Is .039 Larger or Smaller than .05?

Fri 9/28/2012 5:42 PM
Teaching and Learning Statistics <EDSTAT-L@LISTS.PSU.EDU>; on behalf of; Wuensch, Karl L <WUENSCHK@ECU.EDU>
Is p < .05 ?

I am not the greatest fan of NHST, but do my duty to teach it. For a good while now I have been disturbed that a substantial proportion of my undergraduate students never figure out how to decide whether or not a test is significant. I tried stressing that p is a measure of the goodness of fit between the data and the null, that p is like the strength of evidence in support of the accused null defendant in statistical court, and so on. Nothing seemed to help much.

Now one of my teaching assistant has discovered why. Given two numbers, these students are unable to identify which is smaller. No, I am not kidding. Yes, this involves numbers between 0 and 1. My TA spent half an hour trying to teach them how to tell which is the smaller of two numbers, without great success.

DeShea, Lise A. (HSC) <Lise-DeShea@OUHSC.EDU>

I wish I were surprised.

Sarah Carroll <scarroll@JFKU.EDU>

I feel your pain, Karl.

Denis, Daniel <daniel.denis@MSO.UMT.EDU>

I usually have about 10% of students drop the course when I introduce sigma summation notation. I don't know if it is high school or first year college that needs to be fixed. Probably both. Then again, since universities pretend to measure something called "teaching effectiveness" based on what these kids think of us, I suppose we shouldn't expect any different. A student who doesn't know whether one number is bigger than another, or what "greater than" or "less than" means or has never seen summation notation, is judging my effectiveness in teaching a stats course where the aforementioned prerequisites are assumed?  My, we take education seriously. No wonder so many profs water down there courses, tenure comes easier that way and everyone likes you.

David Winsemius <dwinsemius@COMCAST.NET>

That is a useful observation. I suspect (or more accurately I sincerely hope) it's primarily an issue in the range -1 to 1.

Bob <bob@STATLAND.ORG>

I taught math in colleges for 30+ years and you are absolutely right. And to think -- we droped common fractions because kids can just use decimals  ;-(

Abhaya Indrayan <a.indrayan@GMAIL.COM>

Can I give a third person perspective? When I first encountered US university students, I was amused to find that 1/3 + 2/3 is 0.99 and not 1 since that is what the calculator gives. Then it is from the same system that great researchers and scientists emerge. Some of these students go on to surprise the world with their original thinking. Many of those now reacting are also product of the same system. I guess this mismatch is the spice of life.

Christopher Green <christo@yorku.ca>

I am now covering my ears and singing "la la la la ... I can't hear you!"

Wuensch, Karl L <WUENSCHK@ecu.edu>

Several of these students told me they expect to get a doctorate in clinical psychology and earn over \$100K annually after they do. They may well end up working for Verizon.

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

Beth Benoit <beth.benoit@gmail.com>

That youtube link is the funniest/saddest thing I've heard all day. A don't-miss-it.

Paul C Bernhardt <pcbernhardt@frostburg.edu>

I hate to say this, but thank you.

I have often wondered why so many students would be baffled by the decision process. [if p < .05, reject the null hypothesis]. It seems so easy… but, if you are not comfortable with the numbers between 0.00 and 1.00, then it is a real problem.

Compound that with the fact that, in general, test statistic values go up as their associated p-values go down and you have now put them in contrasting information territory. That is, thinking I'm clarifying things with my graphs and sketches of distributions and shading of rejection regions showing how bigger t-values are associated with smaller p-values, it seems likely they get confused by the two ways of making the decision: greater than critical value, or less than alpha… I can see I'll be rethinking some lectures next semester.

William Scott <wscott@wooster.edu>

I am gob-smacked. Karl's observation, if true, might explain many things that until now have been mysterious to me.

Deborah S. Briihl <dbriihl@valdosta.edu>

Btw, you are not the only person with this problem. I cannot tell you the number of students who just do not grasp this. What works best for us is to have the students think about it as if it were money. Then they can get the concept of which is greater.

Wuensch, Karl L <WUENSCHK@ECU.EDU>

Twice in recent years I have taken over the undergrad stats class of a departed colleague who had the reputation of teaching at the 4th grade level. It was in these two classes where the typical student could NOT decide whether .043 is less than or more than .05 and where many students could not convert feet into inches even when told how to do it. This semester I have a much better group, most of whom knew what they were getting into when they registered for my section.

McDonald's quarter pounder was selling like hotcakes, so A&W offered customers a burger with more meat (one third of a pound) for the same price, but customers were not impressed.  Subsequent focus group research revealed that the majority of customers thought that one fourth of a pound is more than one third of a pound.  The same thing happened to McDonalds later, twice, when they attempted to introduce one third pound burgers.

Well, if the customers are that stupid, why not just introduce a sixth-pound burger at the same price as a quarter-pound burger.

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