Additional notes 1997
Additional notes 1997
Here are some brief notes about other things I said is lectures that
did not get into the notes. (This is partly to help me remember next year
what I want to say or should have said.)
Lecture 1
I made 250 copies of handouts. About 210 were taken.
I discussed the structure of the course, explaining my method
of course organisation.
I spent nearly 20 minutes chatting at the start about general issues
and so didn't really have time to go through the reviews of random
variables in 1.3, as I had thought I might do.
I only properly did sections 1.1, 1.2, 1.3(a)
1.5, 1.6 and 1.7. I hope this will be OK; the rest of the notes
is just revision of IA Probability and students should be capable of
refreshing their knowledge from these notes.
I should have said more about the difference between an
estimator and an estimate. I can pick this up next time. It would
also have been good to remark about the convention for using
upper letters for random variables and lower case letters for data
values.
I did the survey about bathing and talked briefly about the issue of
"anchoring" that can occur when people are asked to make subjective
estimates.
Lecture 2
I made just 220 handouts this time, of which 200 were taken.
There is quite a lot in this lecture, but I got through it all, apart from
calculating the expected value of the estimator of the MLE in Page 12,
(c). I will start with this next time.
I discussed the results from the anchoring experiement and showed
how we estimate the proportion who have not bathed. It was about 20%.
A student asked me at the end if there were any good reasons for
liking MLE. This is exactly what I shall be talking about next time.
But it would be good to have mentioned asyptotic unbiasedness in this
lecture.
I forgot to mention that sufficient statistics are not unique.
Lecture 3
I handed out the first examples sheet and copies of
some statistical tables.
With hindsight, it would be better to prepare the chi-squared tables
to include some lower percentage points, since these tables will not be
enough for computing confidence intervals.
I did a digression on "How many words did Shakespeare know?"
When doing the examples I emphasised the key ideas, often not
well-remembered from last year, that the
var(sum X_i)=sum var(X_i) and that var(cX)= c^2 var(X).
Lecture 4
I did a digression on the rule of 39 for calculating a 95% confidence
interval for remaining life and applied this to determining a confidence
interval for the remaining life of humanity.
I told students about the TV programmes on applicable maths on BB2
on Tuesdays.
Lecture 5
I did a digression on utility functions and lotteries.
I slightly ran out of time for section 5.3. The digressions are
becoming a bit too long. I can should myself work by making less of these.
I forgot to mention the
Lecture 6
I did a digression on the Allias paradox.
This lecture went quite smoothly. The discussion of null hypothesis and
type I and II errors in terms of a murder trial seems to be quite helpful.
Lecture 7
I did a digression on the Ellsberg paradox.
Lecture 8
I did a digression on an estimation game.
Lecture 9
Since tomorrow is Valentine's Day I did a
digression on a statistical love story.
Lecture 10
I mentioned that Simpson's paradox is also called Yule's paradox.
Yule (who was a fellow of Johns and lived 1871-1951, wrote about it 40
years before Simpson did. I displayed a photograph of Yule.
I showed and commented upon the table of 21 distributions and 44
connections between them that appears on page 630 of Casella and Berger's
book.
I did a digression on Benford's distribution of the leading
digit.
I explained that Lemma 10.4 (iii) is just Pythagoras's Theorem
and drew a picture for the case n=2 to illustrate it. Understanding
this makes the result that the sample mean and variance are
independent much more intuitive. There was no room to put this
picture in the notes, but it is worth seeing.
The attendance at lectures is rather disappointing now, well
less than 200.
Lecture 11
I did a digression about testing the difference between Jane
Austen's writings and those of an imitator.
I spoke for a bit about some justifications for using the
normal distribution.
I commented that the researchers who did the fruitfly study were
both women.
Lecture 12
I commented that the mean of a F distribution is in general
greater than 1, but near 1. I also talked about how to look
up values in F tables.
I did a digression on Latin squares and experimental design.
I displayed several scatter plots for the fruitfly data. There
is no space to reprint these in the notes.
I forgot to mention that ANOVA would have given a significant
result if in Example 12.2 we had been testing for equality of
all five means.
I didn't discuss the bits in my notes on page 51 about `explaining
variability', or the final comments on page 52 about experimental
design and other ANOVAs. These are really there for the bright and
interested student.
My experience as a supervisor is that ANOVA is a difficult topic
for students when they first meet it, because the symbols and
algebra are a lot to take in. But that the idea clicks into
place once they have done an example for themselves. There are a
couple such on the examples sheets.
Attendance was again disappointing; only a bit over half of the
potential audience was there.
Lecture 13
I did a digression on Stein's paradox.
I handed out Examples Sheet 3.
I displayed and discussed several scatter plots and graphs
which were not reproduced in lecture notes.
Lecture 14
I did a digression on the Myers-Briggs test and introduced the
idea of factor analysis.
This lecture seemed rushed, but it needn't have been.
I think I was rather tired this morning. The stuff about testing linearity
perhaps might be deleted. The ANOVA test in the final section is more
interesting and we only need to give one example of hypothesis testing of
regression models.
I forgot to show the residuals plot of the frutifly data after effect of
thorax size is removed. I can do this in Lecture 15 when I talk about
residuals analysis.
Lecture 15
I handed out the feedback questionaire.
I handed out printed corrections to the notes.
Lecture 16
I handed out new versions of the table of contents, notation and index.
Return to the Statistics course home page.
Richard Weber ( r.r.weber@statslab.cam.ac.uk )
Last modified: Tue Mar 11 10:17:28 1997