Lecture 7: Mixed design ANOVA Flashcards
What is mixed design? - (2)
A mixture of between-subject and within-subject
Several independent variables or predictors have been measured; some have been measured with different entities, (pps) whereas others used the same entities (pps)
You will need at least two IVs for
mixed design
What is decision tree for mixed design ANOVA? - (7)
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: Both
This leads us to and Factorial mixed ANOVA
Example of mixed design scenario for ANOVA - (2)
a mixed ANOVA is often used in studies where you have measured a dependent variable (e.g., “back pain” or “salary”) over two or more time points or when all subjects have undergone two or more conditions (i.e., where “time” or “conditions” are your “within-subjects” factor),
but also measure DV when your subjects have been assigned into two or more separate groups (e.g., based on some characteristic, such as subjects’ “gender” or “educational level”, or when they have undergone different interventions). These groups form your “between-subjects” factor.
In mixed design ANOVA, in SPSS we would use both
within-subject variables and between-suject variables
In mixed design, one way to think is having - (2)
a repeated measures design applied more than once to different groups of individuals.
All participants take part in all conditions, but participants can be divided by some other variable, either manipulated by the experimenter or that is a feature of the participants, e.g. male or female
An organizational psychologist is hired as a consultant by a person planning to open a coffee house for college students. The coffee house owner wants to know if her customers will drink more coffee depending on the ambience of the coffee house. To test this, the psychologist sets up three similar rooms, each with its own theme (Tropical; Old Library; or New York Café ) then arranges to have thirty students spend an afternoon in each room while being allowed to drink all the coffee they like. (The order in which they sit in the rooms is counterbalanced.) The amount each participant drinks is recorded for each of the three themes.
- Independent variable(s)
- Is there more than 1 IV?
- The levels the independent variable(s)
- Dependent variable
- Between (BS) or within-subjects (WS)?
- What type of design is being used?
Theme
No
Tropical, Old Library,
New York Café
Amount of coffee consumed
Within-subjects
1-way Repeated measures
A manager at a retail store in the mall wants to increase profit. The manager wants to see if the store’s layout (one main circular path vs. a grid system of paths) influences how much money is spent depending on whether there is a sale. The belief is that when there is a sale customers like a grid layout, while customers prefer a circular layout when there is no sale. Over two days the manager alternates the store layout, and has the same group of customers come each day. Based on random assignment, half of the customers told there is a sale (20 % will be taken off the final purchases), while the other half is told there is no sale. At the end of each day, the manager calculates the profit.
- Independent variable(s)
- Is there more than 1 IV?
- The levels the independent variable(s)
- Dependent variable
- Between (BS) or within-subjects (WS)?
- What type of design is being used?
Sale/ No Sale, Store’s layout
Yes
Sale-No Sale, Grid-Circular
Profit
BS (Sale) and WS (Layout)
2-way mixed Measures
A researcher at a drug treatment center wanted to determine the best combination of treatments that would lead to more substance free days. This researcher believed there were two key factors in helping drug addiction: type of treatment and type of counseling. The researcher was interested in either residential or outpatient treatment programs; and either cognitive-behavioral, psychodynamic, or client-centered counseling approaches. As new clients enrolled at the center they were randomly assigned to one of six experimental groups. After 3 months of treatment, each client’s symptoms were measured.
- Independent variable(s)
- Is there more than 1 IV?
- The levels the independent variable(s)
- Dependent variable
- Between (BS) or within-subjects (WS)?
- What type of design is being used?
Type of treatment, Type of counseling.
Yes
Residential or outpatient/ cognitive-behavioural, psychodynamic or client-centered.
Substance-free days
Between subjects
2-way independent measures ANOVA.
Assumptionsof mixed ANOVA - (3)
Normal Distribution
Independent and Repeated Factors
Homogeneity of Variance for the Independent factor
+
Sphericity for the Repeated factor
Assumptions of repeated-measures ANOVA -(3)
Normal Distribution
Repeated Measure Design (same participants)
Sphericity (Mauchly’s Test)
Assumptions of independent ANOVA - (3)
Normal Distribution
Independence of Scores
Homogeneity of Variance (Levene’s Test)
Leven’s test tests if the variances in independent groups are similar, would levene’s test be significant in this case?
