General Statistics |
Chi-Square Analysis
The Chi-square Test of Independence. |

The
Chi-square Test of Independence.
The chi-square test of independence is used to
test whether two populations or variables are related or independent to
each other with
The Sometimes individual items are classified into categories in terms of
two different criteria. For example, in studying the wear of tires, tires
The table above where categorical cells are combined to show their rows
and column totals is called a
A A
Where:
Each cell in the contingency table have some theoretical or expected
frequency and unless otherwise known (explicitly) it is determined
The expected frequency,
The chi-sqaure test for independence evaluates the closeness of the
observed frequencies ( E), E,
_{ij}good agreement between these two information favors the null hypothesis and large departure of the observed frequencies from the expected frequencies favors the alternate hypothesis (larger values of ). Remember the chi-square statistics is
The cell frequencies found in the contingency table when divided by
the grand total yield the proportions, of the total number of observations. This proportions is also a probability score of cells posibilities out of total possible outcome or score. If
(frequency of row_{m} divided by the grand total
and row_{m} is the column proportion of p(k)
(probability, column_{k})
p_{k}then: The Where
is the probability or frequency of both
p(mk) = occuring
(assumes that both m and k are indepedent events
m and kor charateristics)
( The chi-square test of independence attempts to compare the expected
proportions using the multiplication rule of independent characteristics
That is, the sum of square of the Observed frequencies minus the expected is small. I is small.
The following table is the observed results of the study: Use chi-square test for independent charateristics to evaluate this
data.
(1) Are the Methods of preperation and number of months after preperation related in terms of students achievement scores (> 80% on test)? (2) Are the two criteria (methods of Preperation and number of months
test is taken after preperation) independent or related to with respect
Note: that the formulation of a problems statement or the question that
the research would like to answer statistically may take on many forms
So
_{o} is not true. (alternate hypothesis):
Methods of Prep and Months after Prep are related.
If you want the be The So
For d.f. = 12,
The following table is the
=
Since after preperation are related each other).
There seems to be some relationship between types of students' preparation and number of weeks after preparation that tests are taken.
Formulate an hypothesis about the relationship between Political view
and Opinion of Nuclear Power from the following survey of 100 students.
(a) What is your hypothesis? (b) What is the value of the chi-square statistics? (c) What conclusion did you make? (d) What inference can you make? Use use |