# 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 x_{a }mean?

x for between-groups

what does x_{s/a }mean?

x for within groups

what does x_{t} mean?

total of x

How do we use the F value to decide wether to accept or reject H_{0}

We reject H_{0} when F_{observed} is greater than F_{critical}, otherwise we accept H_{0}.

How do we find a value for F_{critical}?

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,