Using Student’s t for Significance Testing

Example of testing literature values with Student’s t.

If you look up the chemical reaction rate constants of CFCl reacting with nitric oxide, NO, in the literature, you find two reports

Upon reading the experimental section of both papers, both works used 5 replicate measurements to arrive at the result. Thus N=5

From that information, we can “back out” the standard deviations from the Student’s t confidence intervals since

We find s₁=1.0´10^-15 and s₂=1.6´10^-15

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With the two standard deviations, the F-test is used to determine if the two came from the same parent population.

First, calculate F_calc

Next, compare to the table value. The table value for 95% confidence and 4 degrees of freedom for each standard deviation is F_table = 6.39

Since F_calc is less than F_table the two standard deviations may have come from the same parent population. And the pooled standard deviation may be used for the Student’s t test.

The pooled standard deviation is obtained from

In this case s_pooled = 1.33´10^-15

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Finally, the Student’s t test for significance is performed. 

1) Invoke the null hypothesis, that both reported rate constants came from the same population of measurements.

2) Calculate a Student’s t using the joint estimate of the standard deviation. 

3) Compare the calculated value to the table value. The table value for 95% confidence and N₁+N₂-2 = 8 degrees of freedom is t_table = 2.306

4) Since t_table is less than t_calc the two means did not come from the same parent population. In this case, a third measurement should be performed to determine the correct value of the rate constant.

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This page last check Tuesday, August 03, 2004