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Water, water everywhere!

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  1. Water, water everywhere! Bottled water is becoming an increasingly popular alternative to ordinary tap water. But can people really tell the difference if they aren’t told which is which? Do you think you can tell the difference?

  2. Water, water everywhere!!! Instructions for the activity: • Get an index card. • Go to the corresponding station number. • Pick up 3 cups (labeled A, B, and C). • Drink all the water in A, then all the water in B, then all the water in C. • WITHOUT DISCUSSING WITH OTHER STUDENTS, on the index card, write the letter of the cup that you think contains the bottled water.

  3. Water, water everywhere!!! • Record your results on the board. • What percent of the class identified the bottled water correctly. • What percent of the class would you expect to guess correctly? How does this compare to the percent of correct identifications?

  4. Can we really tell the difference? • Perform a simulation • Roll the die • Rolling a 1 or 2: Correct guess • Rolling a 3, 4, 5, or 6: Incorrect guess • Based upon the simulation results… • How many correct identifications would make you doubt that students were just guessing? Why? • What conclusions might we make?

  5. Observational Study vs. Experiment • In an observational study, we observe individuals and measure variables of interest but do not attempt to influence the responses. • In an experiment, we deliberately impose some treatment on (that is, do something to) individuals in order to observe their responses.

  6. Variables • A response variable measures an outcome of a study. • An explanatory variable helps explain or influences changes in a response variable.

  7. Population and Sample • The population in a statistical study is the entire group of individuals about which we want information. • A sample is a part of the population that we actually examine in order to gather information.

  8. Sampling • A census attempts to include everyone in the population. • Unlike a census, sampling involves studying a part in order to gain information about the whole. • Sampling techniques include: voluntary response, convenience, simple random, stratified, systematic, and cluster. • The sampling method is biased if it systematically favors certain outcomes.

  9. The Idea of a Sample Survey • Conclusions about a whole population are often drawn on the basis of a sample. • Choosing a representative sample is not easy. Careful planning must take place. • What population do we want to describe? • What do we want to measure? • Example: • Current Population Survey (CPS) • Contact 60,000 household each month. • Produces the monthly unemployment. • Other Examples?

  10. Sampling Poorly • Bias • Systematically favors certain outcomes • Convenience sampling • Choosing individuals who are easiest to reach. • Where’s the Bias? • Voluntary response • Consists of people who choose themselves by responding to a general appeal • Where’s the Bias?

  11. Sampling Well • Simple Random Sample (SRS) • A SRS of size n consists of n individuals from the population chosen in such a way that every set of n individuals has an equal chance to be the sample actually selected. • NOTE: In this instance “random” does not mean haphazard as in “OMG that’s so random.” In statistics, random means “due to chance.”

  12. Sampling Errors • Undercoverage • Occurs when some groups in the population are left out of the process of choosing the sample. • Nonresponse • Occurs when an individual chosen for the sample can’t be contacted or does not cooperate.

  13. Nonsampling Errors • Response Bias • Giving incorrect responses • Wording of Questions • Confusing, leading, or order of questions can influence the outcome of a survey • Example: • “How happy are you with your life in general? • “How many dates did you have last month?”