Comparisons Between Means

Question 1

Critical F’s for comparisons use the

Answer 1

degrees of freedom for the numerator and the denominator of the F-ratio.
•There are 1 and 12 degrees of freedom for this comparison.
•Fcritical(1, 12) for p≤0.05=4.75
•Given that Fobservedl=14.29, we can reject the null hypothesis and conclude that A1 leads to better scores than A2

Question 2

If we consider the ratio of the between groups variability and the within groups variability

Differences among treatment means / difference among subjects treated alike

Then we have:

Answer 2

Experimental error + treatment effects /

Experimental error

Question 3

Analysis of variance uses the

Answer 3

ratio of two sources of variability to test the null hypothesis
•Between group variability estimates both experimental error and treatment effects
•Within subjects variability estimates experimental error

Question 4

Between group variability estimates both

Answer 4

experimental error and treatment effects

Question 5

Within subjects variability estimates

Answer 5

experimental error

Question 6

In order to evaluate the null hypothesis, it is necessary to

Answer 6

transform the between group and within-group deviations into more useful quantities, namely, variances.

Question 7

Analysis of variance is the

Answer 7

statistical analysis involving the comparison of variances reflecting different sources of variability

Question 8

For the purposes of analysis of variance a variance is defined as follows

Answer 8

Variance =

Sum of squared deviations from the mean / degrees of freedom

Question 9

The sums of squares

Answer 9

From the basic deviations
AS-T= (AS-A) + (A-T)

A similar relationships holds up for the sum of squares

In other words
SStotal = SSwithin + SSbetween

Question 10

A basic ratio is defined as

Answer 10

(Score or sum) to the power of 2 /

Divisor

Question 11

The numerator term for any basic ratio involves two steps:

Answer 11

• the initial squaring of a set of quantities

* summing the squared quantities if more than one is present.

Question 12

The denominator term for each ratio is the

Answer 12

number of items that contribute to the sum or score.

Question 13

Basic Ratios make the

Answer 13

calculation of the sum of squares relatively simple

Question 14

distinctive symbol to designate basic ratios and to distinguish among them

Answer 14

AS = the basic observations or scores

A = the treatment sums

T= the grand sums

Question 15

The sums of squares can be calculated by combining these basic ratios:

Answer 15

Total Sum of Squares
AS-T

Between Group Sum of Squares
A-T

Within Group Sum of Squares
AS-A

Question 16

The ratio we are interested in is the

Answer 16

ratio of the between groups variability and the within groups variability

Question 17

Variability is defined by the equation:

Answer 17

SS / df

•where SS refers to the component sums of squares and df represent the degrees of freedom associated with the SS

Question 18

The degrees of freedom associated with a sum of squares correspond to the

Answer 18

number of scores with independent information which enter into the calculation of the sum of squares

Question 19

Degrees of freedom are the number of

Answer 19

observations that are free to vary when we know something about those observations

Question 20

The F-Ratio is defined as

Answer 20

F = MSA / MSSA

Question 21

The results of the ANOVA are usually displayed by

Answer 21

Computer programs in a summary table

Question 22

In order to decide whether or not the null hypothesis is rejected we need to

Answer 22

find out what value of F is necessary to reject the null hypothesis

• There is a simple rule for this.
• Reject H0 when Fobserved> Fcritical otherwise do not reject H0
• We obtain a value for Fcritical by looking it up in the F tables.

Question 23

To find the Critical value

Answer 23

• Take the degrees of freedom for the effect (A) and look along the horizontal axis of the F table.
• Take the degrees of freedom for the error term (S/A) and look down the vertical axis of the F table.

Question 24

Where is the Critical value of F?

Answer 24

The place were the column for the degrees of freedom of the effect A meets the row for the degrees of freedom of the error (S/A)

Question 25

The F-ratio includes information about…

Answer 25

all the levels of the independent variable that we have manipulated

Question 26

What is the Omnibus F Ratio?

Answer 26

The F-ratio for an overall difference between the means as reported in the ANOVA summary table

Question 27

The best the Omnibus F-ratio can tell us

Answer 27

• is that there are differences between the means.

* It cannot tell us that what those differences are.

Question 28

With a nonsignificant omnibus F we are prepared to

Answer 28

assert that there are no observed differences among the means
We can stop the analysis here

Question 29

A significant omnibus F…

Answer 29

• demands further analysis of the data.

* Which differences between the means are real and which are not?

Question 30

Analytical comparisons

Answer 30

• Before we set out to collect the data, we could have made specific predictions about the direction of the effects
• In this case we can use a technique known as planned (a priori) comparisons.
• We might have designed an experiment where we couldn’t be precise enough to say what the differences would be.
• In this case we use post hoc (after the event) comparisons.

Question 31

Before we set out to collect the data…

Answer 31

we could have made specific predictions about the direction of the effects

Question 32

Planned (a priori) comparisons

Answer 32

made specific predictions about the direction of the effects before collecting data

Question 33

We might have designed an experiment where we couldn’t be precise enough to say what the differences would be…

Answer 33

In this case we use post hoc (after the event) comparisons.

Question 34

Planned comparisons are based on the calculation of an…

Answer 34

f ratio

• This requires us to calculate the variability inherent in the comparison
• We calculate a sum of squares associated with the comparison. This is given by:

N (psychology sign) to the power of 2 / c to the power of 2

Psychology sign- difference between the compared means
N- number of subjects that contribute to the mean
C- the coefficient with which we weight the mean

Question 35

A F ratio is calculated to test the comparison. For this a …

Answer 35

Mean square is required