Week 8_Group Differences - ANOVA and Error Rates

Question 1

What is a planned comparison?

Answer 1

A focused linear combination of means of two or more levels of the factor that is formulated and specified on a priori grounds

Question 2

What is a linear combination of means?

Answer 2

The weighted sum of the means of all levels of the between subjects factor, where each level is given its own comparison weight.

Question 3

What should the weights in a linear combination of means add up to?

Answer 3

Zero

Question 4

What is a linear contrast?

Answer 4

A set of comparison weights that equal zero

Question 5

What is an alternative name for linear contrast?

Answer 5

Planned Contrast

Question 6

What are orthogonal contrast weights?

Answer 6

Weights of two planned comparisons that are independent and have no redundancy (overlap). Determined when their paired values are multiplied and summated and this value is equal to zero.

Question 7

What are non-orthogonal contrast weights?

Answer 7

Weights of two planned comparisons that are not independent and have overlap between them (sum of cross products = not zero)

Question 8

What is the advantage of using both an orthogonal set of contrast weights and balanced design?

Answer 8

The SS between can then be broken down into the constituent SScontrast for each planned comparison.

Question 9

What is meant by a balanced design?

Answer 9

All the groups have the same number of individuals in them.

Question 10

What is an unbalanced design?

Answer 10

When the sample size differs in one or more groups (even if by 1 individual).

Question 11

What value must the contrast weights sum when calculating standardised mean differences?

Answer 11

Positive weights must sum to +1 and Negative Weights must sum to -1.

Question 12

What is the alpha level?

Answer 12

A value that is set a priori at which we decide to reject the null hypothesis (eg. 0.05), it is the criteria we set to define the false rejection error rate (NOT the same as the false rejection error rate).

Question 13

What is the False Rejection Error Rate?

Answer 13

The actual number of times a true null hypothesis is erroneously rejected.

Question 14

For a single comparison, what are the chances of falsely rejecting a true null hypothesis in the long run?

Answer 14

1 in 20 with an alpha level of 0.05

Question 15

With an alpha level of 0.05, what is the probability of rejecting a true null hypothesis?

Answer 15

0.05

Question 16

What is a false rejection error?

Answer 16

Falsely rejecting a null hypothesis that is true. Usually on the basis of whether it falls within the region of rejection set by alpha.

Question 17

When can’t a false rejection error be made?

Answer 17

When the null hypothesis is not true.

Question 18

What is the false rejection error rate?

Answer 18

The probability that a null hypothesis is true, given that it has been rejected.

Question 19

What is the probability notation for the false rejection error rate?

Answer 19

ER = Pr (Ho = T/ Ho has been rejected)

Question 20

What is the probability notation for alpha?

Answer 20

Alpha = Pr (Rejecting Ho / Ho = T)

Question 21

What is a family wise error rate?

Answer 21

ERfw is the probability of making at least one false rejection error among ‘j’ comparisons when the null hypothesis is true for each comparison.

Question 22

What is ERpc?

Answer 22

The per comparison error rate. The probability of making a false rejection of a true Ho for each comparison

Question 23

What is the ERfw formula?

Answer 23

ERfw = 1 - (1 - alpha per comparison)*J

• to the power of the number of comparisons.

Question 24

When is the Bonferroni Inequality used?

Answer 24

When comparisons are not independent (ie. when they are not orthogonal and when the same MSwithin has been used to calculate planned comparisons).

Question 25

What does the Bonferroni Correction do?

Answer 25

Ensures that the familywise Error Rate is no higher than the sum of the error rate for each planned comparison

ERfw = ERpc1 + ERpc2 + ERpc3…….

Question 26

What adjustment does the Bonferroni Correction make to the per comparison alpha levels?

Answer 26

Using the Bonferroni Correction

Alpha PC = 0.5/j

(the per comparison alpha level is divided by the number of comparisons, so that the overall alpha level is only 0.05).