback on tips and back channel (I quickly ran out of my 3 daily posts so I was talking directly to folks). TIPSters rock!
Now just one last question. I’m writing an article where this is a problem for just two correlations (in a big table with lots of correlations). Do I just add a footnote to those two cells and say “disregard – see Simpson’s paradox (ref)”? Marie Helweg-Larsen, Ph.D. Associate Professor l Department of Psychology Kaufman 168 l Dickinson College Phone 717.245.1562 l Fax 717.245.1971 Office Hours: Mondays and Tuesdays 2:00-3:30 http://users.dickinson.edu/~helwegm/index.html From: John Kulig [mailto:[email protected]] Sent: Monday, February 27, 2012 2:33 PM To: Teaching in the Psychological Sciences (TIPS) Subject: Re: [tips] Statistical question-correlations OK, I think the mystery of Marie's data is solved. I was on the right track inititially. If you look at non-Smokers, notice the Y axis where ALL the data is above 2, going up to 5, and there is a slight positive correlation. Now take the smoker data and visually superimpose it or sketch it in. Notice two things: the smoker data is mostly lower, with data between 1.5 and 4.5 .. Now you'd think these effects would wash out, but also notice this: Non-smokers, chance of lung cancer = 4 OR 5, there are only a few points, all high on Y axis. When you look at smokers, chance of lung cancer = 4 OR 5, there are much more data points, between 2.5 and 4.5 on Y, enough to tilt the best fit line downward as X increases Now, when you look at the combined data, on the one hand it looks positive, because when X = 4 or 5 the Y values overall seem higher because the _range_ of data seems higher, but notice that the _concentration_ of high Y points when X = 1 and 2 .. they are bunched up at the upper end of Y and the circles are squashed on top of each other.. that will pull the regression line up when X is low, and my first paragraph shows how it will pull down when X is high ... ========================== John W. Kulig, Ph.D. Professor of Psychology Coordinator, University Honors Plymouth State University Plymouth NH 03264 ========================== ________________________________ From: "John Kulig" <[email protected]<mailto:[email protected]>> To: "Teaching in the Psychological Sciences (TIPS)" <[email protected]<mailto:[email protected]>> Sent: Monday, February 27, 2012 2:02:25 PM Subject: Re: [tips] Statistical question-correlations OOPS .. didn't see the scatterplot , just notice it, let me look ========================== John W. Kulig, Ph.D. Professor of Psychology Coordinator, University Honors Plymouth State University Plymouth NH 03264 ========================== ________________________________ From: "Arlie Belliveau" <[email protected]<mailto:[email protected]>> To: "Teaching in the Psychological Sciences (TIPS)" <[email protected]<mailto:[email protected]>> Sent: Monday, February 27, 2012 1:37:05 PM Subject: Re: [tips] Statistical question-correlations Hi Marie, Have you calculated your effect sizes? It could be that the positive correlations of .23 and .16 are so small that, when the groups are combined, the error (or noise) turns them into negative correlations. At a glance, the scatter plots don't looks as though the relationships between variables are very significant. Just a thought. Cheers, Arlie -- Arlie R. Belliveau, BA (Hons), MA History & Theory of Psychology, PhD2 York University Department of Psychology 059 Behavioural Science Building 4700 Keele St. Toronto, ON [email protected]<mailto:[email protected]> On Mon, Feb 27, 2012 at 11:30 AM, Helweg-Larsen, Marie <[email protected]<mailto:[email protected]>> wrote: I have a simple statistical question. I have a sample of 307 people. 111 are in the red group and 196 are the blue group. The correlation between variables x and y in the red group is r= .226 (n=111), p <.05 and in the blue group r=.164 (n=196), p<.05. However, when I run the correlation between x and y in the entire sample (red and blue combined, no missing data) I get a negative correlation, r=-.142 (n=307), p < .05. Now what doesn’t make sense to me that two groups individually have positive and significant correlations but the two groups combined can have a negative and significant correlation. So you stats tipsters. Is that statistically possible? I have checked everything I possibly can in terms of errors in the data or the analyses and have found none. Some suggestions about what I ought to look at? Marie Marie Helweg-Larsen, Ph.D. Associate Professor l Department of Psychology Kaufman 168 l Dickinson College Phone 717.245.1562<tel:717.245.1562> l Fax 717.245.1971<tel:717.245.1971> Office Hours: Mondays and Tuesdays 2:00-3:30 http://users.dickinson.edu/~helwegm/index.html<http://users.dickinson.edu/%7Ehelwegm/index.html> --- You are currently subscribed to tips as: [email protected]<mailto:[email protected]>. 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