Between and within
Section of Analysis of variance, part of Statistical inference
Between and within
| Type | Section |
| Taught in | Analysis of variance |
| Part | Statistical inference |
Four age groups of 10 people each do a physical test, and the increase in heart rate is recorded.
| Age 10–19 | Age 20–39 | Age 40–59 | Age 60–69 |
|---|---|---|---|
| 29 | 24 | 37 | 28 |
| 33 | 27 | 25 | 29 |
| 26 | 33 | 22 | 34 |
| 27 | 31 | 33 | 36 |
| 39 | 21 | 28 | 21 |
| 35 | 28 | 26 | 20 |
| 33 | 24 | 30 | 25 |
| 29 | 34 | 34 | 24 |
| 36 | 21 | 27 | 33 |
| 22 | 32 | 33 | 32 |
The group means are 30.9, 27.5, 29.5 and 28.2. Do the age groups differ in mean increase?
There is no four-sample t test. A t statistic compares two means through their difference, and four means have six differences, which are not independent. The way forward is to compare the variation of the group means about the grand mean with the variation of the observations inside each group. Here the spread within every group, about 4 to 5 beats, is much larger than the spread between the four means. That suggests the means are equal and age is not a factor that explains the increase.
Used in
See also
One-way analysis of variance · ANOVA sum of squares decomposition · ANOVA F distribution · Contrast · Tukey intervals · Randomised block design · One-factor analysis of variance · Multiple comparisons