A Chi-Square Goodness of Fit Test is used to determine whether or not a categorical variable follows a hypothesized distribution.
This tutorial explains how to perform a Chi-Square Goodness of Fit Test on a TI-84 calculator.
Example: Chi-Square Goodness of Fit Test on a TI-84 Calculator
A shop owner claims that an equal number of customers come into his shop during each weekday. To test this hypothesis, an independent researcher records the number of customers that come into the shop on a given week and finds the following:
- Monday: 50 customers
- Tuesday: 60 customers
- Wednesday: 40 customers
- Thursday: 47 customers
- Friday: 53 customers
We will use the following steps to perform a Chi-Square goodness of fit test to determine if the data is consistent with the shop owner’s claim.
Step 1: Input the data.
First, we will input the data values for the expected number of customers each day and the observed number of customers each day. Press Stat and then press EDIT . Enter the following values for the observed number of customers in column L1 and the values for the expected number of customers in column L2:
Note: There were 250 customers total. Thus, if the shop owner expects an equal number to come into the shop each day then that would be 50 customers per day.
Step 2: Perform the Chi-Square goodness of fit test.
Next, we will perform the Chi-Square goodness of fit test. Press Stat and then scroll over to TESTS. Then scroll down to X2GOF-Test and press Enter.
For Observed, choose list L1. For Expected, choose list L2. For df (degrees of freedom), enter # categories – 1. In our case, we have 5-1 = 4. Then highlight Calculate and press Enter.
The following output will automatically appear:
Step 3: Interpret the results.
The X2 test statistic for the test is 4.36 and the corresponding p-value is 0.3595. Since this p-value is not less than 0.05, we fail to reject the null hypothesis. This means we do not have sufficient evidence to say that the true distribution of customers is different from the distribution that the shop owner claimed.
What does the Chi-squared variable tell us about the data?
I followed these steps but cannot figure out why my calculator keeps giving me “Sum of the lists Must be equal”
Hi Britney…The error message **“Sum of the lists must be equal”** on the **TI-84** during a **Chi-Square Goodness-of-Fit Test** usually means that the **sum of the observed frequencies (L1)** and the **sum of the expected frequencies (L2)** are not the same.
### Here’s how to troubleshoot:
#### ✅ Step-by-step checklist:
1. **Enter observed values into L1**:
Press `STAT` → `1:Edit` → Enter your **observed counts** in **L1**.
2. **Enter expected values into L2**:
Still in `Edit`, enter your **expected counts** in **L2`.
3. **Double-check that L1 and L2 have the same length**:
Both lists must have the **same number of entries**. If L1 has 5 values, L2 must also have 5 values.
4. **Check that the sums of L1 and L2 match**:
Press `2nd` → `STAT` (LIST) → `MATH` → `5:sum(`
Then type `sum(L1)` and `sum(L2)` and compare.
– If they are not equal, that’s the source of your error.
– In a **Goodness-of-Fit Test**, expected values are **calculated to match the total observed count**.
For example, if your expected proportions are equal (uniform distribution) and your total observed count is 100, the expected values should also sum to 100.
#### 🔧 How to fix it:
– If you calculated expected values using percentages or proportions, **make sure to multiply them by the total of observed values**.
For example:
“`
Observed values: [20, 25, 30, 25] → Total = 100
Expected %: [0.2, 0.3, 0.3, 0.2]
Expected counts: [20, 30, 30, 20] → Total = 100 ✔
“`
#### 🧪 Running the Test:
Once L1 and L2 are corrected:
1. Press `STAT` → `TESTS`
2. Scroll to `D:χ²GOF-Test`
3. Set `Observed: L1`, `Expected: L2`, and `df = n – 1` (number of categories minus one)
4. Select `Calculate`
what does CNTRB mean?
Hi Joseph…On a TI-84 calculator, when you perform a Chi-Square Goodness-of-Fit Test, the results screen usually displays several abbreviations, one of which is “CNTRB”.
CNTRB stands for “Contribution.”
Each CNTRB value represents how much a particular category (or class) contributes to the overall Chi-Square test statistic.