Lecture 6: Two way independent ANOVA

Question 1

What is the decision tree of choosing a two-way independent ANOVA? - (5)

Answer 1

Q: What sort of measurement? A: Continuous
Q:How many predictor variables? A: Two or more
Q: What type of predictor variable? A: Categorical
Q: How many levels of the categorical predictor? A: Not relevant
Q: Same or Different participants for each predictor level? A: Different

Question 2

Partial eta-squared should be reported for

Answer 2

ANOVA and ANCOVA

Question 3

How is partial-eta squared calculated?

Answer 3

SS effect/ SS effect + SS error

Question 4

What is the two drawbacks of eta-squared?

Answer 4

as you add more variables to the model, the proportion explained by any one variable will automatically decrease.

Question 5

How is eta-squared calculated?

Answer 5

Sum of squares between (squares of effect M) divided by sum of squared total (squares of everything - effects, errors and interactions)

Question 6

In one-way ANOVA eta-squared and partial-eta squared will be eequal but not true in models with

Answer 6

more than one IV

Question 7

Two-way Independent ANOVA is also called an

Answer 7

Independent Factorial ANOVA

Question 8

What is a factorial design?

Answer 8

When experiment has two or more IVs

Question 9

What are the 3 types of factorial design? - (3)

Answer 9

1. Independent factorial design
2. Repeated-measures (related) factorial design
3. Mixed design

Question 10

What is independent factorial design?

Answer 10

• There is many IVs or predictors that each have been measured using different pps (between grps)

Question 11

What is repeated-measures (related) factorial design?

Answer 11

• Many IVs or predictors have been measured but same pps used in all conditions

Question 12

What is mixed design?

Answer 12

• Many IVs or predictors have been measured; some measured with diff pps whereas others used same pps

Question 13

Which design does independent factorial ANOVA use?

Answer 13

Independent factorial design

Question 14

What is factorial ANOVA?

Answer 14

When we use ANOVA to analyse a situation in which there is two or more IVs

Question 15

What is difference between one way and two way ANOVA?

Answer 15

A one-way ANOVA has one independent variable, while a two-way ANOVA has two.

Question 16

Example of two-way independent factorial ANOVA

The study tested the prediction that subjective perceptions of physical attractiveness become inaccurate after drinking alcohol which is IV, DVs

• What are the IVs, DVs- (3)

Answer 16

IV = Alcohol - 3 levels = Placebo, Low dose, High dose
Iv = face type 2 levels = unattractive, attractive
DV = Physical attractiveness score

Question 17

Two way independent ANOVA can be fit into the idea of

Answer 17

linear model

Question 18

The study tested the prediction that subjective perceptions of physical attractiveness become inaccurate after drinking alcohol which is IV, DVs (example of two-way ANOVA)

IV = Alcohol - 3 levels = Placebo, Low dose, High dose
Iv = face type 2 levels = unattractive, attractive
DV = Physical attractiveness score

Fit this into a linear model

Answer 18

Question 19

The study tested the prediction that subjective perceptions of physical attractiveness become inaccurate after drinking alcohol

IV = Alcohol - 3 levels = Placebo, Low dose, High dose
Iv = face type 2 levels = unattractive, attractive
DV = Physical attractiveness score

Create a linear model for this two-way ANVOA scenario which adds interaction term and explain why is it important - (3)

Answer 19

• The first equation models the two predictors in a way that allows them to account for variance in the outcome separately, much like a multiple regression model
• The second equation adds a term that models how the two predictor variables interact with each other to account for variance in the outcome that neither predictor can account for alone.
• The interaction is important to us because it tests our hypothesis that alcohol will have a stronger effect on the ratings of unattractive than attractive faces

Question 20

The study tested the prediction that subjective perceptions of physical attractiveness become inaccurate after drinking alcohol ,

IV = Alcohol - 3 levels = Placebo, Low dose, High dose
Iv = face type 2 levels = unattractive, attractive
DV = Physical attractiveness score

What is shown in the interaction table? - (2)

Answer 20

Coding 0 or 1 for categorical variables of type of face and alcohol

interaction codes is zero for all conditions other than the one when both predictors are ‘present’.

