Statistical Concepts

**Session 5: The General
Linear Model**

Dependent Variable - Interval

(can bend rules by using Ordinal if there are at least 5 ordered
categories)

ANOVA - Independent variables are
categorical (no more than 5 categories)

Regression - Independent variables are ordinal and/or interval
(can use binary categorical variables)

Mixed - either use ANCOVA (covariates before factors) or Regression (create one dummy variable for each degree of freedom for each categorical factor)

N.B. By default, ANOVA also analyses interactions, but Regression does not.

ANOVA Example

288 students given essays to mark.

Mean essay marks and sample sizes by same/opposite sex and level
of attractiveness.

Same sex | Opposite sex | Overall | n | ||

Attractiveness of author | Low | 22.8 | 23.2 | 22.9 | 96 |

Medium | 28.6 | 22.9 | 25.8 | 96 | |

High | 25.1 | 28.0 | 26.6 | 96 | |

Overall | 25.5 | 24.7 | 25.1 | 288 | |

n | 144 | 144 | 288 |

Source of Variation |
Sum of Squares |
Degrees of Freedom |
Mean Square |
F Ratio |

Same/opposite sex (A) |
686.85 |
|||

Attractiveness (B) |
46.85 |
|||

Interaction (AxB) |
942.35 |
|||

Residual |
21053.14 | |||

Total |
22729.19 |