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- The chi-square distribution
- Summary of formulas
This module provides a summary on formulas used in Chi-Square Distribution as a part of Collaborative Statistics collection (col10522) by Barbara Illowsky and Susan Dean.
The chi-square probability distribution
and
Goodness-of-fit hypothesis test
- Use goodness-of-fit to test whether a data set fits a particular
probability distribution.
- The degrees of freedom are
.
- The test statistic is
, where
= observed values (data),
= expected values (from theory), and
= the number of different data cells
or categories.
- The test is right-tailed.
Test of independence
- Use the test of independence to test whether two factors are
independent or not.
- The degrees of freedom are equal to
.
- The test statistic is
where
= observed values,
= expected values,
= the number of rows in the
table, and
= the number of columns in
the table.
- The test is right-tailed.
- If the null hypothesis is true, the expected number
.
Test of homogeneity
- Use the test for homogeneity to decide if two populations with unknown distributions have the same distribution as each other.
- The degrees of freedom are equal to
.
- The test statistic is
where
= observed values,
= expected values,
= the number of rows in the
table, and
= the number of columns in
the table.
- The test is right-tailed.
- If the null hypothesis is true, the expected number
.
The expected value for each cell needs to be at least 5 in order to
use the Goodness-of-Fit, Independence and Homogeneity tests.
Test of a single variance
- Use the test to determine variation.
- The degrees of freedom are the number of samples - 1.
- The test statistic is
, where
= the total number of data,
= sample variance, and
= population variance.
- The test may be left, right, or two-tailed.
Questions & Answers
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in what situation (s) would be the use of a scanning electron microscope be ideal and why?
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Hilary
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Source:
OpenStax, Collaborative statistics. OpenStax CNX. Jul 03, 2012 Download for free at http://cnx.org/content/col10522/1.40
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