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This module describes how the chi-square distribution can be used to test for independence.

Tests of independence involve using a contingency table of observed (data) values. You first saw a contingency table when you studied bivariate descriptive statistics in the Bivariate Descriptive Statistics chapter.

The test statistic for a test of independence is:

Σ ( i j ) ( O - E ) 2 E

where:

  • O = observed values
  • E = expected values
  • i = the number of rows in the table
  • j = the number of columns in the table

There are i j terms of the form ( O - E ) 2 E .

The Chi-square test of independence determine if there is a relationship between 2 categorical variables. Remember that in the chapter on bivariate data we examined two-way tables (pivot tables) for a relationship by examining either the row or column percentages. We will now test this relationship between categorical variables by calculating a test statistics and determining a p-value.

The null hypothesis for a chi-square test of independence is that there is no relationship between the two categorical variables or that they are independent.

The alternative hypothesis is that there is some kind of relationship between the two categorical variables or that they are dependent.

Before we test the hypothesis we need to check the assumptions and conditions for the chi-square test of independence.

The expected value for each cell needs to be at least 5 in order to use this test.

    Assumptions:

  1. Counted Data Condition
  2. Independence Assumption
  3. Random Sample
  4. 10% Condition
  5. Expected Cell Frequency Condition

The new assumptions for this test are the counted data condition and the expected cell frequency condition. The counted data condition is checking to see if we have counts of respondents categorized on two categorical variables. The numbers in each cell of the two-way table should be whole numbers showing how many people gave that combination of responses to the two categorical questions.

The other new condition, the expected cell frequency condition, is asking us to find how many people we would expect to be in each cell if the null hypothesis is true and there is no relationship between the two variables. To do this we will need to calculate the expected value for each cell in the two-way table. All of the excepted values must be larger than 5.

To find the expected values we will need the row and column totals and the overall sample size. The mathematics for the expected values is;

Expected Value = (row total)(column total) (sample size)

Once all the expected values are calculated check to make sure they are all larger than 5.

Your next step before calculating the test statistics is to calculate the row or column percentages, which is most appropriate. We discussed this in the bivariate data chapter. Remember to determine the dominate variable (look at the research question) and then make the percentage based on if the dominate variable is making rows or columns.

Like the other hypothesis tests we have looked at in this text we will calculate a test statistic. The formula for the chi-square test for independence is:

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
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Source:  OpenStax, Collaborative statistics using spreadsheets. OpenStax CNX. Jan 05, 2016 Download for free at http://legacy.cnx.org/content/col11521/1.23
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