Transcript Measures of Central Tendency for Interval data

DESCRIPTIVE
STATISTICS
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 Description
Analysis of single variables

Central tendency

Variation
Description vs inference?
 Descriptive Statistics
Methods of organizing, summarizing,
and presenting data in an informative way
 Inferential Statistics
A decision, estimate, prediction, or generalization
about a population based on a sample
Description or Inference?
According to Consumer Reports, General
Electric washing machine owners reported
9 problems per 100 machines in 2001.
Wine tasters sip a few drops of wine
to make a decision with respect to
all the wine waiting to be
released for sale.
Types of data (level of measurement)
1. Nominal
2. Ordinal
3. Interval/ratio
What type of data?
 Which party did you vote for in the general
election?
1. Conservative
2. Labour
3. Liberal Democrat
4. Scottish National Party
What type of data?
 How much interest do you generally have in what is
going on in politics?
1. A great deal
2. Quite a lot
3. Some
4. Not very much
What type of data?
 Now, a few questions about yourself and your
background. What was your age last birthday?
 Age in years __34____
Measures of Central tendency
Exercise: Mean, Median, Mode
 The ages for a sample of seven voters are:
 21, 25, 19, 20, 22, 22, 70
The mean is………
The median is ……….
The mode is ………
Reorganize it in an ascending order:
19 20 21 22 22 25 70
Measures of Central Tendency for
nominal data
 Which party did you vote for in the general
election?
1. Conservative
2. Labour
3. Liberal Democrat
4. Scottish National Party
 The number is of no interest itself, we are only
interested in what the number refers to.
 You can’t measure the mean and the median for
nominal data. You can only find the mode.
Measures of Central Tendency for
ordinal data
 How much interest do you generally have in what is
going on in politics?
1. A great deal
2. Quite a lot
3. Some
4. Not very much
 someone who is coded 4 is not twice as less interested in politics
as someone who is coded 2.
 We can only make meaningful statements about the order of the
responses, not the magnitude of the differences between them.
 You can’t measure the mean for ordinal data. You can find the
median and the mode.
Measures of Central Tendency for Interval
data
 With Interval data, the numbers do make sense.
Indeed there is no distinction between the value
and the label.
 If someone is 34 years old they are coded as 34.
The numbers have an order, so someone who is 40
is older than someone who is 30
 You can find the mean, the median and the mode
for interval data!
Measures of Variation
 What is the Range of {5,17,35,76,90}?
 90-5 = 85
 What does a high standard deviation indicate?
 It indicates that the data are spread out or dispersed
across a large range of values.
Case: The AV Referendum (5th May 2011)
First Past The Post (Simple majority voting)
 Voters put a cross in a box next to their favoured candidate
and the candidate with the most votes in the constituency
wins. All other votes count for nothing.
Alternative Vote (Ranked Choice Voting)
 The voter puts a '1' by their first choice a '2' by their second
choice, and so on, until they no longer wish to express any
further preferences. Candidates are elected outright if they
gain more than half of the first preference votes. If not, the
candidate with least first preferences is eliminated and their
votes are redistributed according to the second preference
marked on the ballot paper.
Pros and cons of the Alternative Vote
 Yes2AV camp said (among other things) that ‘AV
was fairer’ and that ‘AV would make MPs work
harder’.
 The NO2AV camp said ‘AV would produce hung
parliaments’ and that ‘AV was too complicated
for people to understand’
Handout/ Exercise
Match the claims to the data on the attached sheet and
answer the following questions:
 How much public support is there for each of
these claims?
 Which claims did the public find most
convincing? Which the least?
 Why do you think people voted against the
reforms?
What’s Next?
 Week 12: Bivariate analysis I: Analysing
Tables
 examine the association between two variables
 going beyond description and trying to explain
 Suggested Reading: De Vaus, David (2002)
Surveys in Social Research (London: Routledge)
Chapter 14.