Statistical significance: chi-squared & t-test
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Flip to reveal answersWhich test compares counts against an expected ratio (or tests an association)?
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Question
Which test compares counts against an expected ratio (or tests an association)?
Answer
The **chi-squared (χ²) test** — it is for **counts/frequencies**, e.g. testing a 3:1 genetic ratio.
Question
Which test compares two means of a measured variable?
Answer
The **t-test** — use it to ask whether **two averages** are significantly different.
Question
What is the chi-squared formula?
Answer
$\chi^2 = \sum \dfrac{(O-E)^2}{E}$ — where **O** = observed count, **E** = expected count; add one term per category.
Question
How do you decide if a result is statistically significant?
Answer
Compare the **calculated** statistic to the **critical value** at **p = 0.05**: if **calculated ≥ critical**, it is **significant** (p < 0.05) → reject H₀.
Question
What are the null (H₀) and alternative (H₁) hypotheses?
Answer
**H₀**: there is **no** real difference/association (any difference is chance). **H₁**: there **is** a real difference/association.
Question
What do overlapping error bars suggest about two means?
Answer
That the means are **probably not significantly different** — a t-test would give t below the critical value (p > 0.05).
Question
How do you find degrees of freedom?
Answer
For **χ²**: (number of categories − 1). For a **t-test of two groups**: $df = n_1 + n_2 - 2$. The df picks the row of the critical-value table.
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