### Behavior in Four Chromosomal Syndromes

On the Trisomy 9 Website, run by the mother of a little boy with partial trisomy 9p, there is a survey. A few years ago, she used to provide the full data set of the survey as well as the results. Back then, I downloaded a copy of it, and now that I have access to SPSS, I've decided to analyze the results myself.

I'm focusing on the subsection regarding behavior ('habits'), because I'm fascinated by behavioral phenotypes. There are many different kids with different conditions described in the survey, but I'll focus on the four most common syndromes - trisomy 13, trisomy 18, partial trisomy 9p, and mosaic trisomy 9. I took all the kids within those four groups (11 with trisomy 13, 16 with trisomy 18, 25 with trisomy 9p and 8 with mosaic trisomy 9) and analyzed their survey results for behavior.

The first thing I did was to run a factor analysis (well, actually, the first thing I did was to recode 'yes' as 2 and 'no' as 1,

I found 10 factors. Here they are, with correlations greater than .3 listed:

Anyway, I was interested in two main questions: do children with different syndromes behave differently, and is there an age-based difference in behavior? (The kids ranged from newborn to 30 years old, with no significant difference in age between syndromes.)

I ran an ANOVA for each factor related to syndrome. The ANOVA indicated that most of the factors weren't significantly associated with syndrome category, but factor 2 was (p=.001). On the post-hoc tests (Tukey HSD, Scheffe and Bonferroni), this turned out to be due to a significant difference between trisomy 18 and trisomy 9p. Trisomy 18 scored the highest on this factor and trisomy 9p scored the lowest, with the other two in between.

I then ran ANOVAs on the specific behaviors with a loading of at least .3 on factor 2, and found significant effects for 'rocks/shakes head' (p>.001), 'must hold something' (p=.026), 'dances' (p=.025), 'stubborn' (p>.001), 'tenacious' (p=.031) and 'great memory' (p=.002). The post-hoc tests (same as above), showed the following:

This was trickier, since there were so many individual values for age. Mean age was 7.36 years, with a standard deviation of 8.165 years. I got it to tell me the 20th (2 years), 40th (3 years), 60th (5 years) and 80th (13 years) percentile, and used those to generate a categorical variable for age - <2.5 years, 2.5-3 years, 3-5 years, 5-13 years and >13 years.

I then ran an ANOVA on the different factors with age. Like the trisomy ANOVA, this one found that only factor 2 (p=.011) showed a significant correlation. The post-hoc tests found that 2.5-3 year olds scored significantly higher (p=.046) on factor 2 than >13 year olds did. (The plot of means shows high scores for the two youngest groups and a steady decrease for the three older groups.)

I then ran ANOVAs on the specific behaviors with a loading of at least .3 on factor 2, and found significant effects for 'throws head back' (p>.001), 'hates eating' (p=.006) and 'rubs hand across face' (p=.022). The post-hoc tests showed the following:

I posted a previous blog entry regarding my adventures with SPSS, where I tested whether wheelchair bowling is easier than regular bowling. I have recently corrected a mistake I made in that post - larger sample sizes should have

* It spat out an error message saying "The group sizes are unequal. The harmonic mean of the group sizes is used. Type I error levels are not guaranteed." Type 1 errors are finding something when nothing is there, so that might explain why the ANOVA claimed a significant difference that the post-hoc tests failed to confirm.

I'm focusing on the subsection regarding behavior ('habits'), because I'm fascinated by behavioral phenotypes. There are many different kids with different conditions described in the survey, but I'll focus on the four most common syndromes - trisomy 13, trisomy 18, partial trisomy 9p, and mosaic trisomy 9. I took all the kids within those four groups (11 with trisomy 13, 16 with trisomy 18, 25 with trisomy 9p and 8 with mosaic trisomy 9) and analyzed their survey results for behavior.

**Factor Analysis**The first thing I did was to run a factor analysis (well, actually, the first thing I did was to recode 'yes' as 2 and 'no' as 1,

*then*I did the factor analysis). I don't really know factor analyses that well, so I may have screwed up stuff. If you know enough about factor analysis to spot a mistake I made, let me know.I found 10 factors. Here they are, with correlations greater than .3 listed:

