Chi Square Goodness of Fit Test in Excel

Chi Square tests in Excel

There are different types of Chi Square tests:

• Chi Square Goodness of Fit Tests - see below
• Chi Square test of a Contingency Table
• Fisher Exact Test for 2X2 Tables - Use Fisher's Exact Test for 2x2 tables.

Chi Square Goodness of Fit Test

A Chi Square Goodness of Fit test evaluates the probabilities of multiple outcomes.

Las Vegas Dice Chi Square Goodness of Fit Test Example

Let's say you want to know a six-sided die is fair or unfair (Advanced Statistics by Dr. Larry Stephens). So we develop a null hypothesis (H₀) that the die is fair (each side will have an equal probability of coming up) and the alternate hypothesis (H_a ) that one or more of the sides will come up more often.:

• H₀: p1 = p2 = p3 = p4 = p5 = p6 = 1/6
• H_a : At least one p is not equal to 1/6

Now, test 120 rolls of the die and enter the data into Excel (120 tries = expected number of 20 per side):

Then, in an empty cell, begin typing the formula "=chitest(". Excel will prompt for the observed and expected ranges:

Use your mouse to select the Observed (actual_range) and Expected range. Put a comma between the two and a parenthesis at the end and hit return.

The Chi Square test will calculate the probability (i.e., p value) of all sides being equal:

Interpreting the Chi Square Goodness of Fit results

In the above results the p value = 4.55759E-05 (0.0000456) which is dramatically lower than our alpha value of 0.05, so, we can reject the null hypothesis that the die is fair.

Chi square is just one of the tools in the QI Macros Statistical Process Control Software for Excel. Other statistical tools include:

• Hypothesis Tests like anova, t test and f tests.
• Data Normality Test
• See table of all QI Macros SPC Software tools

Download the FREE 30-day Evaluation copy of the QI Macros Excel SPC Software for Six Sigma