### Visualising sampling Variation at Level 7

```
A look through, and go at, some activities designed to
give students visual and conceptual appreciation of
what sampling variation is and how it impacts on
statistical investigation in 91264.

Bring a laptop with iNZight and MS Word (or similar)
running.
Why wait for year 13?
 Sample variation is a problem from years 9 & 10!!
 Students should be given the chance to really
appreciate this in year 12.

Sample Variation is inherent in the sampling process. It
is the problem that the inferential statistical methods
we study are designed to overcome.
 We need to have a picture of sample variation in our
heads that helps us quantify and understand it if we
want to overcome it.


I’m concerned that we risk training a bunch of parrots
in our students who can spout a memorised sentence
or two without really knowing what they’re saying.

These are my ideas, some borrowed, some new, to try
to bring some understanding to student responses to
inferential problems.

Perhaps the biggest hurdle is really understanding why
we bother with sample variation ideas as teachers…
 What is sample variation?
 How have you communicated this to students?
 Write down what you think your students would say
sample variation is.
 Write down what you wish your students would say
sample variation is.

What do you see?

Try writing it down

How would you
communicate this to
students at level 2?

Medians from samples, n=30, will vary by
that much.

Most of them will be pretty close to the
population median.

If we are using any one of these random
samples, we’d like our methods to
consistently, or at least mostly, give us the
same message.
Have a play with the iNZight VIT Sample Variation
module, using NZIncomes03_11000.csv from the
iNZight data file.
 NB: you need to feed it a sufficiently large data set so
that it effectively becomes the population.
 Change the sample size, but stick to the median at
this level.
 What can we learn about the ‘problem’ of sample
variation here.



Run this at the front of the class with students telling you
what numbers to input.

In years 9 to 11...
In year 12...
 Median in red, quartiles in blue

64
66
68
70
72
74
76
78
80
82
84
86
88
90
92
94
What do you see? What does it mean?
 Try writing it down
 How would you communicate this to students at level 2?

96
98
Sample medians are clustered around the population
median.
 Medians vary by about one third of the variation we
see in the box/interquartile range.
 So if the difference between two medians is greater
than ⅓ of the distance covered by the two ‘boxes’
(overall visible spread) we can make a call that the
two sampled populations tend to be different because
the difference between the two sample medians is
more than we would expect to see as a result of
sample variation alone.
 If it isn’t, then the difference we see could well have
been generated by the sampling process.


1.
2.
3.
4.
5.
What happens as we change the sample size?
Use NZIncomes03_11000.csv
Run the Sample Variation module for the median and
both quartiles with n=100
Don’t forget to ‘record your choices’ for each one!
Copy the images into MS Word and overlay them,
making whites transparent.
Students can use this method to explore the 1/5 and
1/ guidelines for themselves.
10
What do you see? What
does it mean?
 Try writing it down
 How would you
communicate this to
students at level 2?

What do you see? What
does it mean?
 Try writing it down
 How would you
communicate this to
students at level 2?


Discussion

Where to from here?

PMI = Cheat’s way to report back to your department
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