Download Homework 7: Chi Square Test for Categories

Research Methods
Homework 7:  2 Test for Categories
When submitting this homework assignment to the dropbox “Homework 7” folder, name the file
using the following format: HW7_your_name.docx (e.g. HW7_Sed_Keller.docx).

Assignment
Purpose: This assignment will familiarize you with a common statistical test used in the scientific
studies. As scientists, we require a basic understanding of statistics in order to draw conclusions
from our data.
Problem
The goal of this problem is to derive and then apply a  2 test. Imagine you ask a sample of N
people their opinion about a topic. There are d possible answers they might give you. For
instance, you ask 200 students so N = 200. You expect that a proportion μi of these people will
give you answer i. For instance, you expect 25 % of the students are seniors, so i = “senior” and

μi = 0.25
(a) What is the number of people Ei you expect to give answer i? Write down the formula, using
the symbols above.
Ei = ...
(b) In your actual data, you observe that a proportion X i actually gives you answer i. For
example, 20 % answer “Yes” to your first question. In general what is the observed number of
people  i you observe giving answer i? Write down the formula using symbols from above.
 i = . ..
(3.58)
 To compute  2 you need to know the standard error associated with measuring X i.
Statisticians have found that when N people choose result i with probability μi, the standard
error involved in measuringX i is

i  i / ;

(3.59)

that is, the uncertainty in the fraction X i is
 it.
N being large, but you can use
i / This result is approximate, and depends upon
To get a more usable formula for use with surveys, do the following steps:

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(c) Write down the formula for  2 in Equation 3.50
 2. . .


(3.60)
Research Methods
Homework 7: Chi Square Test for Categories
(d) Rewrite the formula, substituting in the expression for standard error from Equation 3.59.
(e) The square-root and squared term in the denominator cancel out so...
(f) Bring the term N up to the numerator.
(g) Bring the N in the numerator inside the squared term. To do that, multiply the whole equation
inside the summation symbol by 
 1
(h) Now bring the N inside the parentheses in the numerator. You should now have a formula
that looks like:

2  
i
i  i2
i
(3.61)
(i) Obtain Equation 3.52.
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