Binomial Test
The binomial test evaluates
whether the proportions of individuals who fall into the categories of a two-category variable are equal to hypothesized values.
The test is more likely to yield significance if the sample proportions for the two
categories differ greatly from the
hypothesized proportions and if the sample
size is large.
Binomial Test
In SPSS, we make a hypothesis about only one of the two categories, the category specified for
the variable’s first case in the data file.
SPSS calls the hypothesized proportion the test proportion.
SPSS computes the hypothesized proportion for the second category by subtracting the
hypothesize proportion for the first category from the value of
1
.Binomial Test
In SPSS data file for the binomial test may be structured two ways.
STANDARD METHOD:
The SPSS data file contains as many cases as individuals . For each
case, there is a single variable that has two values that represent the
two categories for the variable of interest.
STANDARD METHOD:
The SPSS data file contains as many cases as individuals . For each
case, there is a single variable that has two values that represent the
two categories for the variable of
interest.
Binomial Test
WEIGHT CASES METHOD:
The SPSS data file contains two cases, one for each category, and two variables.
The two variables are the focal variable with two values for the two categories and the weight variable containing frequencies
for two categories.
WEIGHT CASES METHOD:
The SPSS data file contains two cases, one for each category, and two variables.
The two variables are the focal variable with two values for the two categories and the weight variable containing frequencies
for two categories.
Understanding the Binomial
The binomial test procedure uses a binomial
Test
distribution if the sample size is 25 or less and z test if the sample size is 26 or more.
We consider two applications of the binomial test.
* Binomial test with equal proportions.
* Binomial test with unequal proportions.
We consider two applications of the binomial test.
* Binomial test with equal proportions.
* Binomial test with unequal proportions.
Binomial Test with equal proportions
Example:
Tucker is interested in assessing whether one- year-old girls prefer boys or girls. He randomly
forms triples of two girls and one boy from a sample of
120
one-year-old girls and 60 one- year-old boys. One of the two girls is randomly determine to be the focal subject, and the othergirl and the boy are designated as companions.
Each triplet is placed in a playroom for 10
minutes and observed behind a one-way mirror.
The gender preference for each focal subject is recorded.
Binomial Test with unequal proportions
Example:
Based on past research, pam knows that children who are seated in a room with four doors are equally
likely to pick any door when asked which door they would choose when leaving the room. As part of a large research program, she wants to demonstrate
that children labeled by a psychologist as oppositional are more likely to choose the door behind them. To determine whether her conjecture
is correct, she conducts a study with 80
oppositional children and ask them to pick one of four door to leave the room.
Exercises
Lesson 39 Exercise File 1
Example (1):
1. Use the weight cases method to weight the data file by the number of cases before conducting
the analysis.
2. Conduct a binomial test to evaluate Tucker’s hypothesis.
3. Write a result based on your analyses.
Prefer boy Prefer girl
40 20
Exercises
Lesson 39 Data File 1
Example (2):
Is the proportion associated with oppositional children choosing the door behind them
different from 0.75, as suggested based
previous research with children in general?
Door behind Other door
25 55
