I had hoped things were better in Germany.  Sigh.

          For the quarter who cannot solve your puzzle, there is a job waiting 
at Verizon:

http://www.youtube.com/watch?v=zN9LZ3ojnxY

Cheers,
[Karl L. Wuensch]<http://core.ecu.edu/psyc/wuenschk/klw.htm>
From: Rainer Scheuchenpflug [mailto:[email protected]]
Sent: Friday, April 26, 2013 11:13 AM
To: Teaching in the Psychological Sciences (TIPS)
Subject: [tips] Numerical challenges (was: Is p<.05)










Dear Tipsters,

a while ago Karl Wuensch mentioned that his students seemed to have problems 
telling which of two numbers was larger ("Is p< .05", Mail: Sept 28th2012, 
http://www.mail-archive.com/[email protected]/msg08713.html)

As probably most of you, I shook my head in disbelief, mentioned the story to 
my students in statistics 1 last semester during introductory sessions and got 
a few chuckles.

But then I decided to collect some data and entered the following item in the 
final test:

"Warm-up 2:

Sort the following letter-number-pairs in numerically increasing order 
(smallest number first, largest number last). Enter the sequence of letters 
that results as one word in the answer field.

A: 1.2%
B: 1/50
C:-0.03
D: 0.05
E: 0.2%
F: -1.2
"

The item was worth 1 of 64 points in a 2-hour final exam and intended as an 
icebreaker. 195 students participated in the exam, 172 of them used a laptop 
with spreadsheet software (Excel or Calc) for computations.
As an exercise: How many students will answer this question correctly? Please 
take a note of your guess (to avoid hindsight bias).







Well, 2 of the 195 participants failed on purpose (left all answers empty), 1 
failed to follow instructions.
Of the remaining 192 students, 142 sorted the numbers correctly (74%).
14 students (7.3%) answered FCBDEA (-1.2, -0.03, 1/50, 0.05, 0.2% , 1.2%), 
i.e.: ignored completely that the last 2 numbers were percentages.
6 students (3.1%) answered FCEBDA (-1.2, -0.03, 0.2%, 1/50, 0.05, 1.2%), i.e. 
showed confusion if percentages were used.
5 students (2.6%) answered CFEABD (-0.03, -1.2, 0.2%, 1.2%, 1/50, 0.05), i.e. 
could not order negative numbers.
3 students (1.6%) answered DBAECF - wrong direction.
The other students were distributed evenly on wrong answers, no pattern 
detectable.
Item-total-correlation (part-whole corrected) was r=.34.

I use percentages and decimal numbers interchangeably during lecture, and 
explain explicitly how compute the decimal number from a percentage (or 
fraction) and vice versa. Nevertheless I found several students who used 
percentages and decimal numbers wildly intermixed within the same formula 
(Bayes).

So Karl: You are not alone. And tell your TAs to discuss percentages and small 
negative numbers too.

Kind regards,
Rainer

Dr. Rainer Scheuchenpflug
Lehrstuhl für Psychologie III
Röntgenring 11
97070 Würzburg
Tel:   0931-31-82185
Fax:   0931-31-82616
Mail:  
[email protected]<mailto:[email protected]>
Web:      http://www.izvw.de



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