Levene’s test would likely be significant as the variance between the two groups are quite different.
Sphereicity is an assumption of both
repeated and mixed models
In sphereicity variances of the differences between data taken from same partiicpant is
equal
Sphereciy applies when there are more than
Applies when there are more than 2 data points from each participant (3 or more levels in an IV)
Spherecity can be lacked with
Mauchly’s test in SPSS needs to be non significant p > 0.05
If p-value significant for checking for spherecity ten - (3)
If GG < 0.75 THEN USE GG
IF GG > 0.75 THEN USE HF
Since GG less than 0.75 report adjusted F, DF and sig which is F(1.24, 21.00) = 212.32 , p < 0.001
Homogenity of variance is
distribution of groups are similar?
Spherecity is asking are the disttibution of differences between groups are
similar
The researcher hypothesized that there would be an interaction between dog breed (Collie or German Shepherd) and week of obedience school training (all dogs measured at 1 week and 5 weeks) as they relate to the number of times the dog growls per week. Specifically, it was hypothesized that Collies would show no difference in growls between 1 week and 5 weeks, but German Shepherds would growl less at 5 weeks than at 1 week.
- Independent variable(s)
- Is there more than 1 IV?
- The levels the independent variable(s)
- Dependent variable
- Between(BS) or within-subjects (WS)?
- What type of design is being used?
- Dog breed and measurement time
- Yes
- Collie-German Shepard/Week 1-Week 5
- Number of growls
- Dog breed Between and measurement time is within
- 2-WAY mixed ANOVA
What does this 2-way mixed ANOVA show? - (3)
- Independent variable(s)
- Is there more than 1 IV?
- The levels the independent variable(s)
- Dependent variable
- Between(BS) or within-subjects (WS)?
- What type of design is being used?
1) is there an effect overall = Yes (green)
2) Is the effect bread = Yes (red)
3) Is there an interaction = Yes (blue)
The F-ratio tells us only whether the model fitted to the data accounts for more variation than extraneous factors, but it doesn’t tell us
where the differences between groups lie.
The F-ratio tells us only whether the model fitted to the data accounts for more variation than extraneous factors, but it doesn’t tell us where the differences between groups lie.
2 ways to do this
One way is to do post-hoc tests which we are now familiar with and the second is to do a contrast where we break down the variance accounted for by the model into component parts.
Partioning of variance of one way vs two way independent
Partioning of variance of repeated vs mixed
Rules of contrast coding - (5)
Rule 1: Groups coded with positive weights compared to groups coded with negative weights.
Rule 2: The sum of weights for a comparison should be zero.
Rule 3: For a given contrast, the weights assigned to the group(s) in one chunk of variation should be equal to the number of groups in the opposite chunk of variation.
Rule 4: If a group is not involved in a comparison, assign it a weight of zero
Rule 5: If a group is singled out in a comparison, then that group should not be used in any subsequent contrasts.
Contrast coding example SPSS how to read
When conducting a Repeated-Measures ANOVA, which of the following assumptions is NOT relevant?
A.Independent residuals
B.Homogeneity of variance
C.Sphericity
D.They are all relevant
B
One advantage of repeated measures designs over independent designs is that we are able to calculate a degree of error for each effect, whereas in an independent design we are able to calculate only one degree of error: true or false?
True or False
True
An experiment was done to look at the positive arousing effects of imagery on different people. A sample of statistics lecturers was compared against a group of students. Both groups received presentations of positive images (e.g., cats and bunnies), neutral images (e.g., duvets and light bulbs), and negative images (e.g., corpses and vivisection photographs). Positive arousal was measured physiologically (high values indicate positive arousal) both before and after each batch of images. The order in which participants saw the batches of positive, neutral and negative images was randomized to avoid order effects. It was hypothesized that positive images would increase positive arousal, negative images would reduce positive arousal and that neutral images would have no effect. Differences between the subject groups (lecturers and students) were also investigated. What technique should be used toanalysethese data?
