Critical value
The cut-off a test statistic is compared with, read from the relevant distribution at the chosen significance level. A statistic beyond it leads to rejecting the null hypothesis.
Where you will meet it
Critical value appears in 5 learning outcomes on the CFA syllabus. A few of them:
- Explain what a simple linear regression's ANOVA table and F-statistic tell you
“The F-statistic, MSR / MSE, tests whether the slope is zero; if it exceeds the critical value the null is rejected.”
- Set up tests of whether a multiple regression's coefficients, taken two or more at a time, are jointly significant and explain what the outcome of such joint tests tells you
“Reject when F exceeds the critical value with q and n − k − 1 degrees of freedom.”
- Set out the kinds of heteroskedasticity and their consequences for statistical inference
“Detect it with the Breusch–Pagan test: regress the squared residuals on the independent variables and compare n × R² from that regression with a chi-square critical value with k degrees of freedom.”
- Set out the stages of testing a series for a unit root (nonstationarity) and explain how the test connects to autoregressive models
“The t-statistic on g1 is compared with Dickey–Fuller critical values, which are more negative than ordinary t-values, so using the standard table rejects the unit root too often.”
See also
Null hypothesis · Test statistic
Practise it
Practise critical value until it is automatic: questions that explain every wrong option.
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