Anova Analysis Of Variance

Question 1

Assumptions underlying analysis of variance

Answer 1

• The measure taken is on an interval or ratio scale.
• The populations are normally distributed
• The variances of the compared populations are the same.
• The estimates of the population variance are independent

Question 2

ANOVA

Analysis of variance uses the

Answer 2

the 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
•The assumptions that underly this technique directly follow on from the F-ratio.

Question 3

Variability and averages

Answer 3

Graph 1: peaks in same place and different width
Different variability
Same averages
Graph 2: peaks in different places and same width
Same variability
Different averages

Question 4

The normal distribution is used in

Answer 4

statistical analysis in order to make standardized comparisons across different populations (treatments).

Question 5

The kinds of parametric statistical techniques we use

Answer 5

assume that a population is normally distributed. This allows us to compare directly between two populations

Question 6

The Normal Distribution is a mathematical function that

Answer 6

defines the distribution of scores in population with respect to two population parameters

Question 7

(Normal distribution)

The first parameter is the

Answer 7

Greek letter (m, mu). This represents the population mean.

Question 8

(Normal distribution)

The second parameter is the

Answer 8

Greek letter (s, sigma) that represents the population standard deviation.

Question 9

Different normal distributions are generated whenever

Answer 9

the population mean or the population standard deviation are different

Question 10

Normal distributions with different population variances and the same population mean

Answer 10

Different length peak troughs but all at the same place

Question 11

•Normal distributions with different population means and the same population variance

Answer 11

Peaks and troughs the same size and width but in different places, overlapping next to each other

Question 12

•Normal distributions with different population variances and different population means

Answer 12

Different size and width peak and troughs and not next to each other

Question 13

Most samples of data are

Answer 13

normally distributed (but not all)

Question 14

When the null hypothesis (Ho) is approximately true we have the following:

Answer 14

There is almost a complete overlap between the two distributions of scores
Very similar in terms of shared variances and similar averages. Same size peak and trough same weak and very close to be completely overlapping

Question 15

When the alternative hypothesis (H1) is true we have the following:

Answer 15

•There is very little overlap between the two distributions

Similar peaks and troughs and width but very far from over lapping

Question 16

The crux of the problem of rejecting the null hypothesis is

Answer 16

the fact that we can always attribute some portion of the difference we observe among treatment parameters to chance factors
•These chance factors are known as experimental error

Question 17

An experimental error

Answer 17

The crux of the problem of rejecting the null hypothesis is the fact that we can always attribute some portion of the difference we observe among treatment parameters to chance factors

Question 18

What are the potential contributors to an experimental error

Answer 18

All uncontrolled sources of variability in an experiment

Question 19

There are two basic kinds of experimental error:

Answer 19

• individual differences error

* measurement error.

Question 20

In a real experiment both sources of experimental error will

Answer 20

influence and contribute to the scores of each subject.
•The variability of subjects treated alike, i.e. within the same treatment condition or level, provides a measure of the experimental error.
•At the same time the variability of subjects within each of the other treatment levels also offers estimates of experimental error

Question 21

Estimate of treatment effects

Answer 21

• The means of the different groups in the experiment should reflect the differences in the population means, if there are any.
• The treatments are viewed as a systematic source of variability in contrast to the unsystematic source of variability the experimental error.
• This systematic source of variability is known as the treatment effect.

Question 22

What is the treatment effect?

Answer 22

Systematic source of variability

Question 23

What is Partitioning?

Answer 23

Dividing the deviation from the grand mean

Question 24

Each of the deviations from the grand mean have a specific name
AS25-T …

Answer 24

Is called the total deviation

Question 25

Each of the deviations from the grand mean have specific names
A2-T

Answer 25

Is called th between groups deviation

Question 26

Each of the deviations from the grand mean have specific names
AS25-À

Answer 26

Is called within subjects deviation

Question 27

The between groups deviation…

Answer 27

Ā2-T

Represents the effects of both error and treatment

Question 28

The within subjects deviation…

Answer 28

AS25- Ā

Represents the effect of error alone

Question 29

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

Answer 29

Differences among treatment means divided by difference among subjects treated alike

Then we have…

Experimental error + treatment effects divided by
Experimental error

Question 30

If the null hypothesis is true then

Answer 30

The treatment effect is equal to zero 
Experimental error + 0
Divided by 
Experimental error 
= 1

Question 31

If the null hypothesis is false then the

Answer 31

Treatment effect is greater than zero 
Experimental error + treatment effect 
Divided by 
Experimental error 
=Greater than 1