Question 21

The study tested the prediction that subjective perceptions of physical attractiveness become inaccurate after drinking alcohol

IV = Alcohol - 3 levels = Placebo, Low dose, High dose
Iv = face type 2 levels = unattractive, attractive
DV = Physical attractiveness score

What does b3 (interaction coefficient ) in this two-way ANOVA situation represent? - (3)

Answer 21

measures how the effect of face type (on face ratings) depends on the dose of alcohol

If b3 is large in size, either positive or negative, we will now that alcohol dose has a large effect on the ratings of different face types.

If, however, the interaction coefficient is small, we would know that difference in ratings of attractiveness resulting from different face types would not depend on the alcohol dose.

Question 22

The study tested the prediction that subjective perceptions of physical attractiveness become inaccurate after drinking alcohol which is IV, DVs

IV = Alcohol - 3 levels = Placebo, Low dose, High dose
Iv = face type 2 levels = unattractive, attractive
DV = Physical attractiveness score

What does these graph show? - (2)

Answer 22

• First graph shows that unattractive faces have a higher attractiveness rating under high dose of alcohol compared to control and attractiveness rating does not differ too much but slightly decline in high dose for attractive faces = interaction term will be large
• Second graph shows difference in rating attract and unattractive faces does not differ between placebo and high dose = interaction effect is small

Question 23

How do we know coefficients in model are significant in two-way ANCOVA?

Answer 23

We follow the same routine , similar to one-way ANOVA, to compute sums of squares for each factor of the model (and their interaction) and compare them to the residual sum of squares, which measures what the model cannot explain

Question 24

How is two-way independent ANOVA similar to one-way ANOVA?

Answer 24

, we still find the total sum of squared errors (SST) and break this variance down into variance that can be explained by the experiment (SSM) and variance that cannot be explained (SSR).

Question 25

How is two-way INDEPENDENT ANOVA different to one-way INDEPENDENT ANOVA? - (3)

Answer 25

in two-way ANOVA, the variance explained by the experiment is made up of not one experimental manipulation but two.

Therefore, we break the model sum of squares down
into variance explained by the first independent variable (SSA), variance explained by the second independent variable (SSB) and variance explained by the interaction of these two
variables (SSA × B)

Question 26

How to calculate total sum of squares SST in two-way independent ANOVA?

Answer 26

Question 27

What is SST DF in two-way independent ANOVA?

Answer 27

N- 1

Question 28

How to compute model sum of squares SSM in two-way independent ANOVA? - (2)

Answer 28

sum of all grps (pairing each level of IV with another)

n = number of scores in each grp which is multipled by the mean value of each group subtracted by grand mean of all pps regardless of grp squared

Question 29

How to compute degrees of freedom of SSM in two-way independent ANOVA?

Answer 29

(g-1)

Question 30

How many groups are there in this research two-way independent ANOVA?

IV = Alcohol - 3 levels = Placebo, Low dose, High dose
Iv = face type 2 levels = unattractive, attractive
DV = Physical attractiveness score

Answer 30

placebo + attractiveness
placebo + untractiveness
low dose +attractiveness
low dose + unattractiveness
high dose +attractiveness
high dose +unattractiveness - 6 grps

Question 31

How is SSA (face type) computed in two-way independent ANOVA?

IV = Alcohol - 3 levels = Placebo, Low dose, High dose
Iv = face type 2 levels = unattractive, attractive
DV = Physical attractiveness score - (2)

Answer 31

considering only two groups at a time and add together - for first IV variable (SSA) (e.g., grps of pps rated attractive and grp of pps that rated unattractive)

number of pps in that grp multiplied by mean of grp subtracted by grand mean overall of all pps squared

Question 32

What is the degrees of freedom in SSA in TWO-WAY INDEPENDENT ANOVA?

Answer 32

DF = (g-1) so if male and female then 2 -1 = 1

Question 33

How to compute SSB in two-way independent ANOVA for alcohol type

IV = Alcohol - 3 levels = Placebo, Low dose, High dose
Iv = face type 2 levels = unattractive, attractive
DV = Physical attractiveness score - (2) - (3)

Answer 33

same formula as SSA but for the second IV

added for all grps of pps in second IV

number of pps in one grp of secondIV(mean score of that grp subtract by grand mean of all pps regardless of grp) squared

Question 34

Example of calculating SSB/SSA

Answer 34

Question 35

What is DF for SSB in two-way independent ANOVA?

Answer 35

number of grps in second IV minus 1

Question 36

SS A X B in two-way independent ANOVA is calculating how much variance is explaiend

Answer 36

by the interaction of 2 variables

Question 37

How is SS A X B (interaction term) calculated in two-way ANOVA?

