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Chi-Square Calculator

How to use Chi-Square Calculator?

The following steps are of use of the Chi-Square Calculator:

Select the value of “Significance Level α”.
To add more rows and columns click on “Add Row” and “Add Column” respectively.
Put the data in the above groups and categories.
Click on “Calculate” to generate an answer.
To erase all inputs, click on “Reset”.

What is Chi-Square distribution?

The chi-square distribution is a test used to test a hypothesis and is denoted by X². In probability theory and statistics, the Chi-Square distribution is also known as the Central Chi-Square distribution.

The formula of Chi-Square distribution:

Generally, we use the following formula to calculate the Chi-Square distribution:

Chi-Square distribution = X² = ∑ (O_i – E_i)² / E_i

In the above formula:

O_i = Original values provided in data
E_i = Expected value calculated by the following formula
E = RT × CT / GT

Here

RT = Row Total
CT = Column Total
GT = Grand Total

Steps to calculate Chi-Square Distribution manually:

These are the following steps of Chi-Square distribution:

Make a null hypothesis and also write an alternate hypothesis
Calculate rows, columns, and Grand total
Calculate the “expected value” E with the help of rows, columns, and grand total
Draw a table and put the original and expected values in separate columns
Calculate (O – E) in the next column
Calculate (O – E)² in the next column
Calculate (O – E)² / E in the next column
The sum of the last column is our calculated value
Find out the degree of freedom by the (r – 1) * (c – 1) formula
Use the degree of freedom and level of significance to find out the table value
Compare the calculated value and table value and write a conclusion

Example section:

In this section, we solve an example with the help of basic rules of Chi-square distribution.

Example 1:

Calculate Chi-Square distribution by taking null hypothesis H_o: µ₁ = µ₂ and H₁: µ₁ ≠ µ₂with the level of significance 5%.

	Category 1	Category 2
Group 1	64	56
Group 2	42	28

Solution:

Step 1: Extract the data.

H_o: µ₁ = µ₂

H₁: µ₁ ≠ µ₂

Step 2: Find RT, CT, and GT

	Category 1	Category 2	Total
Group 1	64	56	120
Group 2	42	28	70
Total	106	84	190

Step 3: Calculate Expected values

	Category 1	Category 2
Group 1	66.947	53.053
Group 2	39.053	30.947

Step 4: Draw a Table and calculate the Chi-Square distribution value

O	E	O – E	(O – E)²	(O – E)² / E
64	66.947	- 2.947	8.6848	0.1297
56	53.053	2.947	8.6848	0.1637
42	39.053	2.947	8.6848	0.2223
28	30.947	- 2.947	8.6848	0.2806
			Total	0.7963

Step 5: Calculate the Degree of freedom

Df = (r – 1) * (c – 1)

Df = (2 – 1) * (2 – 1)

Df = 1 * 1

Df = 1

Step 6: Find out the table value

Table value = 0.3720

Step 7: Conclusion

Because the calculated value is greater than the table and lies in the critical region. So we reject the null hypothesis and accept the alternate hypothesis.