# Is there a case for ditching any of the paper tables in elementary statistics courses?

The textbook I'm using explains the it is "impractical" to have a normal distribution for all values of $\sigma$ and $\mu$, hence the standard normal distribution table.

To me, this simply doesn't ring true. We could have a phone app, to generate a distribution for $\sigma$ and $\mu$, then highlight the desired area.

http://homepage.stat.uiowa.edu/~mbognar/applets/normal.html

$P(x)=\frac{1}{\sigma \sqrt{2\pi}}e^{\frac{-(x-\mu)^2}{2\sigma^2}}$

But, is the standard normal distribution important beyond being a time-saving calculation tool? There are so many important concepts in statistics and so little time that it feels like a wasted opportunity to teach outdated calculation methods.

HOWEVER: Until there is a revision in the way that we teach elementary statistics, my students must learn these methods. The standard normal distribution is ubiquitous in math and science education. Students may need to learn about it to understand how other people may talk about statistics.

What should be the future of paper tables?

• The title asks whether we should ditch paper-based statistical tables, but the question asks why we need to convert to the standard normal distribution. These aren't quite the same thing. Can you make the connection clearer? – DavidButlerUofA Apr 22 '15 at 7:43
• In exam situations phone apps (or any device which can communicate electronically with other devbices) is usually not allowed ... Standardizing a variable is also a very basic operation which should be understood? – kjetil b halvorsen Apr 22 '15 at 8:26
• "The standard normal distribution is ubiquitous in math and science education." -- is it? I haven't seen it outside of a statistics course, honestly. – Chris Cunningham Apr 22 '15 at 14:47
• See also the related (but different) question matheducators.stackexchange.com/questions/5949/… – Chris Cunningham Apr 22 '15 at 14:58
• @Richard -- and not exactly "ubiquitous" is it? – DavidButlerUofA Apr 22 '15 at 22:41

This answer is not necessarily specific to statistical tables, but to table reading in general. I basically learned how to read and understand all types of tables including spreadsheets, train tables, and various mathematical tables by analyzing a physical table in my high school statistics class. The visual aspect of both the standard normal distribution, which most people will recognize without even knowing exactly what it is, and the layout of the table made it very easy for me to understand how the data was structured and organized. We had graphing calculators that could do it, but after some practice I actually found using the tables in the back of the textbook for quick check ups. I believe there is a lot of value in being able to read tables and the normal distribution is a great entry point into being able to really understand how to read them, and more importantly how to make them.

As far as pedagogical practice, I would suggest to let your students choose which to use on a day-to-day basis, but I would defiantly push them to at least be comfortable with both methods for the sake of testing etc. One thing that immediately comes to mind is to set up a weekly "competition" where students race using one of the two methods to solve a problem. Having them switch between the two each week could allow them to try to get Personal Bests and would be a great way to have them make a table to keep track of their own times :)

• Interesting perspective! – Chris Cunningham Apr 23 '15 at 16:42

As @kjetilbhalvorsen mentioned, tables are useful useful for old style pen and paper exams. They should be readily duplicated in a decent graphics calculator, but there are more important reasons that the days of the paper normal distribution table are dated.

First, the validity of using an exam to asses statistics has been largely jettisoned in some education systems, even where it is retained for other areas of maths.

Second, I find the conceit of using tables to get accurate values for a normal distribution, while the normal distribution itself is usually only a very rough approximation of the real life situation to be bizarre. IMHO a course specification asking that a rough approximation be applied to 3 sig.fig. is indicative of deep conceptual deficiencies in traditional statistics education.

The heuristic usefulness of normal distributions can be provided by a few critical values for hypothesis testing, without the use of tables.

As you suggested, there are much more important things to learn.

The standard normal distribution is very important concept that is completely separate from the standard normal table. The standard normal allows us to compare unlike variables. A typical example is comparing an athlete in one sport to another. You can understand and use the standard normal distribution without relying on the tables to do this. It is for this reason that I no longer paper tables and instead I have chosen have my students use the following normal distribution calculator:

http://davidmlane.com/hyperstat/z_table.html

I believe the table itself gets in the way of students seeing the big picture of what they are doing in using the normal distribution. The fact that the table only gives P(z<=Z) means extra computation steps that are basically irrelevant to understanding how the normal distribution works. It is another typical statistics example where computation obfuscates what is actually going on.

To address concerns about students using apps on quizzes, I have designed my quizzes to focus on interpretation rather than computation. I will only ask students to compute values for labs and projects. This makes it so that apps are not necessary on quizzes and so I can evaluate my students ability to understand the meaning of important ideas. I have found that when computation is necessary, I can ask students to apply the empirical rules to demonstrate understanding.

A final note: This choice also depends on what your students' next courses will be. I teach an introductory high school course. I expect that my students will take an introductory college course. If that course does not use a table, great! If it does, they will have adequate conceptual preparation that will prepare them to learn it during that class.

• But we could use any normal distribution as the standard. There is nothing special about having sigma=1 and mu=0-- that said I do think a problems that as students to compare more than one distribution or find regions of equivalent area for different scales are very important. – futurebird Apr 23 '15 at 19:24