Answer 37

SS A X B = SSM - SSA - SSB

Question 38

How is SS A X B’S DF calculated in two-way independent ANOVA?

Answer 38

df A X B = df M - df A - df B

Question 39

The SSR in two-way independent ANOVA, is similar to one-way ANOVA as it represents the

Answer 39

individual differences in performance or the variance that can’t be explained by factors that were systematically manipulated.

Question 40

How to calculate SSR in two-way independent ANOVA?

Answer 40

• use individual variances of each grp (e.g., attractiveness face type + placebo) and multiply by one less than number of people within the group (n - in this case 6) and do it for each group and add it together

Question 41

How to calculate SSR in two-way independent ANOVA?

Answer 41

number of grps you have in study(number of scores you have per group minus 1)

Question 42

Each effect in two-way ANOVA (two main effect and interaction) has its own F-ratio and to calculate it we first need to calculate

Answer 42

the mean squares for each effect by taking sum of squares and dividng by respective DF

Question 43

Diagram of calculating mean sums of squares in two-way ANOVA independent

Answer 43

Question 44

Diagram of calculating F ratios for two independent and interaction

Answer 44

Question 45

Each F-ratios for each IV and interaction can be compared against critical value (based on its DF) and tell us

Answer 45

whether these effects are likely to
reflect data that have arisen by chance, or reflect an effect of our experimental manipulations

Question 46

Each of these F-ratios can be compared against critical values (based on their degrees of
freedom,

If observed F exceeds critical value then

Answer 46

it is significant

Question 47

What effect sizes can we calculate with two-way independent ANOVA? - (2)

Answer 47

• Partial eta-squared
• Omega-squared if advised

Question 48

What to do whe assumptions are violated in factorial independent ANOVA? - (3)

Answer 48

• There is not a simple non-parametric counterpart of factorial ANOVA
• If assumption of normality is violated then use robust methods described in Wilcox’s and files in R
• If assumptions of homogenity of variance then implement corrections based on Welch procedure

Question 49

Example of a research scenario of two-way independent ANCOVA

Pick out IVs and DVs - (4)

Answer 49

• Independent samples design
• Two Ivs, both 2 conditions: drug type (A, B) and onset (early, late)
• One DV is cognitive performance
• Two way ANOVA

Question 50

What does this two-way ANOVA independent design SPSS output show?

Answer 50

• The levene’s test is not significant so assume equal variances

Question 51

What happens if Levene’s test is significant in two-way independent ANOVA?

Answer 51

steps taken to equalise variances through data transformation

Question 52

What does this two-way independent ANOVA table show - (4)

Answer 52

• Drug : F(1,24) = 5.58, p = 0.027, partial eta-squared = 0.19 (large effect + sig effect)
• Onset: F(1,24) = 14.43, p = 0.001, partial eta-squared = 0.38 (large effect + sig effect)
• Interaction Drug * Onset: F(1,24) = 9.40, p = 0.005, partial eta-squared = 0.28 (large effect + sig effect)
• We got two sig main effects and sig interaction effect which are all quite large effect sizes

Question 53

What does this SPSS output show for two-way independent ANOVA? - (3)

Answer 53

drug B has higher score on cognitive test than A and is sig main effect (CI does not contain 0 and also main effect analysis)

early onset scoring higher on average than late onset (CI does not contain 0 and also main effect analysis)

Important of these main effect as main effects ignoring the effec tof other IV so results for drug at top is regardless of whether late/onset for example , does not tell anything for interaction

Question 54

What does this interaction plot show TWO WAY ANOVA? - (6)

Answer 54

• Blue line is early onset
• Green line is late onset
• For late onset, drug B lead to higher mean scores on test than drug A
• For early onset, drug A led to slightly higher mean scores than drug B
• Drug A more effective then drug b for early onset but different marginal
• Drug B was substantially more effective than Drug A for late

Question 55

Non-parallel lines in interaction plot indicate an

Answer 55

sig interaction effect

Question 56

We can follow interactions in two-way ANOVA with simple effects analysis which - (2)

Answer 56

• looks at the effect of one IV at individuals levels of other IV
• Seeing whether differences margina/substantial is sig

Question 57

The SSM in two-way independent ANOVA is broken down into three components:

Answer 57

variance explained by the first independent
variable (SSA), variance explained by the second independent variable (SSB ) and variance explained by the interaction of these two variables (SSA × B
).

