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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
Explain the following terms .
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Abiotic factors are non living components of ecosystem.These include physical and chemical elements like temperature,light,water,soil,air quality and oxygen etc
Qasim
passive process of transport of low-molecular weight material according to its concentration gradient
AI-Robot
what is production?
Catherine
how did the oxygen help a human being
how did the nutrition help the plants
Biology is a branch of Natural science which deals/About living Organism.
evolutionary history and relationship of an organism or group of organisms
AI-Robot
cell is the smallest unit of the humanity biologically
Abraham
HOW CAN MAN ORGAN FUNCTION
the diagram of the digestive system
allimentary cannel
Ogenrwot
They formed in two ways first when one sperm and one egg are splited by mitosis or two sperm and two eggs join together
Oluwatobi
what is respiration
Deborah
Genetics is the study of heredity
Misack
how does twins formed?
Misack
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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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