Section 1.2 Random Samples. 2 Sampling Using a small group to represent the population Census includes the entire population usually not practical, and.

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Presentation transcript:

Section 1.2 Random Samples

2 Sampling Using a small group to represent the population Census includes the entire population usually not practical, and often impossible Simulation A small-scale model of a real-world situation Random number generator Experiment (discussed in 1.3) 4 Ways to gather data

3 characteristics of the sample should be similar to those of the population A “good” sample is representative; a “bad” sample isn’t.

4 Simple Random Samples Assign a number all objects/individuals in your population Generate random numbers using a calculator/random number table Those numbers selected are your sample Everyone in the population has an equal chance of being selected Ex: sampling from numbered popsicle sticks assigned to each desk in class

5 Examples Random number table: Calculator: Math -> PRB -> randInt(lower, upper, # in sample)

6 Stratified Sampling Divide the population into groups (or strata), based on some characteristic (race, sex, etc.) Randomly choose samples from each group Do this if you think different groups yield different results Ex: sampling a little from the freshman, sophomores, juniors, and senior classes

7 Cluster Sampling Divide the population into clusters (or groups with mixed characteristics) Randomly choose one (or a few) clusters Include everybody (census) within that cluster for your sample Ex: sampling every student in one or two classrooms (clusters) at TMHS

8 Systematic Sampling Number off individuals or objects Randomly choose a starting point Pick every k th person for your sample Ex: on an assembly line pick every 10 th chocolate to taste test

9 Convenience Sampling A sample chosen because it is EASY to obtain Examples: Asking your friends or co-workers Self-selected samples, like internet or phone-in polls

10 Multistage Sampling More than one method applied Ex: Divide by gender and sample from each (stratified) Then divide that sample into teams of 5 and sample everyone in two teams (clustering)

11 Extra Definitions Sampling frame: the list of individuals you’re sampling from. Not always the entire population. Ex: using a telephone directory to poll would not include unlisted numbers. Undercoverage: excluding members from a population in your sampling frame

12 Sampling error: occurs when measurements from your sample don’t match measurements from the entire population Other types of error occur when your sampling design is biased or poorly constructed

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