Lecture 2 - Analysis of Variance (ANOVA)

Question 1

What is variability?

Answer 1

It is to do with the range/spread of data. Data can have the same mean but different variabilities, or the same variability but different averages

Question 2

What do parametric tests assume?

Answer 2

They assume a normal population distribution

Question 3

What is the normal distribution?

Answer 3

a mathematical function that defines the distribution of scores in a population. It does this with regard to two ‘population parameters’ - Mu/µ and Sigma/σ

Most (but not all) data is normally distributed

Question 4

What does Mu/µ represent?

Answer 4

the population mean

is involved in calculating the normal distribution

Question 5

What does Sigma/σ represent?

Answer 5

the population standard deviation (variance)

is involved in calculating the normal distribution

Question 6

What does this show in terms of a normal distribution?

Answer 6

The same µ (pop mean) but different σ (std. dev./variance)

Question 7

What does this show in terms of a normal distribution?

Answer 7

The same σ (pop std. dev /variance) but different µ (pop mean)

Question 8

What does this show in terms of a normal distribution?

Answer 8

A different σ (pop std dev) and the same µ (pop mean)

Question 9

What do variances look like when:

H0 is true

H1 is true

Answer 9

H0 is true - scores almost completely overlap

H1 is true - very little overlap between score distribution

Question 10

What are the two kinds of experimental error?

Answer 10

individual differences error

measurement error

these are the two main kinds, there are others but these are the main ones. In a real experiment, both would contribute to each subjects’ score

Question 11

Why do we look at experimental error?

Answer 11

It contributes to the differences found between treatment conditions

So we must try to find out how much of the difference can be attributed to experimental error

Question 12

What can tell us about experiemental error?

Answer 12

The variability of subjects in the same condition ought to tell us about experimental error

Question 13

What are treatment effects?

Answer 13

the systematic source of variability that comes from the different conditions of the IV used in each treatment grouo

Question 14

What does partitinoning the deviations mean?

Answer 14

Basically, finding out the standard deviations

Question 15

What does A1, A2, A3 etc mean?

Answer 15

the different treatment conditions

Question 16

Why are the mean and standard deviation sometimes referred to as models?

Answer 16

Because they are values not actually present in the data, but they are used to describe and represent the data that is present

Question 17

What does standard deviation look at?

Answer 17

How far away individual values are from the mean
. In this way it assesses how good the mean is as a model of the data

Question 18

How do we calculate the size of a deviation? (NOT STD DEV)

How and why do we use this to calculate the sum of squares?

Answer 18

We subtract the mean (called x with a line on top) from the observed values.

Deviances may be positive or negative so it can give silly total deviances when some of the individual deviances are positive and some are negative.

That’s why we create a squared error (we square the deviations) - adding all of these together forms the Sum of Squares

Question 19

What is variance?

How is it calculated?

Why do we use it?

Answer 19

Variance is the average error between the mean and the actual data value

It is the sum of squares divided by n (the number of samples)

We use it because lots of data gives us a higher sum of squares so it can be hard to compare a larger dataset with a smaller one.

Question 20

How do we calculate a standard deviation?

Why do we use it instead of variance?

Answer 20

It is the square root of the variance

We use this frequently because it is a more meaningful way to describe the data - variance is squared and you can’t have ‘3.2 words squared’!

Question 21

What is the grand mean?

Answer 21

the mean of several treatment conditions together

Question 22

What is a sample mean?

Answer 22

the mean of each treatment group alone

Question 23

What does the between groups deviation represent?

Answer 23

both error and treatment effects

Question 24

What does the within-subjects deviation represent?

Answer 24

error alone

Question 25

What are the 4 assumptions of a between-groups ANOVA?

Answer 25

interval or ratio level data

normal distribution

equal variances between groups

scores are independent