David B. Howell
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A. Objectives—students will be able to
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1. define sample;
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2. describe and give examples of random sample;
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3. Iist factors compromising randomness;
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4. describe variations among samples.
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B. The experimental question—What percent of the population is taller than 5’7” ?
C. Issues, and some possible resolutions—
What
population? (This class. 9th Grade. The school. Hew Haven. The world.)
Let’s start with this class. How do we find out? (Measure everybody. Ask everyone. put a mark at 5’7” and check everyone against it.)
Let’s just ask. If you don’t know, we won’t count you this time. [Record data on Worksheet 1 or board or overhead. Here is a sample showing class data for everyone who knows his/her height and just for the subgroup of boys:]
(figure available in print form)
Is that a fair picture of this whole class? (Yes. No. It depends whether we counted everyone.) Did we have to count everybody? What happens if we count only boys? (Boys are taller than girls.) Record it. [See above.] Only girls? The second row? Each row separately? A coin-toss group? [We’ll toss a coin for each person; only students matched with ‘heads’ get counted.] A coin-toss group again? [Re-toss.]
D. Observations and discussion to Objectives—
Each different group we counted was a
sample
of the population. A
sample
is simply a part or subset of a group or population. A
random sample
is a sample in which every member of the group or population has the same chance of being chosen.
Which of our samples—if any—were clearly random samples? [Any coin-toss group is generally random. Other techniques might also have been used.] Which were clearly HOT random? About which aren’t you sure? What might have made a coin-toss group HOT random? (Unfair coin. Unfair toss.) How might we have made the Second Row group “more” random? (Assign seats randomly—by lot.) Did all samples give the same or almost the same results? Describe how they were the same. Describe how they were different.