﻿ Likelihood-Ratio Chi-Square Test

# Likelihood-Ratio Chi-Square Test

### Statistics > Basic Statistics > Chi-Square > Likelihood-Ratio Test

Likelihood-ratio test on a two-dimensional contingency table.

The likelihood-ratio chi-square statistic involves the ratios between the observed and expected frequencies. The statistic is computed as

When the row and column variables are independent, G2 has an asymptotic chi-square distribution with (r-1)(c-1) degrees of freedom.

### Dialog box items

Rows:
Select the variables displayed in rows in the crosstabulation. Selected variables should be factors with at least two levels. A crosstabulation is produced for each combination of row and column variables.

Columns:
Select the variables displayed in columns in the crosstabulation. Selected variables should be factors with at least two levels. A crosstabulation is produced for each combination of row and column variables.

DataSet is a Contingency Table:
Select if the data set specified is a contingency table.

Report:
The display of outputs of VisualStat.

### Data

To use Cross Tabulation, your data should be categorical. To define the categories of each table variable, use values of a numeric or short string (eight or fewer characters) variable. For example, for gender, you could code the data as 1 and 2 or as male and female.

### Statistics

Measures of Association
Describes the association between the two variables of the contingency table

oCramer's V: Check to display Cramer's V coefficient.

oPhi Coefficient: Check to display Phi Coefficient.

oContingency Coefficient: Check to display Contingency Coefficient.

oKappa Coefficient: Check to display Kappa Coefficient.

oObserved values: Check to display each cell's observed count.

oExpected values: Check to display each cell's expected count.

### Options

Confidence Level: Enter the level of confidence desired. Enter any number between 0 and 100. Entering 90 will result in a 90% confidence interval. The default is 95%.

### Example

The data show test scores for 34 children in two class (1 or 2). The child's gender ("male" or "female") and grade (4, 5, or 6) is also recorded.

1.Open the DataBook summary.vstz

2.Select the sheet crosstab

3.Choose the tab Statistics, the group Basic Statistics and the command Likelihood-Ratio Test

4.In Rows, select Gender. In Columns, select Class

5.Click OK

Report window output

Likelihood-Ratio Chi-Square Test

Null hypothesis under test >>>  Independence of the rows and columns

data:  Gender and Class from data sheet summary.vstz

NB                   34

Likelihood-Ratio G2  4.3447

Degree of freedom    1

p-value              0.0371

alpha-level          0.05

Critical Value       3.8415

Conclusion           Reject the Null Hypothesis

i.e. there is a general association between the row variable and the column variable at the 5% level.