- factor 1: chews on toys (.696), dances (.643), chews on clothes (.588), touches everything (.573), stubborn (.561), tantrums (.550), throws head back (.543), throws objects (.503), shows no fear of falling (.438), bites self (.436), tenacious (.432), rubs hand across face (.411), great memory (.400), kicks feet (.381), loves mirrors (.349), affectionate (.325), must hold something (.307) and loves baths (.303)
- factor 2: great memory (-.714), rocks/shakes head (.663), hates eating (.636), kicks feet (.536), throws head back (.520), sucks finger/thumb (.477), dances (-.460), loves eating (-.449), rubs hand across face (.411), drools (.384), very happy (-.378), tenacious (-.365), stubborn (-.353) and must hold something (-.346)
- factor 3: drools (.608), sucks on finger/thumb (.517), loves music (.445), very happy (.444), loves eating (.430), socializes (.405), stubborn (-.399), bites self (.346), kicks his/her feet (-.342), throws objects (-.339), chews on clothes (.316), tantrums (-.313) and rocks/shakes head (.312)
- factor 4: very happy (.598), dislike solitude (.446), loves mirrors (.441), throws objects (.435), rubs hand across face (-.407), tenacious (-.382), grumpy (-.362), socializes (.352), loves baths (.326), throws head back (-.322) and touches everything (.321)
- factor 5: high pain threshold (.697), no fear of falling (.485), loves mirror (-.422), grumpy (.343), loves music (-.340), tenacious (.322), socializes (.314) and bites self (-.302)
- factor 6: loves music (-.589), bangs head (.528), tantrums (.384), touches everything (.363), hates eating (-.350), no fear of falling (-.330), loves eating (.314) and high pain threshold (-.311)
- factor 7: affectionate (.617), loves baths (-.608), grumpy (.433), dislikes being alone (.380) and socializes (.331)
- factor 8: tenacious (.428), drools (.387), touches everything (-.380), grumpy (-.312), throws head back (.303) and tantrums (.302)
- factor 9: bangs head (-.590), dislikes solitude (.462), loves mirrors (-.336) and affectionate (-.328)
- factor 10: loves mirrors (-.466), grumpy (-.408), must hold something (.394) and rubs hand across face (-.302)

Anyway, I was interested in two main questions: do children with different syndromes behave differently, and is there an age-based difference in behavior? (The kids ranged from newborn to 30 years old, with no significant difference in age between syndromes.)

**Syndrome differences**I ran an ANOVA for each factor related to syndrome. The ANOVA indicated that most of the factors weren't significantly associated with syndrome category, but factor 2 was (p=.001). On the post-hoc tests (Tukey HSD, Scheffe and Bonferroni), this turned out to be due to a significant difference between trisomy 18 and trisomy 9p. Trisomy 18 scored the highest on this factor and trisomy 9p scored the lowest, with the other two in between.

I then ran ANOVAs on the specific behaviors with a loading of at least .3 on factor 2, and found significant effects for 'rocks/shakes head' (p>.001), 'must hold something' (p=.026), 'dances' (p=.025), 'stubborn' (p>.001), 'tenacious' (p=.031) and 'great memory' (p=.002). The post-hoc tests (same as above), showed the following:

- rocks/shakes head: T-13 > T-9p, T-9mosaic; T-18 > T-9p - so trisomy 13 kids were most likely to do this behavior, followed by trisomy 18 kids, then mosaic trisomy 9 and lastly trisomy 9p kids
- must hold something: oddly enough, no differences were significant, but trisomy 9p was approaching significance with all three other groups. So, they
*might*be less likely to engage in this behavior than the other three groups* - dances: T-9p > T-18 - partial trisomy 9p kids were more likely to dance than trisomy 18 kids
- stubborn: T-13, T-9p, T-9mosaic > T-18 - trisomy 18 kids were significantly less stubborn than the other three groups, who didn't differ from each other
- tenacious: T-9p > T-18 - partial trisomy 9p kids were more tenacious than trisomy 18 kids
- great memory: T-9p > T-18 - partial trisomy 9p kids seemed to have better memory skills than trisomy 18 kids

**Age differences**This was trickier, since there were so many individual values for age. Mean age was 7.36 years, with a standard deviation of 8.165 years. I got it to tell me the 20th (2 years), 40th (3 years), 60th (5 years) and 80th (13 years) percentile, and used those to generate a categorical variable for age - <2.5 years, 2.5-3 years, 3-5 years, 5-13 years and >13 years.

I then ran an ANOVA on the different factors with age. Like the trisomy ANOVA, this one found that only factor 2 (p=.011) showed a significant correlation. The post-hoc tests found that 2.5-3 year olds scored significantly higher (p=.046) on factor 2 than >13 year olds did. (The plot of means shows high scores for the two youngest groups and a steady decrease for the three older groups.)

