## Teaching Statistics is Hard – Expected Value Edition

I alluded to one difficulty in teaching statistics at the end of this earlier post.  Here is another – also gleaned from Daniel Kahneman’s book  Thinking, Fast and Slow.

My lecture on expected value usually seems to fall flat.  I think this table for gambles of modest stakes from Kahneman’s book (page 315) explains why.

Probability versus Decision Weight - from Thinking, Fast and Slow

The table says that unlikely events are overrated.  We think a 1% chance is more like a 5.5% chance .  Also a two percent uncertainty of winning lowers the utility of the gamble by 13%.  These phenomena are called the possibility effect and the certainty effect. Read Kahneman’s excellent book for details, but what this means for teachers of probability is that the typical expected value discussion will not fly.  For instance students will take a sure \$900 rather than a gamble where they have a 98% chance of winning \$1000 and a 2% chance of losing \$20 even though the expected value of the gamble is \$974.

Somewhere in Kahneman’s book he talks about a course in decision making that he and others attempted to develop for Israeli high schools.  It was never implemented and Kahneman discusses why.  But I think that the ideas he so clearly describes in Thinking, Fast and Slow need to be a part of statistical reasoning curriculum.