Statistical Thinking Measuring Chapter 8 Measuring Chapter 8 Chapter 8

Statistical Thinking Thought Question 1 A local health club is doing a survey to see if there is a relationship between strength and fitness. They want to measure the strength and fitness of a sample of 100 members of the club. Which of these two attributes do you think will be easier for them to measure? Explain. Chapter 8 Chapter 8

Statistical Thinking Thought Question 2 You are at the beach and want to know the depth of the water at a sandbar that is just offshore. One of your friends (whose height you know) stands on the sandbar and you measure the depth of the water by seeing how much of his body is underwater. You report that the depth is 4 ft., 6 in. Do you think this measurement is accurate? Would you get the same result if you measured it again? Chapter 8 Chapter 8

Statistical Thinking Thought Question 3 A study on customer service found that there were more customer complaints registered at a large local grocery store in the past year than at a small local market. Is it fair to conclude that the local market had better customer service? What would be a fairer way to present the numbers? Chapter 8 Chapter 8

Statistical Thinking Measurement Validity A measurement is valid if it is an appropriate representation of the property of interest often the rate (or percent) at which something happens is more valid than a count of occurrences (see TQ #3) often it is difficult to determine if a measurement is “valid” (especially for behavioral properties) A measurement has predictive validity if it can be used to adequately predict some outcome related to the property of interest Chapter 8 Chapter 8

Predictive Validity: Case Study Statistical Thinking Predictive Validity: Case Study Reading Performance Improving? “Percent of students in New York City public schools who read at or above their grade level has increased” used “reading score by grade” to measure reading performance but, the school system tightened standards and held back the poorest readers in lower grades a valid predictor of reading performance would be “reading score by age” Chapter 8 Chapter 8

Measurement Reliability Statistical Thinking Measurement Reliability Errors in measurement: measurement value = true value + bias + random error Bias means that each measurement has the same systematic error is one direction Random error means that repeated measurements on the same individual give different results A measurement is reliable if the random error is small (i.e., we get “repeatable” results) the reliability of a measurement can be improved by taking repeated measurements and using the average Chapter 8 Chapter 8

Key Concepts Valid Measures Rates and Counts Predictive Validity Statistical Thinking Key Concepts Valid Measures Rates and Counts Predictive Validity Reliable Measures Chapter 8 Chapter 8