Data for Decisions - William & Mary Mathematics

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MATHEMATICS IN DAILY
LIFE
DATA FOR DECISIONS
POON TENG HIN
Introduction
Critical thinking
When we are reading articles or making
decisions, we need to ask:
What is the statements?
What is the conclusion/decision?
What are the reasons for supporting the
Conclusion/decision?
Data as reason
One of the effective reasons to support a
conclusion is Data.
More examples
Consumer
survey
Marketing
Plan
Sampling
Sampling
Demo ?
Sampling methods
Nonprobability Sampling
Probability Sampling
Purposive Sampling
Simple Random
Sampling
Accidental sampling
System Random
Sampling
Quota Sampling
Stratified Random
Sampling
Convenience Sampling
Cluster Sampling
Snowball sampling
Multi-Stage Sampling
Sampling Methods
• Non Probability sampling
Does not involve random selection
• Probability sampling
Involve random selection
For your reference(explanation from web)
Purposive Sampling: Select particular group of people. The accuracy
depends on how to select.
Accidental sampling: involves the sample being drawn from that part
of the population which is close to hand. That is, a sample
population selected because it is readily available and convenient.
Quota sampling: means the population is first segmented
into mutually exclusive sub-groups and select samples in each subgroup with a quota.
Convenience sampling: the researcher uses subjects that are easy to
reach.
Snowball sampling: existing samples recruit future sample from
among their acquaintances. Thus the sample group appears to grow
like a rolling snowball.
For your reference(explanation from web)
Simple random sample: each unit of the population has an equal
chance of being selected for the sample.
System Random Sampling: starting point is chosen at random, and
thereafter take sample at regular intervals.
Stratified Random Sampling: process of dividing members of the
population into homogeneous subgroups before sampling. Then
random or systematic sampling is applied within each stratum.
Cluster Sampling: the total population is divided into these groups
(or clusters) and a sample of the groups is selected. Then the
samples are collected from the elements within each selected
group.
Multi-Stage Sampling: First stage is cluster sampling, then
randomly selects elements from each cluster.
Non Probability sampling
Nonprobability Sampling
Purposive Sampling
Accidental sampling
Quota Sampling
Convenience Sampling
Snowball sampling
Login
E.G I have been invited in a event
Which sampling method does it
involved?
Purposive Sampling
Accidental Sampling
Quota Sampling
Convenience sampling
Topic: Compare the motivation of leisure activities
between working people and people in school
Snowball sampling
If the people attended in the event
can invite their friends into it, then
it is a kind of Snowball Sampling
Voluntary response sample
When participants could
choose to participate or not.
This causes some bias.
Response rate
However, Some people do not
attend…..
Response rate
Response rate =
(Respondents
100%
⁄ Sample size) X
How response rate effect the result?
If the response rate are low:
E.g. Sample size = 100, response rate = 40%
Result:
Agree: 25 (most people agree)
Disagree:15
Non attended: Agree: 25
Disagree:35 (most people disagree)
Total:
Agree : 50 (Different results)
Disagree:50
Response Bias
• If response rate is low, the accuracy of the
sampling will decrease.
• We should aware of the response rate when
we make decision.
Non Probability sampling
Probability Sampling
Simple Random
Sampling
System Random
Sampling
Stratified Random
Sampling
Cluster Sampling
Multi-Stage Sampling
Simple Random Sampling
Each unit of the population has an equal chance
of being selected for the sample.
Methods:
Drawing
Table of random numbers
Computer programs
Table of random numbers
Use the table
Decide how large a number you need before.
Decide how to across the page. To the right, to
the right, down the page or up the page.
E.G
If we marked 100 tigers, and fond 2 marked tigers in
60 afterward
so:
2⁄60
N
3000 tigers in the area.
=
100⁄N
= 3000
How can the conclusion be affected?
Tigers are live animal, we cannot control it.
Marked tiger may die, or be alertness.
Non Living may get better accuracy.
Conclusion
Should aware of the choosing of sampling
methods and understand how a survey
conducted before believe in it.
Homework
1. Suggest a process using simple random
sampling to determine the height of UST
students
2. 2. If I marked 200 fish and released them in
the pool, after 2 days, I catch 200 fish and
there are 40 of them are marked. What is the
population of the fish in the pool? What
factors may affect the result?
[Extra credit] What factors will affect the sample
size?
End

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