Lecture 3 - Comparisons Between Means Flashcards
What is the equation for a basic ratio?
Σ (score or sum)2
____________
divisor
How do we calculate the numerator in a basic ratio?
There are two steps:
- squaring a set of scores
- adding together the squares of the scores, if multiple are present
What is the denominator in a basic ratio?
the number of items which contribute to each score
E.g. 3
E.g. (3) (5) - because 3 data points make up the data used here, and each of those is made of 5 individual scores
what are the three types of basic ratio?
- [AS] = the basic observations/scores
- [A] = the treatment sums
- [T] = the grand sums
How do we calculate the total Sum of Squares from a basic ratio?
[AS] - [T]
that is to say….. outputs from the equations for the following
[basic observations/scores] - [grand sums]
How do we calculate the between groups sum of squares using basic ratios?
[A]-[T]
that is to say….. outputs from the equations for the following
[treatment sums] - [grand sums]
How do we calculate the within-groups sum of squares using basic ratios?
[AS] - [A]
that is to say….. outputs from the equations for the following
[basic observations/scores] - [the treatment sums]
Define ‘degrees of freedom’
the number of observations that are free to vary when we know something about those observations (I dont really know what this means)
What is the equation for the F-Ratio?
F= MSa
______
MSs/a
What does xa mean?
x for between-groups
what does xs/a mean?
x for within groups
what does xt mean?
total of x
How do we use the F value to decide wether to accept or reject H0
We reject H0 when Fobserved is greater than Fcritical, otherwise we accept H0.
How do we find a value for Fcritical?
We obtain a value for f-critical by looking it up in the F-table using the degrees of freedom
Take the degrees of freedom for the effect (A) and look on the horizontal axis
Take the degrees of freedom for the error (s/a) and look down the vertical axis.
Where they meet is the critical F-value
What is the omnibus F?
It is the f-ratio for an overall difference between the means (it is reported in ANOVA summary tables)
It may only tell us if there are differences between the means, not what these differences are
If the omnibus f is non-significant, we can just stop there. If it is significant, we must go on to conduct further analysis to find out mroe about the differences between means,
When do we use a priori comparisons? (also called planned comparisons)
If, before we collected data, we made specific predictions about the direction of the effects we expected to find
such as: We conducted a replication of a famous study and we wanted to know if our results would match the results the other researcher found in this area of research
All a priori comparisons have 1 degree of freedom
When do we use post-hoc comparisons?
If, before collecting our data, we did not make any specific predictions on what we expected to find.