A. Two-way mixed ANOVA
B.Three-way mixed ANOVA
C.Two-way mixed analysis of covariance
D.Three-way repeated-measures ANOVA
B
DV - positve arousing effects
IV: Group (student vs lexturor), Image (pos/neu/neg), arousal (before and after).
a 2 (Time: before and after)×2 (Group: students and lecturers)×3 (Image: positive, negative and neutral) mixed ANOVA with between subjects on the Group variable
An experiment was conducted to see how people with eating disorders differ in their need to exert control in different domains. Participants were classified as not having an eating disorder (control), as having anorexia nervosa (anorexic), or as having bulimia nervosa (bulimic). Each participant underwent an experiment that indicated how much they felt the need to exert control in three domains: eating, friendships and the physical world (this final category was a control domain in which the need to have control over things like gravity or the weather was assessed). So all participants gave three responses in the form of a mean reaction time; a low reaction time meant that the person did feel the need to exert control in that domain. The variables have been labelled as group (control, anorexic, or bulimic) and domain (food, friends, or physical laws). Of the following options, which analysis should be conducted?
A. Analysis of covariance
B. Two-way repeated measures ANOVA
C. Two-way mixed ANOVA
D. Three-way independent ANOVA
C
Two IVs = Group (Control, Anroexic, Bullimic) and Domain (Food, Friends, Physical Laws)
Group is between
Each partiicpant underwent domains so within
DV = Participannts measured
An experiment was done to compare the effect of having a conversation via a hands-free mobile phone, having a conversation with an in-car passenger, and no distraction (baseline) on driving accuracy. Twenty participants from two different age groups (18–25 years and 26–40 years) took part. All participants in both age groups took part in all three conditions of the experiment (in counterbalanced order), and their driving accuracy was measured by a layperson who remained unaware of the experimental hypothesis.
How do we interpret the main effect of distraction from the SPSS table (next slide)? - (2)
The assumption of sphericity has been met, indicated by Mauchly’s test (p > .05).
There was a significant main effect of distraction (F(2, 36) = 45.95, p < .001). This effect tells us that if we ignore the effect of age, driving accuracy was significantly different in at least two of the distraction groups.
Two-way repeated-measures ANOVA compares:
A. Several means when there are two independent variables, and the same entities have been used in all conditions
B. Two means when there are more than two independent variables, and the same entities have been used in all conditions.
C. Several means when there are two independent variables, and the same entities have been used in some of the conditions.
D. Several means when there are more than two independent variables, and some have been manipulated using the same entities and others have used different entities.
A
When conducting a repeated-measures ANOVA which of the following assumptions is not relevant?
A. Homogeneity of variance
B. Sphericity
C. Independent residuals
D. They are all relevant
A
The table shows hypothetical data from 3 conditions
For these data, spherecity will hold when
(Hint: Sphericity refers to the equality of variances of the differences between treatment levels.)
A.The variances of the differences between treatment levels are roughly equal
B. The variance of each condition is roughly equal
C. The variance of each condition is not equal
D. The variances of the differences between treatment levels are not equal
A
Imagine we were interested in the effect of supporters singing on the number of goals scored by soccer teams. We took 10 groups of supporters of 10 different soccer teams and asked them to attend three home games, one at which they were instructed to sing in support of their team (e.g., ‘Come on, you Reds!’), one at which they were instructed to sing negative songs towards the opposition (e.g., ‘You’re getting sacked in the morning!’) and one at which they were instructed to sit quietly. The order of chanting was counterbalanced across groups. Looking at the output below, which of the following sentences is correct?#
A.The results showed that the number of goals scored was significantly affected by the type of singing from the supporters, F(2, 18) = 11.24, p = .001.
B. The results showed that the number of goals scored was significantly affected by the type of singing from the supporters, F(1.58, 14.19) = 11.24, p = .002.
C. The results showed that the number of goals scored was significantly affected by the type of singing from the supporters, F(2, 12.4) = 11.24, p = .001.
D. The results showed that the number of goals scored was significantly higher when supporters sang positive songs towards their team than when they sat quietly, F(2, 18) = 11.24, p = .001.