Question 60

Example of difference of one-way ANOVA vs two-way ANOVA (independent) - (2)

Answer 60

• One-way ANOVA have one IV categorical variable (level of educaiton - college degree, grad degree, high school)
• Two-way ANOVA , you have 2 categorical IV variables - level of education (college degree, grad degree, high school) and zodaic sign (libra, pisces)

Question 62

In two-way independent ANOVA, you need how many DV and IV?

Answer 62

1 DV and 2 or more categorical predictors

Question 63

What test is used for this scenario?

A psychologist wanted to test a new type of drug treatment for ADHD called RitaloutTM. The makers of this drug claimed that it improved concentration without the side effects of the current leading brand of ADHD medication.

To test this, the psychologist allocated children with ADHD to two experimental groups, one group took RitaloutTM(New drug), the other took the current leading brand of medication (Old drug) (Variable = Drug).

To test the drugs’ effectiveness, concentration was measured using the Parker-Stone Concentration Scale, which ranges from 0 (low concentration) to 12 (high concentration) (Variable = Concentration).

In addition, the psychologist was interested in whether the effectiveness of the drug would be affected by whether children had ‘inattentive type’ ADHD or ‘hyperactive type’ ADHD (Variable = ADHD subtype).

Answer 63

Two-way independent ANOVA

Question 64

A researcher was interested in measuring the effect of 3 different anxiety medications on patients diagnosed with anxiety disorder. They measured anxiety levels before and after treatment of 3 different treatment groups plus a control group. The researchers also collected data on depression levels.

Identify the IV, DV, and covariates! - and design (3)

Answer 64

IV = 3 different types anxiety medications and control grp
DV: Anxiety levels after treatment of grps
Covariate = anxiety before treatment, depression levels

ANCOVA

Question 65

Researchers wanted to see how much people of different education levels are interested in politics. They also believed that there might be an effect of gender. They measured political interest with a questionnaire in males and females that had either school, college or university education.

Identify the IVs and DV and design - (3)

Answer 65

• IV: Level of education - school, college or uni edu and gender (m, f)
• DV: Political interest in questionnaire
• Two-way independent ANOVA

Question 66

An experiment was done to look at whether there is an effect of both gender and the number of hours spent practising a musical instrument on the level of musical ability.
A sample of 30 participants (15 men and 15 women) who had never learnt to play a musical instrument before were recruited. Participants were randomly allocated to one of three groups that varied in the number of hours they would spend practising every day for 1 year (0 hours, 1 hours, 2 hours). Men and women were divided equally across groups.
All participants had a one-hour lesson each week over the course of the year, after which their level of musical skill was measured on a 10-point scale ranging from 0 (you can’t play for toffee) to 10 (‘Are you Mozart reincarnated?’).

Identify IVs and DV and design - (3)

Answer 66

• IV: Gender (m,f) , number of hrs spent practicisng
• DV: Level of muscial skill after a year
• Two-way independent ANOVA, not t-tests since more than one IV

Question 67

Whic graphs show an interaction effect?
A or B?\

Answer 67

B

Question 68

In these outputs is there a effect of gender, education or interaction level TWO WAY ANOVA INDEPENDENT

Answer 68

• Is there an effect of gender overall?
  No, F(1,54) = 1.63, p = .207
  Is there an effect of education level?
  Yes, F(2,54) = 147.52, p < .001
  Is there an interaction effect?
  Yes, F(2,54) = 4.64, p = .014

Question 69

How to interpret these findings?

Answer 69

• Main effect of Aspirin: Aspirin reduces heart attackes compard to placebo (1)
• Main effect of carotene: Beta carotene reduces heart attack (2)
• Interaction effect: Yes, bigger effect when aspirin and beta carotene taken together (3) - also lines drawn more its an interaction

Question 70

WHICH STATEMENT BEST DESCRIBES A COVARIATE?

A variable that is not able to be measured directly.

A variable that shares some of the variance of another variable in which the researcher is interested.

A pair of variables that share exactly the same amount of variance of another variable in which the researcher is interested.

A variable that correlates highly with the dependent variable.

Answer 70

A variable that shares some of the variance of another variable in which the researcher is interested.

