#### Transcript Data for Decisions - William & Mary Mathematics

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