The core AI hypothesis test: check whether data fit a distribution, or whether two variables are independent.
In short: The chi-squared test checks whether observed frequencies differ from expected frequencies by more than chance would explain. It is used for goodness of fit and for testing independence in a contingency table. The GDC returns the χ² value, the degrees of freedom and the p-value; compare the p-value with the significance level to decide.
| TI-84 Plus CE | Casio fx-CG50 and fx-CG100 | TI-Nspire CX | |
|---|---|---|---|
| Key sequence | Goodness of fit: STAT → TESTS → χ²GOF-Test. Independence: put the data in a matrix (2nd → x⁻¹ → EDIT), then STAT → TESTS → χ²-Test. | Main menu → Statistics → TEST → CHI → GOF, or 2WAY for a contingency table. | menu → Statistics → Stat Tests → χ² GOF, or χ² 2-way Test (enter the observed matrix). |
Tip: Compare the p-value to the significance level: p < level ⇒ reject H₀. Check every expected frequency is ≥ 5; the degrees of freedom are (rows−1)(cols−1) for independence.
Tip: Compare the p-value to the significance level: p < level ⇒ reject H₀. Check every expected frequency is ≥ 5; the degrees of freedom are (rows−1)(cols−1) for independence.
Tip: Compare the p-value to the significance level: p < level ⇒ reject H₀. Check every expected frequency is ≥ 5; the degrees of freedom are (rows−1)(cols−1) for independence.
Here's a real IB-style question that uses exactly this technique.
A 2×2 contingency table has observed values 20, 30 (row 1) and 25, 25 (row 2). Test for independence at the 5% significance level.
The core AI hypothesis test: check whether data fit a distribution, or whether two variables are independent. Testing whether observed data fits a claimed distribution (goodness of fit). Testing whether two categorical variables are independent, from a contingency table.
1. State H₀ and H₁ and the significance level first. 2. Goodness of fit: STAT → TESTS → χ²GOF-Test. Independence: put the data in a matrix (2nd → x⁻¹ → EDIT), then STAT → TESTS → χ²-Test.
1. State H₀ and H₁ and the significance level first. 2. Main menu → Statistics → TEST → CHI → GOF, or 2WAY for a contingency table.
1. State H₀ and H₁ and the significance level first. 2. menu → Statistics → Stat Tests → χ² GOF, or χ² 2-way Test (enter the observed matrix).
Compare the p-value to the significance level: p < level ⇒ reject H₀. Check every expected frequency is ≥ 5; the degrees of freedom are (rows−1)(cols−1) for independence.
In the worked example on this page (4 marks, Paper 2), the marks are: M1: Find the expected frequencies from the row/column totals; M1: χ² = Σ(O − E)²/E; A1: χ² = 1.01, p = 0.315; R1: p > 0.05, so fail to reject H₀ (independent).
Questions that need this technique link back to this guide. Try one in practice mode, or see every GDC guide.