Lecture 3 - Comparisons Between Means

Question 1

What is the equation for a basic ratio?

Answer 1

Σ (score or sum)²
____________

divisor

Question 2

How do we calculate the numerator in a basic ratio?

Answer 2

There are two steps:

1. squaring a set of scores
2. adding together the squares of the scores, if multiple are present

Question 3

What is the denominator in a basic ratio?

Answer 3

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

Question 4

what are the three types of basic ratio?

Answer 4

1. [AS] = the basic observations/scores
2. [A] = the treatment sums
3. [T] = the grand sums

Question 5

How do we calculate the total Sum of Squares from a basic ratio?

Answer 5

[AS] - [T]

that is to say….. outputs from the equations for the following

[basic observations/scores] - [grand sums]

Question 6

How do we calculate the between groups sum of squares using basic ratios?

Answer 6

[A]-[T]

that is to say….. outputs from the equations for the following

[treatment sums] - [grand sums]

Question 7

How do we calculate the within-groups sum of squares using basic ratios?

Answer 7

[AS] - [A]

that is to say….. outputs from the equations for the following

[basic observations/scores] - [the treatment sums]

Question 8

Define ‘degrees of freedom’

Answer 8

the number of observations that are free to vary when we know something about those observations (I dont really know what this means)

Question 9

What is the equation for the F-Ratio?

Answer 9

F= MSa

______

MSs/a

Question 10

What does x_a mean?

Answer 10

x for between-groups

Question 11

what does x_s/a mean?

Answer 11

x for within groups

Question 12

what does x_t mean?

Answer 12

total of x

Question 13

How do we use the F value to decide wether to accept or reject H₀

Answer 13

We reject H₀ when F_observed is greater than F_critical, otherwise we accept H₀.

Question 14

How do we find a value for F_critical?

Answer 14

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

Question 15

What is the omnibus F?

Answer 15

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,

Question 16

When do we use a priori comparisons? (also called planned comparisons)

Answer 16

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

Question 17

When do we use post-hoc comparisons?

Answer 17

If, before collecting our data, we did not make any specific predictions on what we expected to find.