Review HW: E1 A) Too high. Polltakers will never get in touch with people who are away from home between 9am and 5pm, eventually they will eventually be dropped from the sample. Because these are the people who are less likely to have children under the age of 5 at home the same will contain an artificially high percentage of children under 5 at home. B) Adults are more likely to be at home during dinnertime then during the day C) Sampling bias due to the problem being with the design of the survey

Review HW: E3 Convenience sample resulting in sampling Bias Students who take statistics are more likely to like math (HAHAHAHA) Estimate will tend to be too high IF stat class is voluntary and “about right” if it is a require class

Review HW: E5 <40 yr old would expect to get an estimate that is too high since that’s higher than average age Too high - Since Rhode Island is so small and NE states so close together

Review HW E7 A) Voluntary Response Sample B)No, volunteer samples are typically biased with stronger feelings one way or the other. C)”Quite a bit less than 92%”. Voluntary response bias inflated response

Review HW E9 Too high a) families with no children don’t get to take the sample b) families with many children are overrepresented

4.2 Random Sampling: Playing It Safe by Taking Chances Understand the two main reasons for relying on chance to choose samples Learn the definition of a simple random sample Recognize and implement several kinds of probability samples

Probability Sample Occurs when each unit in a population has a fixed probability of ending up in the sample. Used to randomize a survey

Simple Random Samples All possible samples of a given fixed size are equally likely. All units have the same chance of belonging to the sample, all possible pairs of units have the same chance of belonging to the sample, all possible triples of units have the same chance, and so on.

Steps in Choosing a Simple Random Sample 1.Start with a list of all the units in the population 2.Number the units in the list 3.Use a random number table or generator to choose units from the numbered list, one at a time, until you have reached the desired population size.

Activity 4.2a Random Triangles – 20 min Pg Follow the steps listed in the activity

PG 234 D11 Describe how you could obtain a simple random sample of all students enrolled in the English classes at your school Make a list of all English instructors. Get a roster for each class. Combine the list, delete repeats, then use a random digit table to select a sample

PG 234 D11 Readability. You’ve decided you must know the proportion of capital letters in this textbook because it can indicate the complexity of the sentences on a page. If the book is your population and each character is a unit. How could you get a simple random sample of 10k characters? What are the advantages and disadvantages of this sampling method? Number the characters in the book. Use a computer or random #table to choose 10k numbers. The corresponding character go in the sample. Obviously, clearly inefficient.

PG 241 P7 Decide whether these sampling methods produce a simple random sample of students from a class of 30 students. If not, explain why not. a)No – students at the end of the list do not get selected b)No - sample size is not predetermined and not thus not simple c)No – all groups of students not chance of selection. 2 rows d)Yes e)No – not all groups; six girls cannot all be in sample. f)No – not all groups; students with last names different letters

Stratified Random Samples Sample created by breaking down a population into non-overlapping subgroups called strata. A sample of each subgroup must be a simple random sample.

Why we want to stratify? Convenience – it is easier to sample in smaller, more compact groups than one very large group Coverage – ensures all stratum are part of the sample Precision – estimates are closer to the value of for the entire population than with SRS aka less variability

Steps to choosing a Stratified Random Sample 1.Divide the units of the sampling frame unto non-overlapping subgroups 2.Take a simple random sample from each subgroup

PG 237 D13 An administrator wants to estimate the average amount of time high school students spend traveling to school. The plan is to stratify the students according to grade level and then take a simple random sample from each grade. What is the potentially good and what is potentially bad about his plan? Good – time spent differs…more juniors and seniors with cars Bad – Best stratum? What about by distance to school.

Other Sampling Methods Cluster Samples – selecting an SRS of non-overlapping groups of units (called clusters) instead of individual units. EX: Classrooms of students instead of individual students Steps in Choosing a Cluster Sample 1.Create a numbered list of all the clusters in your population 2.Take a simple random sample of clusters 3.Obtain data on each individual in each cluster in your SRS

Two Stage Cluster Samples Variation of cluster sample Choose clusters so that variation within each cluster reflects variation in population. Then SRS from with only some of your clusters. Step in choosing a Two-Stage Cluster Sample 1.Create a numbered list of all clusters in your population, and then take a simple random sample of clusters. 2.Create a numbered list of all the individuals in each cluster already selected, then take an SRS from each cluster.

Systematic Sample with Random Start 1. Divide your population into groups of size you want for sample by a method such as counting off. 2. Use a chance method to choose one of the groups for your sample

Pgp 239 D15 Why isn’t taking a systematic sample with random start equivalent to taking a simple random sample? Two friends in line together at the time of counting wouldn’t both be in the sample

PG 239 D18 Both cluster sampling and stratified random sample involve viewing the sampling frame as a collection of subgroups. Explain the differences? Stratified random sampling divides population into groups as different as possible. Cluster sampling tends to be used when people are stuck in groups that are difficult to separate.

4.2 Summary Simple Random Sample Stratified random sample Cluster sample Two-stage cluster sample Systematic sample with random start

Pg P8 – P11 & P13 HW: PG #E15-17, E22