Heart rates in four age groups

Topic: Analysis of variance · more questions on this topic
A Tukey interval for two varieties ›

Four age groups each have 10 measurements of the increase in heart rate. The group totals are 309, 275, 295 and 282. The error sum of squares about the four group means is 935.500.

  1. Compute the treatment sum of squares and the F statistic for equal means.

  2. The 0.95 quantile of F_{3,36} is about 2.87. What does the test conclude at level 0.05?

The grand total is 309+275+295+282=1161, so the grand mean is 1161/40=29.025. The group means are 30.9, 27.5, 29.5 and 28.2. With 10 observations in each group,

\mathrm{SS}_{\mathrm{treatment}}=10\bigl[(30.9-29.025)^2+(27.5-29.025)^2+(29.5-29.025)^2+(28.2-29.025)^2\bigr]=67.475.

F=\frac{67.475/3}{935.500/36}=\frac{22.492}{25.986}\approx 0.866.

This is smaller than 2.87, so the test does not reject equal mean increases at level 0.05. The p-value is 0.47.