A = Mauchly’s test was non-significant, so we can report the result in the row labelled ‘sphericity assumed’
Imagine we were interested in the effect of supporters singing on the number of goals scored by soccer teams. We took 10 groups of supporters of 10 different soccer teams and asked them to attend three home games, one at which they were instructed to sing in support of their team (e.g., ‘Come on, you Reds!’), one at which they were instructed to sing negative songs towards the opposition (e.g., ‘You’re getting sacked in the morning!’) and one at which they were instructed to sit quietly. The order of chanting was counterbalanced across groups. An ANOVA with a simple contrasts using the last category as a reference was conducted. Looking at the output tables below, which of the following sentences regarding the contrasts is correct?
a.The first contrast revealed that soccer teams scored significantly more goals when their supporters sang positive songs compared to when they did not sing. The second contrast revealed that soccer teams scored significantly fewer goals when their supporters sang negative songs compared to when they did not sing.
b. The first contrast revealed that soccer teams scored significantly fewer goals when their supporters did not sing compared to when they sang negative songs. The second contrast revealed that soccer teams scored a similar amount of goals when their supporters sang positive songs compared to when they did not sing.
c. The first contrast revealed that soccer teams scored significantly more goals when their supporters sang positive songs compared to when they did not sing. The second contrast revealed that soccer teams scored significantly fewer goals when their supporters sang negative songs compared to when they sang positive songs.
d. The first contrast revealed that soccer teams scored significantly more goals when their supporters sang positive songs compared to when they did not sing. The second contrast revealed that soccer teams did not significantly differ in the number of goals scored when their supporters sang negative songs compared to when they did not sing.
a = see from the means in the Descriptive Statistics table that positive singing resulted in the highest number of goals scored and negative singing resulted in the least number of goals score
An experiment was done to compare the effect of having a conversation via a hands-free mobile phone, having a conversation with an in-car passenger, and no distraction (baseline) on driving accuracy. Twenty participants from two different age groups (18–25 years and 26–40 years) took part. All participants in both age groups took part in all three conditions of the experiment (in counterbalanced order), and their driving accuracy was measured by a layperson who remained unaware of the experimental hypothesis.
Which of the following sentences is the correct interpretation of the main effect of distraction?
AThere was a significant main effect of distraction, F(2, 36) = 45.95, p < .001. This effect tells us that if we ignore the effect of age, driving accuracy was significantly different in at least two of the distraction groups.
B. There was no significant main effect of distraction, F(2, 36) = 45.95, p = .719. This effect tells us that if we ignore the effect of age, driving accuracy was the same for no distraction, hands-free conversation and in-car passenger conversation.
C. There was a significant main effect of distraction, F(2, 36) = 45.95, p < .001. This effect tells us that driving accuracy was different for no distraction, hands-free conversation and in-car passenger conversation in the two age groups.
D. There was no significant main effect of distraction, F(2, 36) = 45.95, p > .05. This effect tells us that none of the distraction groups significantly distracted participants across both age groups.
A = We can read the results in the row labelled ‘sphericity assumed’, as we can see from the output of Mauchly’s test that the assumption of sphericity has been met, p > .05. However, we would need to do some follow-up tests to investigate exactly where the differences between groups lie
Field and Lawson (2003) reported the effects of giving children aged 7–9 years positive, negative or no information about novel animals (Australian marsupials). This variable was called ‘Infotype’. The gender of the child was also examined. The outcome was the time taken for the children to put their hand in a box in which they believed either the positive, negative, or no information animal was housed (positive values = longer than average approach times, negative values = shorter than average approach times). Based on the output below, what could you conclude?
A. Approach times were significantly different for the boxes containing the different animals, but the pattern of results was unaffected by gender.
B. Approach times were significantly different for the boxes containing the different animals, and the pattern of results was affected by gender.
C. Approach times were not significantly different for the boxes containing the different animals, but the pattern of results was affected by gender.
D.Approach times were not significantly different for the boxes containing the different animals, but the pattern of results was unaffected by gender.
A
