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Ch 1 Section 1.3-1.6

by: Alyssa Notetaker

Ch 1 Section 1.3-1.6 MA155-70

Alyssa Notetaker
Statistical Reasoning
Yanping Xia

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About this Document

These notes deal with simple random sampling, other effective sampling methods, bias in sampling, and the design of experiments.
Statistical Reasoning
Yanping Xia
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This 7 page Bundle was uploaded by Alyssa Notetaker on Sunday September 13, 2015. The Bundle belongs to MA155-70 at Southeast Missouri State University taught by Yanping Xia in Summer 2015. Since its upload, it has received 40 views. For similar materials see Statistical Reasoning in Mathematics (M) at Southeast Missouri State University.

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Date Created: 09/13/15
Ch 1 Section 13 Simple Random Sampling Objective 1 Obtain a simple random sample 0 Random samplind is the process of using chance to select individuals from a population to be included in the sample 0 A sample of size n from a population of size N is obtained through simple random sampling if every possible sample of size n has an equally likely chance of occurring The sample is then called a simple random sample Steps for Obtaining a Simple Random Sample 1 Obtain a frame that lists all the individuals in the population of interest Number the individuals in the frame from 1 to N 2 Use a random number table graphing calculator or statistical software to randomly generate 11 numbers Where n is the desired sample size Section 14 Other Effective Sampling Methods Objective 1 Obtain a Strati ed Sample Stratified Random Sampling 0 First divide the population into homogeneous groups called strata 0 Second choose a separate simple random sample in each stratum 0 Third combine these simple random samples to form the full sample Objective 2 Obtain a Systematic Sample 0 A systematic sample is obtained by selecting every kth individual from the population The first individual selected is a random number between 1 and k STEPS IN SYSTEMATIC SAMPLING POPULATION SIZE KNOWN Step 1 Determine the population size N Step 2 Determine the sample size desired 11 Step 3 Compute Nn and round down to the nearest integer This value is k Step 4 Randomly select a number between 1 and k Call this number p Step 5 The sample will consist of the following individuals ppkp2kpn 1k Objective 3 Obtain a Cluster Sample 0 A cluster sample is obtained by selecting all individuals within a randomly selected collection or group of individuals 0 A convenience sample is one in which the individuals in the sample are easily obtained Section 15 Bias in Sampling Objective 1 Explain the sources of bias in sampling If the results of the sample are not representative of the population then the sample has m Sampling bias means that the technique used to obtain the individuals to be in the sample tends to favor one part of the population over another Under coverage is a type of sampling bias Under coverage occurs when the proportion of one segment of the population is lower in a sample than it is in the population Three Sources of Bias 1 Sampling Bias 2 Nonresponse Bias 3 Response Bias Nonresponse bias exists when individuals selected to be in the sample who do not respond to the survey have different opinions from those who do Response bias exists when the answers on a survey do not re ect the true feelings of the respondent Types of Response Bias 1 Interviewer error 2 Misrepresented answers 3 Words used in survey question 4 Order of the questions or words within the question 0 Non sampling errors are errors that result from sampling bias nonresponse bias response bias or dataentry error Such errors could also be present in a complete census of the population 0 Sampling error is error that results from using a sample to estimate information about a population This type of error occurs because a sample gives incomplete information about a population Section 16 The Design of Experiments Objective 1 Describe the Characteristics of an Experiment 0 An experiment is a controlled study conducted to determine the effect of varying one or more explanatory variables or factors has on a response variable Any combination of the values of the factors is called a treatment 0 The experimental unit or subject is a person object or some other welldefined item upon which a treatment is applied 0 A control group serves as a baseline treatment that can be used to compare to other treatments 0 A placebo is an innocuous medication such as a sugar tablet that looks tastes and smells like the experimental medication 0 Blinding refers to nondisclosure of the treatment an experimental unit is receiving 0 A singleblind experiment is one in which the experimental unit or subject does not know which treatment he or she is receiving 0 A doubleblind experiment is one in which neither the experimental unit nor the researcher in contact with the experimental unit knows which treatment the experimental unit is receiving Objective 2 Explain the Steps in Designing an Experiment 0 To design an experiment means to describe the overall plan in conducting the experiment 0 Steps in Conducting an Experiment Should be explicit Should provide the experimenter direction Should identify the response variable and the population to be studied Often referred to as the claim Once the factors are identified it must be determined which factors are to be fixed at some predetermined level the control which factors will be manipulated and which factors will be uncontrolled 1 Control There are two ways to control the factors a Fix their level at one predetermined value throughout the experiment These are variables whose effect on the response variable is not of interest b Set them at predetermined levels These are the factors whose effect on the response variable interests us The combinations of the levels of these factors represent the treatments in the experiment 2 Randomize Randomize the experimental units to various treatment groups so that the effects of variables whose level cannot be controlled is minimized The idea is that randomization averages out the effect of uncontrolled predictor variables b Replication occurs when each treatment is applied to more than one experimental unit This helps to assure that the effect of a treatment is not due to some characteristic of a single experimental unit It is recommended that each treatment group have the same number of experimental units c Collect and process the data by measuring the value of the response variable for each replication Any difference in the value of the response variable is a result of differences in the level of the treatment a This is the subject of inferential statistics b Inferential statistics is a process in which generalizations about a population are made on the basis of results obtained from a sample Provide a statement regarding the level of confidence in the generalization Methods of inferential statistics are presented later in the text Objective 3 Explain the Completely Randomized Design 0 A completelv randomized design is one in which each experimental unit is randomly assigned to a treatment Objective 4 Explain the MatchedPairs Design 0 A matchedpairs design is an experimental design in which the experimental units are paired up The pairs are matched up so that they are somehow related that is the same person before and after a treatment twins husband and wife same geographical location and so on There are only two levels of treatment in a matchedpairs design Objective 5 Explain the Randomized Block Design 0 Grouping similar homogeneous experimental units together and then randomizing the experimental units Within each group to a treatment is called blocking Each group of homogeneous individuals is called a M 0 Confounding occurs When the effect of two factors explanatory variables on the response variable cannot be distinguished 0 A randomized block design is used When the experimental units are divided into homogeneous groups called blocks Within each block the experimental units are randomly assigned to treatments


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