Chi-Square Goodness of Fit Calculator
Compare the observed frequency of each category with equal proportions or proportions you specify.
Updated · By Bibin XavierData 90 × 12
| IDtext · 90 levels | Grouptext · 3 levels | Gendertext · 2 levels | Agenumeric | Hours_Studynumeric | Anxietynumeric | Motivationnumeric | Pre_Scorenumeric | Post_Scorenumeric | Exam_Scorenumeric | Passednumeric · coded | Satisfactionnumeric · coded |
|---|---|---|---|---|---|---|---|---|---|---|---|
| S001 | Control | Male | 23 | 11.2 | 29 | 4.6 | 60 | 62 | 67 | 1 | 2 |
| S002 | Workshop | Female | 23 | 3.9 | 28 | 3.5 | 54 | 70 | 54 | 0 | 2 |
| S003 | Online | Female | 18 | 10.1 | 32 | 4 | 55 | 57 | 66 | 0 | 3 |
| S004 | Control | Male | 26 | 13.6 | 41 | 3.5 | 52 | 55 | 59 | 0 | 3 |
| S005 | Workshop | Female | 22 | 9.7 | 27 | 3.6 | 56 | 63 | 65 | 0 | 4 |
| S006 | Online | Female | 20 | 7.9 | 32 | 3.8 | 65 | 82 | 65 | 0 | 2 |
| S007 | Control | Female | 20 | 6.3 | 28 | 3 | 72 | 83 | 61 | 0 | 3 |
| S008 | Workshop | Male | 22 | 8 | 29 | 3.1 | 64 | 72 | 62 | 1 | 3 |
Variables and options
Results
90 rows · example dataObserved and expected frequencies
| Category | Observed | Expected | Residual | Expected % |
|---|---|---|---|---|
| 1 | 4 | 18.0 | -14.0 | 20.0 |
| 2 | 19 | 18.0 | 1.0 | 20.0 |
| 3 | 36 | 18.0 | 18.0 | 20.0 |
| 4 | 20 | 18.0 | 2.0 | 20.0 |
| 5 | 11 | 18.0 | -7.0 | 20.0 |
Test statistics
| χ² | df | p | N |
|---|---|---|---|
| 31.89 | 4 | < .001 | 90 |
Observed and expected
Interpretation
The observed distribution of Satisfaction differs significantly from the expected proportions.
How to cite this tool
Using these results in a thesis, journal article, report or class assignment? Please cite this free tool so others can find it. It keeps the site free.
APA 7
Xavier, B. (2026). Chi-Square Goodness of Fit Calculator [Web application]. FreeStatisticalTools.com. https://freestatisticaltools.com/chi-square-goodness-of-fit-calculator/
BibTeX
@software{xavier_chisquaregoodnessoffit_2026,
author = {Xavier, Bibin},
title = {Chi-Square Goodness of Fit Calculator},
publisher = {FreeStatisticalTools.com},
year = {2026},
url = {https://freestatisticaltools.com/chi-square-goodness-of-fit-calculator/},
note = {Web application}
}Suggested sentence for your methods section: “The analysis was carried out with the free Chi-Square Goodness of Fit Calculator tool on FreeStatisticalTools.com (Xavier, 2026).”
What is the chi-square goodness of fit test?
The chi-square goodness of fit test compares the observed frequency of each category with the frequencies you would expect, either equal across categories or in proportions you specify.
When to use the chi-square goodness of fit test
Use it to test whether categories occur in the proportions you expect, such as equal preference among options or a known population distribution.
Assumptions
- Independent observations.
- Expected counts of at least 5 in each category.
How to use this tool
- Enter your data. Paste columns from Excel, Google Sheets or SPSS with variable names in the first row, or upload a CSV or Excel file. The example data shows the expected layout.
- Choose the variables. Select the categorical variable.
- Set the options. Fill in expected proportions.
- Read the results. Results update automatically. Read the plain-English interpretation, then use Copy table to paste APA-style tables into Word and Copy for the results sentence.
Frequently asked questions
What is the null hypothesis?
That the population proportions equal the expected proportions you specified.
How do I enter custom expected proportions?
Type one proportion per category, separated by commas, in the order the categories appear. They are rescaled to sum to 1.
How many degrees of freedom are there?
The number of categories minus one.
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