Systematic Sampling Robb T Koether Homework Review 1 in k Systematic Sampling Systematic Sampling Lecture 9A Section 2 7 The Sample Size The Language of Studies Variables Observational and Experimental Studies Confounding Variables Causation vs Correlation Assignment Robb T Koether Hampden Sydney College Wed Sep 10 2008 Outline Systematic Sampling 1 Homework Review 2 1 in k Systematic Sampling The Sample Size 3 The Language of Studies 4 Variables Variables 5 Observational and Experimental Studies Observational and Experimental Studies 6 Confounding Variables Confounding Variables 7 Causation vs Correlation Causation vs Correlation 8 Assignment Robb T Koether Homework Review 1 in k Systematic Sampling The Sample Size The Language of Studies Assignment Systematic Sampling Robb T Koether Homework Review 1 in k Systematic Sampling The Sample Size The Language of Studies Variables Observational and Experimental Studies Confounding Variables Causation vs Correlation Assignment Exercise 2 23 p 116 A class consists of 100 students Suppose that we are interested in the heights of the people in the class We could take a stratified random sample using gender as the stratification variable Suppose that it is known that 60 of the 100 students in the class are female Someone shakes a box containing the 60 female tags and with a blindfold on reaches in and draws 10 tags Then this same person shakes a box containing the 40 male tags and with a blindfold on reaches in and draws 10 tags Systematic Sampling Robb T Koether Exercise 2 23 p 116 Homework Review 1 in k Systematic Sampling The Sample Size The Language of Studies Variables Observational and Experimental Studies Confounding Variables Causation vs Correlation Assignment Now we have two simple random samples one for the males and one for the females each of size 10 Suppose that the average height of the males in the sample is 70 inches while the average height for the females in the sample is 63 inches How should these two average heights be combined to produce an estimate of the average height of the people in the class Systematic Sampling Robb T Koether Homework Review 1 in k Systematic Sampling The Sample Size The Language of Studies Variables Observational and Experimental Studies Confounding Variables Causation vs Correlation Assignment Solution We should use a weighted average Weight the female average with 0 60 and the male average with 0 40 The estimated average for the class is est avg 0 60 63 0 40 70 37 8 28 65 8 Systematic Sampling Systematic Sampling Robb T Koether Homework Review 1 in k Systematic Sampling The Sample Size The Language of Studies Variables Observational and Experimental Studies Confounding Variables Causation vs Correlation Assignment Definition 1 in k systematic sampling 1 in k systematic sampling is a sampling method in which one of the first k members of the population is selected at random Then beginning with that member every kth member is selected For example if k 10 then one of the first 10 members is selected at random Suppose member 6 is selected Then beginning with member 6 every 10th member is selected i e members 6 16 26 36 and so on Systematic Sampling Systematic Sampling Robb T Koether Homework Review 1 in k Systematic Sampling The Sample Size The Language of Studies Variables Observational and Experimental Studies Confounding Variables Causation vs Correlation Assignment To select a 1 in k systematic sample Number the members of the population 1 through N Using randInt 1 k choose a random starting point from 1 to k That represents the first member of the sample From that starting point put every kth member in the sample Example Systematic Sampling Robb T Koether Homework Review 1 in k Systematic Sampling The Sample Size The Language of Studies Variables Observational and Experimental Studies Confounding Variables Causation vs Correlation Assignment Let s choose a 1 in 5 systematic sample from the 22 students in this class Use randInt 1 5 to choose the first member Then choose every 5th student thereafter The Sample Size Systematic Sampling Robb T Koether In the last example notice that 22 5 4 4 Homework Review 1 in k Systematic Sampling The Sample Size The Language of Studies Variables Observational and Experimental Studies Confounding Variables Causation vs Correlation Assignment So the sample size could end up being either 4 or 5 depending on the starting point If the starting point is 3 then we get 4 members 3 8 13 18 If the starting point is 2 then we get 5 members 2 7 12 17 22 Either way each member has a 1 5 chance of being in the sample The Sample Size Systematic Sampling Robb T Koether Homework Review 1 in k Systematic Sampling The Sample Size The Language of Studies Variables Observational and Experimental Studies Confounding Variables Causation vs Correlation Assignment N 22 The Sample Size Systematic Sampling Robb T Koether Homework Review 1 in k Systematic Sampling 3 8 13 18 23 The Sample Size The Language of Studies Variables Observational and Experimental Studies Confounding Variables Causation vs Correlation Assignment n 4 The Sample Size Systematic Sampling Robb T Koether Homework Review 1 in k Systematic Sampling 2 7 12 The Sample Size The Language of Studies Variables Observational and Experimental Studies Confounding Variables Causation vs Correlation Assignment n 5 17 22 How to Determine k Systematic Sampling Robb T Koether Homework Review 1 in k Systematic Sampling The Sample Size The Language of Studies Variables Observational and Experimental Studies Confounding Variables Causation vs Correlation Assignment To determine k Divide the population size N by the desired sample size n Let k N n rounded off Example Systematic Sampling Robb T Koether Homework Review Suppose we want to select n 12 members from a population of size N 187 1 in k Systematic Sampling Compute k 187 12 16 The Sample Size The Language of Studies Variables Observational and Experimental Studies Confounding Variables Causation vs Correlation Assignment Use randInt 1 16 to get a random integer from 1 to 16 Say we get 9 Then beginning with member 9 select every 16th member 9 25 41 57 73 89 105 121 137 153 169 and 185 The Language of Studies Robb T Koether Homework Review The Language of Studies 1 in k Systematic Sampling Lecture 9B Sections 3 1 3 3 The Sample Size The Language of Studies Variables Robb T Koether Observational and Experimental Studies Hampden Sydney College Confounding Variables Wed Sep 10 2008
View Full Document
Unlocking...