Chapter 12 GLM 1: Comparing Several Independent Means

Question 1

Analysis of Variance (ANOVA) (3)

Answer 1

1. A statistical procedure that uses the F-statistic to test the overall fit of a linear model.
2. In experimental research this linear model tends to be defined in terms of group means,
3. And the resulting ANOVA is therefore an overall test of whether group means differ.

Question 2

Brown - Forsythe F (1)

Answer 2

1. A version of the F-statistic designed to be accurate when the assumption of homogeneity of variance has been violated.

Question 3

Cubic Trend (3)

Answer 3

1. If you connected the means in ordered conditions in a line
2. Then a cubic trend is shown by two changes in the direction of this line.
3. You must have at least four ordered conditions.

Question 4

Deviation Contrast (3)

Answer 4

1. A non-orthogonal planned contrast
2. That compares the mean of each group
3. (Except for the first or last, depending on how the contrast is specified) to the overall mean.

Question 5

Difference Contrast (reverse Helmet contrast) (3)

Answer 5

1. A non-orthogonal planned contrast
2. that compares the mean of each condition (except the first)
3. to the overall mean of all previous conditions combined.

Question 6

Eta Squared (6)

Answer 6

1. An effect size measure
2. that is the ratio of the model sum of squares to the total sum of squares.
3. So, in essence, the coefficient of determination by another name.
4. It doesn’t have an awful lot going for it: not only is it biased,
5. but it typically measures the overall effect of an ANOVA
6. and effect sizes are more easily interpreted when they reflect specific comparisons (e.g. the difference between two means).

Question 7

General Linear Model (4)

Answer 7

1. A term to represent the fact that the linear model can encompass a range of different research designs
2. Such as multiple outcome variables (e.g. MANOVA),
3. Comparing means of categorical predictors (e.g. t-test, ANOVA),
4. And including both categorical and continuous predictors (e.g. ANCOVA).

Question 8

Grand Variance (1)

Answer 8

1. The variance within an entire set of observations.

Question 9

Harmonic Mean (5)

Answer 9

1. A weighted version of the mean
2. That takes account of the relationship between variance and sample size.
3. It is calculated by summing the reciprocal of all observations,
4. Then dividing by the number of observations.
5. The reciprocal of the end product is the harmonic mean.

Question 10

Helmert Contrast (3)

Answer 10

1. A non-orthogonal planned contrast
2. That compares the mean of each condition (except the last)
3. To the overall mean of all subsequent conditions combined.

Question 11

Independent ANOVA (1)

Answer 11

1. Analysis of variance conducted on any design in which all independent variables or predictors have been manipulated using different participants (i.e. all data come from different entities).

Question 12

Omega Squared (5)

Answer 12

1. An effect size measure associated with ANOVA
2. That is less biased than eta squared.
3. It is a (sometimes hideous) function of the model sum of squares and the residual sum of squares
4. And isn’t actually much use because it measures the overall effect of the ANOVA
5. And so can’t be interpreted in a meaningful way.

Question 13

Orthogonal (2)

Answer 13

1. Means perpendicular.
2. It tends to be equated to independence in statistics because of the connotation that perpendicular linear models in geometric space are completely independent.

Question 14

Pairwise Comparisons (1)

Answer 14

1. Comparisons of pairs of means.

Question 15

Planned Contrasts (5)

Answer 15

1. A set of comparisons between group means
2. That are constructed before any data are collected.
3. These are theory-led comparisons
4. And are based on the idea of partitioning the variance created by the overall effect of group differences into gradually smaller portions of variance.
5. These tests have more power than post hoc tests.

Question 16

Polynomial Contrast (3)

Answer 16

1. A contrast that tests for trends in the data.
2. In its most basic form it looks for a linear trend
3. (i.e. that the group means increase proportionately).

Question 17

Post Hoc Tests (6)

Answer 17

1. A set of comparisons between group means
2. That were not thought of before data were collected.
3. Typically these tests involve comparing the means of all combinations of pairs of groups.
4. To compensate for the number of tests conducted, each test uses a strict criterion for significance.
5. As such, they tend to have less power than planned contrasts.
6. They are usually for exploratory work for which no firm hypotheses were available on which to base planned contrasts.

Question 18

Quadratic Trend (3)

Answer 18

1. If the means in ordered conditions are connected with a line
2. Then a quadratic trend is shown by one change in the direction of this line (e.g. the line is curved in one place); the line is, therefore, U-shaped.
3. There must be at least three ordered conditions.

Question 19

Quartic Trend (3)

Answer 19

1. If the means in ordered conditions are connected with a line
2. Then a quartic trend is shown by three changes in the direction of this line.
3. There must be at least five ordered conditions.

Question 20

Repeated Contrast (2)

Answer 20

1. A non-orthogonal planned contrast

2. that compares the mean in each condition (except the first) to the mean of the preceding condition.

Question 21

Simple Contrast (3)

Answer 21

1. A non-orthogonal planned contrast
2. That compares the mean in each condition to the mean of either the first of last condition,
3. Depending on how the contrast is specified.

Question 22

Weights (2)

Answer 22

1. A number by which something (usually a variable in statistics) is multiplied.
2. The weight assigned to a variable determines the influence that variable has within a mathematical equation.

Question 23

Welch’s F (2)

Answer 23

1. A version of the F-statistic

2. Designed to be accurate when the assumption of homogeneity of variance has been violated.