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Two-Sample Comparison:
A Classroom Activity
Presented by
Carol Kuper
Jo Wilson
Grace Zhang
Learning Objectives
Explain the importance of data
Compare means of two independent
groups using a t test.
Explain the difference between onesample and two-sample
Previous Statistical Knowledge
Students have learned how to
calculate the mean and standard
Students have learned about the tdistribution
Students will have conducted a
single sample t-test
Background for Instructors
Verbal Fluency—The ability to generate
words rapidly
Research has shown that women (girls)
have higher verbal fluency than men (boys)
Recent reference: Burton, L.A., Henninger, D., &
Hafetz, J. (2005). Gender differences in relations
of mental rotation, verbal fluency, and SAT
scores to finger length ratios as hormonal
indexes. Developmental Neuropsychology, 28,
Data Collection Procedure
Before discussing the hypothesis, give the
students 3 minutes to list things that are
yellow on a sheet of paper.
Ask the students to exchange papers with a
neighbor and verify that all items are in fact
yellow (instructor’s note: encourage class
discussion about the integrity of the data).
Have the students switch back and count
the number of correctly identified items that
are yellow.
Hypothesis Formulation
Define verbal fluency for the class, and
discuss gender differences. Ask the class
to formulate the null and alternative
Hypothesis formulation usually comes
before data collection, but the data will be
biased if students know about gender
differences related to verbal fluency.
Data Analysis Procedure
List data on the board under two columns
male and female. (instructor’s note: be sure
not to have the column headings on the
board prior to data generation).
Have students calculate the mean and
standard deviation.
Construct a histogram of the means for
males and females.
Calculate t-test statistic and complete
hypothesis testing.
Connecting Past to Present
Discuss the difference between a onesample t-test and a two-sample t-test.
One group vs. two groups
The differences in stating the null hypotheses.
Discuss data integrity and sampling
Checking data for accuracy
Controlling for age and education level
Follow up
Paired t-test—May refer back to the
independent sample design and
emphasize the difference between
independent and dependent samples.
Regression—May use gender as an
indicator variable.
ANOVA—Compare a two-sample design
to a multivariate or multisample design.
Data that have not been verified and checked
will lack integrity and will lead to erroneous
When you have two independent samples, you
can use a two-sample t test to test for
differences between the means.
For a one sample t test, the null hypothesis is
µ = k. For a two sample t test, the null
hypothesis is 1  2 .
Two Sample Comparison Assessment