Question

1. Assume you have been given the task to design a Chi Square test  to determine if student's attitudes toward statistics is Positive, Negative or Neutral. Would this be a One-Way Chi-Square or a Two-Way Chi-Square? Why (you must answer the why in your own words)

2. Assuming above is a One-Way how could you make it a Two-Way or if you selected Two-Way how could you make it a One-Way

Answer 1

1) This would be a One-Way Chi-Square or a Two-Way Chi-Square.

A One-Way Chi-Square is an analysis of an experimental design with one independent variable and a nominal dependent variable.

A Two-Way Chi-Square is used when you have two independent variables and a nominal dependent variable.

Since in this context student's attitudes is our only independent variable and one dependent variable i.e. frequency data. We will use the chi-square test to determine whether the frequencies observed across the categories of one variable differ from what are expected to be by chance. Because there is only one variable, this type of a design is a oneway design; thus, the test is an oneway chi-square.

Table for one way chi square test is given below:

	Positive	Negative	Neutral
Observed Frequency	fo1	fo2	fo3
Expected Frequency	n*p1 =fe1	n*p2= fe2	n*p3= fe3

The test statistics is :

2) When we have two nominal independent variables and the dependent variable is frequency we perform a two-way chi-square analysis

So, to make One-Way chi square to Two-Way chi square by assuming one more nominal independent variable i.e. student's sex. This will test for the presence of a relationship between the two independent variables when the dependent variable is frequency data.

So in this context we will have two independent variable student's attitudes and student's sex and the dependent variable will be the frequency data.

Both test use exactly the same procedures and have the same assumptions. The only difference is how the frequency data is collected and how results are interpreted.