Question 71

TWO-WAY ANOVA IS BASICALLY THE SAME AS ONE-WAY ANOVA, EXCEPT THAT:

The model sum of squares is partitioned into two parts

The residual sum of squares represents individual differences in performance

The model sum of squares is partitioned into three parts

We calculate the model sum of squares by looking at the difference between each group mean and the overall mean

Answer 71

C. The model sum of squares is partitioned into three parts

The model sum of squares is partitioned into the effect of each of the independent variables and the effect of how these variables interact (see Section 13.2.7)

D is also true, but we also do this for both one-way and two-way ANOVA (see Section 13.2.7).

Question 72

IF WE WERE TO RUN A FOUR-WAY BETWEEN-GROUPS ANOVA, HOW MANY SOURCES OF VARIANCE WOULD THERE BE?

4
16
12
15

Answer 72

16 because 4*4 = 16 (if it was 3x2 then would be 6)

Question 73

Which of the following sentences best describes a covariate?

A. A variable that shares some of the variance of another variable in which the researcher is interested.

B. A variable that correlates highly with the dependent variable

C. A variable that is not able to be measured directly

D. A pair of variables that share exactly the same amount of variance of another variable in which the researcher is interested

Answer 73

A

Question 75

An experiment was done to look at whether there is an effect of both gender and the number of hours spent practising a musical instrument on the level of musical ability.
A sample of 30 participants (15 men and 15 women) who had never learnt to play a musical instrument before were recruited. Participants were randomly allocated to one of three groups that varied in the number of hours they would spend practising every day for 1 year (0 hours, 1 hours, 2 hours). Men and women were divided equally across groups.
All participants had a one-hour lesson each week over the course of the year, after which their level of musical skill was measured on a 10-point scale ranging from 0 (you can’t play for toffee) to 10 (‘Are you Mozart reincarnated?’).

A. Two-way independent ANOVA

B. Two-way repeated ANOVA

C. Three way ANOVA = only 2 IVs so no

D. T-test

Answer 75

A

Question 76

Which of the designs below would be best suited to ANCOVA?

A. Participants were randomly allocated to one of twostress management therapy groups, or a waiting listcontrol group. Their baseline levels of stress weremeasured before treatment, and again after 3months of weekly therapy sessions

B. Participants were randomly allocated to one of twostress management therapy groups, or a waiting listcontrol group. Their levels of stress were measuredand compared after 3 months of weekly therapysessions.

C. Participants were randomly allocated to one of twostress management therapy groups, or a waiting listcontrol group. The researcher was interested in therelationship between the therapist’s ratings ofimprovement and stress levels over a 3-monthtreatment period.

D. Participants were allocated to one of two stressmanagement therapy groups, or a waiting listcontrol group based on their baseline levels ofstress. The researcher was interested ininvestigating whether stress after the therapy wassuccessful partialling out their baseline anxiety

Answer 76

A - baseline levels of stress used as covariate

. We can use the baseline, pre-treatment measures as a control when looking at the impact the treatment has on the 3-month assessment.

Question 77

A music teacher had noticed that some students went to pieces during exams. He wanted to testwhether this performance anxiety was different for people playing different instruments. He tookgroups of guitarists, drummers and pianists (variable = ‘Instru’) and measured their anxiety(variable = ‘Anxiety’) during the exam. He also noted the type of exam they were performing (inthe UK, musical instrument exams are known as ‘grades’ and range from 1 to 8). He wanted tosee whether the type of instrument played affected performance anxiety when accounting for thegrade of the exam. Which of the following statements best reflects what the effect of ‘Instru’ in theoutput table below tells us?

(Hint: ANCOVA looks at the relationship between an independent and dependent variable, takinginto account the effect of a covariate.

A. The type of instrument played in the exam had asignificant effect on the level of anxietyexperienced, even after the effect of the grade ofthe exam had been accounted for

B. The type of instrument played in the exam had asignificant effect on the level of anxietyexperienced

C. The type of instrument played in the exam did nothave a significant effect on the level of anxietyexperienced

Answer 77

A

Question 79

Question 5A psychologist was interested in the effects of different fear information on children’s beliefs aboutan animal. Three groups of children were shown a picture of an animal that they had never seenbefore (a quoll). Then one group was told a negative story (in which the quoll is described as avicious, disease-ridden bundle of nastiness that eats children’s brains), one group a positive story(in which the quoll is described as a harmless, docile creature who likes nothing more than to bestroked), and a final group weren’t told a story at all. After the story children rated how scared theywould be if they met a quoll, on a scale ranging from 1 (not at all scared) to 5 (very scaredindeed). To account for the natural anxiousness of each child, a questionnaire measure of traitanxiety was given to the children and used in the analysis. The SPSS output is below.

