HELPING STUDENTS LEARN TO THINK LIKE A STATISTICIAN SESSION S034. Roxy Peck Cal Poly, San Luis Obispo

Transcription

1 HELPING STUDENTS LEARN TO THINK LIKE A STATISTICIAN SESSION S034 1 Roxy Peck Cal Poly, San Luis Obispo rpeck@calpoly.edu

2 Source: Sedona Red Rock News, August 21,

3 Consider the map of counties shown below. The number in each county is last month s incidence rate for a disease in cases per 100,000 population. (Dick Schaeffer, 2005) 3

4 STATISTICAL VERSUS MATHEMATICAL THINKING Mathematical Thinking Explain patterns Often a deterministic way of thinking Statistical Thinking Search for patterns in the presence of variability Acknowledge role of chance variation Statisticians ask: Could this have happened by chance? 4

5 THREE ACTIVITIES THAT DEVELOP STATISTICAL THINKING The Cookie Game SpongeBob SquarePants A Nurse Accused (if time ) 5

6 The Cookie Game 6

7 THE COOKIE GAME Statistical Thinking Involved Could this have happened by chance if Convincing evidence versus proof Acknowledging the risk of an incorrect conclusion 7

8 SPONGEBOB SQUAREPANTS (THANKS TO DOUG TYSON FOR THE IDEA FOR THIS ACTIVITY) Activity: Does SpongeBob Make Kids Dumber? Reference: The Immediate Impact of Different Types of Television on Young Children s Executive Function, Pediatrics,

9 THE EXPERIMENT Randomly assigned 60 children to one of three groups: 1. Cartoon (SpongeBob) 2. Educational cartoon 3. Drawing After 9 minutes, children were given several tests that measured working memory and acceptance of delayed gratification. 9

10 SIMPLIFYING A BIT We will focus on just two groups the SpongeBob group and the educational cartoon group. Did watching SpongeBob make a difference? Task 1: Measure of working memory Task 2: Measure of Acceptance of Delayed Gratification 10

11 TASK 1 WORKING MEMORY Children were told When I say touch your head, I want you to touch your toes, but when I say touch your toes, I want you to touch your head 10 trials. On each trial, 2 points if done correctly, 1 point if done incorrectly but then corrected, 0 points if done incorrectly. 10 more trials using shoulders/knees 10 more trials using head/shoulders Results in scores between 0 and 60 11

12 TASK 2 DELAYED GRATIFICATION Children were shown a bag of marshmallows and a bag of goldfish crackers and asked which they wanted for a snack. 10 pieces of the chosen snack were put on one plate and 2 pieces on a second plate. A bell was placed between the two plates. Children were told that if they waited for the experimenter to return, they could have the plate with 10 pieces, but that at any time, they could ring the bell to get the experimenter to return, in which case they would get the plate with 2 pieces. Measured time until child rang the bell, or to when the experimenter returned (330 seconds) if no bell. Resulted in times from 0 to 330 seconds. 12

13 THE DATA FOR TASK 1 (WORKING MEMORY) Mean Scores SpongeBob Group: Educational Group: Difference in means: =

14 COULD THIS HAVE HAPPENED BY CHANCE?? Know that if we took the 20 SpongeBob kids and divided them into two groups, the two group means wouldn t have been the same just due to chance differences resulting from the division into two groups. Might two SpongeBob groups have had means as different at 14.15? 14

15 SUPPOSE THAT THERE IS NO REAL DIFFERENCE BETWEEN THE TWO GROUPS For example, suppose that first child would have scored 0 no matter which group the child was in that is, the cartoon watched didn t make any difference. If this is the case, the observed difference is just due to randomly dividing the 20 children into two groups and not a result of which cartoon was watched. Is this likely to have been the case?? 15

16 LET S INVESTIGATE Demonstration with cards Technology html 16

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18 TASK 2 (DELAYED GRATIFICATION) Mean Scores SpongeBob Group: Educational Group: Difference in means: =

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20 CONCLUSIONS Mean score for both working memory and acceptance of delayed gratification was significantly lower for the SpongeBob group than for the educational cartoon group. Significantly lower means we don t think the observed difference is likely to have happened by chance. 20

21 A NURSE ACCUSED From Statistics: A Guide to the Unknown Kristen Gilbert was a nurse at the Veteran s Administration (VA) hospital in Northampton, Massachusetts. She had a reputation of being particularly good in a crisis. If a person went into cardiac arrest, she was often the first to notice something was wrong, signal code blue and administer epinephrine. Often the patient s life was saved. Other nurses became suspicious both because of the number of cardiac arrests when Gilbert was on duty and also the number of deaths. Eventually, Gilbert was accused and prosecuted for murder of a number of patients by administering a powerful heart stimulant. 21

22 THE EVIDENCE Proportion of shifts with a death: 74/1641 = Proportion of Gilbert shifts with a death: 40/257 =

23 COULD THIS HAVE HAPPENED BY CHANCE?? If probability of a death on a shift is 0.045, what is the chance that Gilberts 257 shifts would have 40 deaths? 23

24 LET S INVESTIGATE THE GILBERT DATA Technology m 24

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27 THANKS! Thanks for attending this talk. Closing challenge Help students practice thinking like a statistician by always keeping the following question in mind: Is it likely that what we are seeing could have happened by chance when? 27