introduction to the t statistic
DESCRIPTION
Introduction to the t statistic. Steps to calculate the denominator for the t-test. 1. Calculate variance or SD s 2 = SS/n-1 2. Calculate the standard error. T-test Procedure. Set the hypotheses (null and alternative) - PowerPoint PPT PresentationTRANSCRIPT
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Introduction to the t statistic
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Steps to calculate the denominator for the t-test
1. Calculate variance or SD
s2= SS/n-1
2. Calculate the standard error
n
sOR
n
ssM
2
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T-test Procedure
Set the hypotheses (null and alternative) Set the decision criteria (by selecting the alpha
level, directionality, and critical values). Compute the test-statistic (t) Compare obtained t-statistic to critical value(s) Make a statistical decision Concluding statement
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Conducting a t-test
It’s not a normal distribution, and you don’t use the unit normal table
Using the t-distribution (William Sealy Gosset, 1908) instead
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T-distribution
Bell-shaped and symmetrical
A ‘family’ of distributions - depends on the degrees of freedom
The mean of the t-distribution is zero
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T-distribution table
When the df is NOT listed in the table provided in Appendix B, you should look up the critical t for both of the surrounding df values listed and use the LARGER value for t
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Measuring Effect Size with the t Statistic (cont.)
Estimated Cohen’s d
s
M
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Measuring Effect Size with the t Statistic (cont.)
percentage of variance accounted for = r2 (aka 2)
dft
tr
2
22
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Assumptions for a One-sample t-Test
1. Independent observations
2. The sample data come from a normal population distribution
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Example 1
The legal highway limit near populated areas in many parts of the US is 55 mph. To determine whether people exceed the 55mph, suppose a state monitored the speeds of 25 cars at selected highway locations. Can we conclude that the average speed is higher than the 55 mph limit?
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Example 1 - Data
55 60 60 55 57 60 55 58 6354 65 56 61 58 55 57 59 5359 65 56 61 55 54 59
Find the following:MeanSSs2
s