Whatanalysis has been used?

(Hint: The analysis is looking at the effects of fear information on children’s beliefs about an animal, taking into account children’s natural fear levels.)

A. ANCOVA

B. Independent analysis of variance

C. Repeated measures analysis of variance

Answer 79

A

Question 81

Imagine we wanted to investigate the effects of three different conflict styles (avoiding, compromising and competing) on relationship satisfaction, but we discover that relationship satisfaction is known to covary with self-esteem. Which of the following questions would be appropriate for this analysis?

A. What would the mean relationship satisfaction be for the three conflict style groups, if their levels of self-esteem were held constant?

B. What would the mean relationship satisfaction be if levels of self-esteem were held constant?

C. What would the mean self-esteem score be for the three groups if their levels of relationship satisfaction were held constant?

D. Does relationship satisfaction have a significant effect on the relationship between conflict style and self-esteem?

Answer 81

A

Question 82

A study was conducted to look at whether caffeine improves productivity at work in different conditions. There were two independent variables. The first independent variable was email, which had two levels: ‘email access’ and ‘no email access’. The second independent variable was caffeine, which also had two levels: ‘caffeinated drink’ and ‘decaffeinated drink’. Different participants took part in each condition. Productivity was recorded at the end of the day on a scale of 0 (I may as well have stayed in bed) to 20 (wow! I got enough work done today to last all year). Looking at the group means in the table below, which of the following statements best describes the data?

A. A significant interaction effect is likely to be present between caffeine consumption and email access.

B. There is likely to be a significant main effect of caffeine.

C. The effect of email is relatively unaffected by whether the drink was caffeinated.

D. The effect of caffeine is about the same regardless of whether the person had email access.

Answer 82

A = for decaffeinated drinks there is little difference between email and no email, but for caffeinated drinks there is

Question 83

What are the two main reasons for including covariates in ANOVA?

A. 1. To reduce within-group error variance
2. Elimination of confounds

B. 1. To increase within-group error variance
2. To reduce between-group error variance

C. 1. To increase within-group error variance
2. To correct the means for the covariate

D. 1. To increase between-group variance
2. To reduce within-group error variance

Answer 83

A

Question 84

A psychologist was interested in the effects of different fear information on children’s beliefs about an animal. Three groups of children were shown a picture of an animal that they had never seen before (a quoll). Then one group was told a negative story (in which the quoll is described as a vicious, disease-ridden bundle of nastiness that eats children’s brains), one group a positive story (in which the quoll is described as a harmless, docile creature who likes nothing more than to be stroked), and a final group weren’t told a story at all. After the story children rated how scared they would be if they met a quoll, on a scale ranging from 1 (not at all scared) to 5 (very scared indeed). To account for the natural anxiousness of each child, a questionnaire measure of trait anxiety was given to the children and used in the analysis. Which of the following statements best reflects what the ‘pairwise comparisons’ tell us?

A. Fear beliefs were significantly higher after negative information compared to positive information and no information, and fear beliefs were not significantly different after positive information compared to no information.

B. Fear beliefs were significantly lower after positive information compared to negative information and no information; fear beliefs were not significantly different after negative information compared to no information.

C. Fear beliefs were significantly higher after negative information compared to positive information; fear beliefs were significantly lower after positive information compared to no information.

D. Fear beliefs were all about the same after different types of information.

Answer 84

A

Question 85

a musical instrument and gender on the level of musical ability. A sample of 30 (15 men and 15 women) participants who had never learnt to play a musical instrument before were recruited. Participants were randomly allocated to one of three groups that varied in the number of hours they would spend practising every day for 1 year (0 hours, 1 hours, 2 hours). Men and women were divided equally across groups. All participants had a one-hour lesson each week over the course of the year, after which their level of musical skill was measured on a 10-point scale ranging from 0 (you can’t play for toffee) to 10 (‘Are you Mozart reincarnated?’). An ANOVA was conducted on the data from the experiment. Which of the following sentences best describes the pattern of results shown in the graph?

A. The graph shows that the relationship between musical skill and time spent practising was different for men and women.

B. The graph shows that the relationship between musical skill and time spent practising was the same for men and women.

C. The graph indicates that men and women were most musically skilled when they practised for 2 hours per day.

D. Women were more musically skilled than men.

Answer 85

A