XLSTAT: Multinomial Goodness of Fit Test in Excel

 

Background

The Multinomial Goodness of Fit Test compares observed and expected category frequencies for a qualitative or discretized quantitative variable, using the multinomial distribution. It tests whether the observed distribution significantly differs from the expected one under the null hypothesis.

 

Dataset for Example

The attached dataset is a simple example based on the distribution of the occupation status in France.

Occupation status is separated into 8 categories (Farmers / Self-employed professionals / Professionals, managers, and intellectual professions / Office worker / Clerks / Workers / Inactive having worked / Other not working).

We want to compare the frequencies obtained on a survey with 560 observations to the national level statistics.

 

Setting Up

• Open XLSTAT.

• Click on the Parametric tests menu and select the Multinomial Goodness of Fit test feature:

• Once you have clicked the button, the dialog box appears.

In the General tab:

• In the Frequencies field, select the column of observed frequencies.

• In the Expected proportions field, select the proportion in the French population.

• Check the Column labels option if the first row contains variable names.

• Activate the Chi-square test and the Monte Carlo method.

• Click on the OK button to launch the computations.

• The results are displayed on a new Excel sheet.

 

Interpreting the Results

The first table shows the Chi-square statistic, critical value, degrees of freedom, and p-value. With a p-value < 0.0001, we confidently reject the null hypothesis, concluding that the observed and expected frequencies differ. Raking can be used to adjust the sample to better match population proportions.

The next table shows the Monte Carlo method’s results. It appears that it reaches the same conclusions as the standard method.