# Chi-Square Calculator for Goodness of Fit

Target: Check if the statistical model fits the observations.
The test uses Chi-square distribution.

Example: checking a fair dice.
Model: the probability of each side is equal - 1/6.
H0: fair dice.
H1: unfair dice.

The groups are the dice's numbers (1,2,3,4,5,6).
In this example, you throw the dice n times.
Expected frequencies - for each group is n/6.
Observed frequencies - the actual times each number appears.

## Hypotheses

 H0: Model Fits H1: Model Doesn't Fit

## χ² distribution

Degree Of Freedom (DF) = n - m - 1

## Test calculation

### Statistic Data

 name: the population's name. α: significant level (0-1), maximum chance allowed rejecting H0 while H0 is correct (Type1 Error). m: number of estimated parameters. For example when the model is the normal distribution, and you need to estimate the mean and the standard deviation, then m = 2. effect size(w) for example, 0.1 small, 0.3 medium, 0.5 large.

Enter raw data directly
Enter raw data from excel

### Enter sample data

Expected Value - choose Expected Frequencies or Expected Probabilities.

GroupObserved
Frequency
Expected
Value

The sum of the expected frequencies/probabilities must be equal to the sum of the observed frequencies or to one.

## Enter sample data

You may copy data from Excel, Google sheets or any tool that separate data with Tab and Line Feed.
Copy the data, one block of 3 consecutive columns includes the top header row and left header column, and paste below.

It is okay to leave empty cells, empty cells or non numeric cells won't be counted

 k: number of groups n: sample size χ² Chi square test statistic

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