Week 8_Group Differences - ANOVA and Error Rates Flashcards
What is a planned comparison?
A focused linear combination of means of two or more levels of the factor that is formulated and specified on a priori grounds
What is a linear combination of means?
The weighted sum of the means of all levels of the between subjects factor, where each level is given its own comparison weight.
What should the weights in a linear combination of means add up to?
Zero
What is a linear contrast?
A set of comparison weights that equal zero
What is an alternative name for linear contrast?
Planned Contrast
What are orthogonal contrast weights?
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.
What are non-orthogonal contrast weights?
Weights of two planned comparisons that are not independent and have overlap between them (sum of cross products = not zero)
What is the advantage of using both an orthogonal set of contrast weights and balanced design?
The SS between can then be broken down into the constituent SScontrast for each planned comparison.
What is meant by a balanced design?
All the groups have the same number of individuals in them.
What is an unbalanced design?
When the sample size differs in one or more groups (even if by 1 individual).
What value must the contrast weights sum when calculating standardised mean differences?
Positive weights must sum to +1 and Negative Weights must sum to -1.
What is the alpha level?
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).
What is the False Rejection Error Rate?
The actual number of times a true null hypothesis is erroneously rejected.
For a single comparison, what are the chances of falsely rejecting a true null hypothesis in the long run?
1 in 20 with an alpha level of 0.05
With an alpha level of 0.05, what is the probability of rejecting a true null hypothesis?
0.05
What is a false rejection error?
Falsely rejecting a null hypothesis that is true. Usually on the basis of whether it falls within the region of rejection set by alpha.
When can’t a false rejection error be made?
When the null hypothesis is not true.
What is the false rejection error rate?
The probability that a null hypothesis is true, given that it has been rejected.
What is the probability notation for the false rejection error rate?
ER = Pr (Ho = T/ Ho has been rejected)
What is the probability notation for alpha?
Alpha = Pr (Rejecting Ho / Ho = T)
What is a family wise error rate?
ERfw is the probability of making at least one false rejection error among ‘j’ comparisons when the null hypothesis is true for each comparison.
What is ERpc?
The per comparison error rate. The probability of making a false rejection of a true Ho for each comparison
What is the ERfw formula?
ERfw = 1 - (1 - alpha per comparison)*J
- to the power of the number of comparisons.
When is the Bonferroni Inequality used?
When comparisons are not independent (ie. when they are not orthogonal and when the same MSwithin has been used to calculate planned comparisons).
What does the Bonferroni Correction do?
Ensures that the familywise Error Rate is no higher than the sum of the error rate for each planned comparison
ERfw = ERpc1 + ERpc2 + ERpc3…….
What adjustment does the Bonferroni Correction make to the per comparison alpha levels?
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).