I then ran ANOVAs on the specific behaviors with a loading of at least .3 on factor 2, and found significant effects for 'throws head back' (p>.001), 'hates eating' (p=.006) and 'rubs hand across face' (p=.022). The post-hoc tests showed the following:

- throws head back: under 2.5 > 5-13, over 13 - this behavior was most common in children under 2, and uncommon in kids 5 or over.
- hates eating: 2.5-3 > under 2.5, 3-5, 5-13, over 13 - this behavior peaked around 2.5-3 years
- rubs hand across face: under 2.5 > 5-13 - this behavior was common in very young children, rare in 5-13 year olds, and moderately common both in 3-5 year olds and over 13 year olds.

**Note**I posted a previous blog entry regarding my adventures with SPSS, where I tested whether wheelchair bowling is easier than regular bowling. I have recently corrected a mistake I made in that post - larger sample sizes should have

*smaller*standard deviations, not larger.* It spat out an error message saying "The group sizes are unequal. The harmonic mean of the group sizes is used. Type I error levels are not guaranteed." Type 1 errors are finding something when nothing is there, so that might explain why the ANOVA claimed a significant difference that the post-hoc tests failed to confirm.

## 3 Comments:

My extremely vague recollection of SPSS when I learned it in graduate school way back when is that for variables such as age that varies on a continum, instead of lumping them into age groups there's supposed to be a way to use a different type of equation (or function in the SPSS)to account for that kind of variable. I want to say "bi-something" analysis but not sure. I'm not explaining this very well ... probably because I don't remember it well ... in part because I learned this more than a decade ago, but also in part because I had the misfortune of having a lousy teacher that semester (the only reason ANY of us passed is because a student taking a different section of the same course under a better teacher, who also had better math and computer skills to begin with, learned it all and tutored every one of us individually throughout the semester ... that student ended up needing to submit an incomplete because he fell so far behind in his own course work!)

I'm guessing you're only a few weeks along in learning about SPSS ... maybe sometime in the next couple of months you'll get to the unit in the curriculum where you go, "Oh, maybe *this* is what Andrea was trying to tell me about but couldn't name or explain" ... then you could try coming back to this study to see if you can analyze the data with your improved understanding of SPSS.

Enjoy. You're lucky to have this ... when my mother was in grad school and the first decade or three of her career, she had to basically memorize (or at least know how to look up) the various complicated equations used in statistical analysis, then she had to write all her own computer programs to do the analysis because there was no off-the shelf software.

There were also no PCs, at least not the kind of desk top that an ordinary family could afford--in grad school, my mother (and father, though not the same field) had to hand write computer program codes or type them on a manual type writer, take it to the computer center for someone at the computer center to key into the computer at an appointed time and print out the results for them. And if they made a mistake in the program code then they couldn't fix it right away, they would have to make a new appointment with the computer people to come back and submit a de-bugged version of their computer code to be keyed in again. They wouldn't have been able to "play" with the data analysis the way you are doing now. (I put quotation marks because even though I think you enjoy this a lot, I know you're also learning by doing it so it serves a serious purpose as well as a fun one.)

Is it bivariate analysis, Andrea?

Or something different altogether...(something-variate was on the right track. Multivariate might work too).

Thank you for the descriptions of history and technology over time.

Discovery; exploration; practice.

Because Wolfram Alpha is so great: MathWorld class for multivariate analysis - all the structure and function here

MathWorld reference for 33-XX [special functions]

Those links above might be some of the things your Mum had to look up, Andrea.

(Was it the time of mainframes and punchcards? Pre-1981 anyway).

Adelaide Dupont:

Yes, bivariate analysis sounds very possible -- I kept thinking it was bi something but couldn't think what the rest of it was and wasn't entirely sure about the bi either. My memory of my own SPSS class is *really* fuzzy at this point.

As to when my Mom first started using computers, I will give you two hints:

1. She (and also Dad, though for different purposes) has been using computers since before I was born. In fact, I believe she may have started using computers around the time she was pregnant with my sister who is 2 years plus a few months older than me.

2. I became 41 in January '11.

Do the math! She may have needed to look up the kind of stuff in what you linked (I think she had some basic equations memorized just not all) , but she certainly wasn't looking them up on the internet! :-) ... because when she was starting to use computers, the internet (the earliest version of which actually began in about '69) didn't exist yet.

'81 was I think a little pass the time that my parents bought a TRS-80 for our home ... partly so Mom could use it for work related stuff (programs had to be saved onto audio tapes then) ... then my older sister got hooked on teaching herself how to program the computer. Of course the TRS-80 had no word processing, web, or anything else word-oriented, so even though I was sort of intellectually interested in the *idea* of the computer it didn't fascinate me nearly as much.

Ettina, hope we are not pulling this discussion too far off track with this "history" lesson :-)

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