Chi-square Hypothesis Testing

The major characteristics of the chi-square distribution are

• It is positive skewed
• It is non-negative
• It is based on degrees of freedom
• When the degrees of freedom change a new distribution is created

Hypothesis testing consists of five steps.

• State Null and alternative hypothesis
• Write down relevant data, select a level of significance
• Identify and compute the test statistic x2 to be used in testing they hypothesis.
• Compute the Critical values x2 C
• Based on the sample arrive a decision
• Use the following formula for test stastistic x2 values as follows:



• Where f0 is the observed frequency and fe is the excepted frequency
• Then the critical values are determined
• Chi-square distribution is a family of distribution but each distribution has a different shape depending on the degrees of freedom, df.
• The data are often presented in a table format. if starting with raw data on two variables, a table must be created first.
• Columns are scores of the independent variable.
• There will be as many columns as there are scores in the independent variable.
• Rows are scores of the dependent variable.
• There will be as many rows as there are scores on the dependent variable.