PSYC 210- Factorial ANOVA
In a 2-way analysis of variance, when we say we have an INTERACTION, we mean that: A. The effect of one independent variable on a dependent variable differs as a function of a second independent variable B. The means for the levels of Factor A after collapsing over Factor B are significantly different from one another C. The effect of one independent variables on a dependent variable is significant, regardless of the second independent variable D. The main source of variance in our experiment is produced by Factors A and B
A. The effect of one independent variable on a dependent variable differs as a function of a second independent variable
When we run a 2-way between-subjects factorial analysis of variance, we are partitioning the ___________ into three meaningful parts. A. between groups variance B. within groups variance C. interaction variance D. total variance
A. between groups variance explanation: interaction, main effect 1, main effect 2
Factorial ANOVA
An Analysis of Variance used when there are two or more independent variables. When there are two, the ANOVA is called a Two-Way ANOVA, three independent variables would use a Three-Way ANOVA, etc. (Def. from allpsych.com)
In a simple analysis of variance (non-factorial), which of the following statements is NOT true? A. SStotal = SSbetween groups + SSwithin groups B. DFbetween = number of groups - number of people per group C. MSbetween groups = MSwithin groups when the null hypothesis is true (approximately) D. all are true
B. DFbetween = number of groups - number of people per group
Why do we subtract out the sum of squares of our main effects from our interaction sum of squares? Because we want to see whether the interaction sum of squares tells us more than the sum of squares of the main effects alone Because the sum of squares of each main effect is accounted for twice in the interaction equation Because the interaction term has nothing to do with the main effects
Because we want to see whether the interaction sum of squares tells us more than the sum of squares of the main effects alone Explanation We only care about the interaction term if it tells us more than we could have learned from the main effects. So, we subtract out the main effects sum of squares to get a sense of how much remaining deviation exists from the interaction!
Need Sum of squares for each predictor
Between groups of variable a Temperature variable → means hot and cold Between groups of variable b Food type variable → Ice cream and pancake Between groups that comprise of interaction AB Hot ice cream, hot pancake, cold ice cream, cold pancake
Which of the following study scenarios would be best tested using a factorial ANOVA? A. A researcher wants to test if happiness levels differ between single and married people B. A researcher wants to test what the strongest predictor of happiness is C. A researcher wants to test if there are differences in happiness level as a function of gender (male, female, non-binary) and marital status (married, single) D. A researcher wants to test if happiness level differs as a function of gender (male, female, non-binary)
C. A researcher wants to test if there are differences in happiness level as a function of gender (male, female, non-binary) and marital status (married, single)
What is a benefit of using an ANOVA test (over other tests)? A. It tells us which groups are different from others B. It gives a sense of how continuous variables are related to each other C. It is an omnibus test so it does not inflate Type I error D. It allows us to compare non-normally distributed data
C. It is an omnibus test so it does not inflate Type I error
Which of the following would require a repeated-measures (within-subjects) ANOVA? A. We want to see whether participants who identify as Democratic vs. Republican and are over 50 vs. under 50 years old have differing opinions on enjoyment of IPA beer. B. We want to see effects of different types of therapy on PTSD symptoms. Some participants get CBT, others get DBT, a third get exposure therapy C. Participants are tested on how well they can draw by only looking at a mirror before completing a coordination task in front of a mirror and after the task is over. We also get a third mirror drawing from them a week later. We are interested in the changes to their mirror drawing speed before the task, immediately after the task, and a week later. D. We want to see if participants are quickest to respond to a flash on the screen if they are getting money for responding quickly or getting no incentive. All participants do both manipulations.
C. Participants are tested on how well they can draw by only looking at a mirror before completing a coordination task in front of a mirror and after the task is over. We also get a third mirror drawing from them a week later. We are interested in the changes to their mirror drawing speed before the task, immediately after the task, and a week later.
Which of the following study scenarios would be best tested using a one-way ANOVA? A. A researcher wants to examine for differences in happiness level between males and females B. A researcher wants to predict happiness level as a function of age, political ideology, and education level C. A researcher wants to examine mortality rates as a function of happiness level D. A researcher wants to examine for differences in happiness level in Fall, Winter, Spring and Summer
D. A researcher wants to examine for differences in happiness level in Fall, Winter, Spring and Summer explanation option A is comparing gender and happiness level (2 way) option b is predicting happiness as a function of age.... (correlation and regression) option c is looking at happiness and mortality rates (2 way)
What does the F-ratio tell us, in simple language? A. Out of two variables, which one is affecting the outcome more significantly B. Where on the normal distribution the difference between two means falls C. How many standard deviations from the mean your sample is D. How large the differences between groups are when you take into account the differences within individual groups
D. How large the differences between groups are when you take into account the differences within individual groups
In a 2-way analysis of variance, when we say we have a MAIN EFFECT, we mean that: A. The main source of variance in our experiment is produced by Factors A and B B. The effect of one independent variable on a dependent variable differs as a function of a second independent variable C. The effect of one independent variables on a dependent variable is significant, taking into account the second independent variable D. The means for the levels of Factor A after collapsing over Factor B are significantly different from one another
D. The means for the levels of Factor A after collapsing over Factor B are significantly different from one another
Pairwise comparisons, made after finding that F is significant, that are used to determine which pairs of means are significantly different are known as: A. effect size measures B. planned contrasts C. omnibuses D. post hoc tests
D. post hoc tests
factorial f-ratio
F-ratio = between group divided by within group variance
partial eta squared
How much that variable alone is contributing to the model/ if all other effects were 0 how much would this alone affect our outcome variable? Key difference- sum of squares of effect divided by sum of sq the effect + residuals/SS within (not the total sum of sqs) Don't add up to 1 (may go over) Ex. 84.1% drugs alone is contributing to the mood change Effect Sizes Together
factorial anova hypothesis
Hypothesis Null mean are the same (main effect)/ mean are the same (interactions) Alt. the means are not all the same (interactions)
main effect
In a factorial design, the overall effect of one independent variable on the dependent variable, averaging over the levels of the other independent variable. observed effects of each factor by themselves Each factor will be associated with a certain amount of variance in scores, not taking into account the other factor(s) An effect called main effect only if it is significant (there is no observed effect) Ex. main effect for food temp → do ppl like hot food more than cold? Main effect food item → do ppl like ice cream more than pancakes?
What type of factorial ANOVA is the following example: I want to look at how people make decisions about what car to buy. I plan to do a 2x2 factorial design, where people are selecting between color (red vs. blue cars) and type (hybrid vs. electric cars). I ask 20 people to rate how likely they are to buy a red hybrid car vs. a red electric car. I get another 20 people to rate how they feel about a blue hybrid car vs. a blue electric car. Between subjects Within subjects Mixed design Not enough information
Mixed design Explanation Because I have separate groups looking at each color of car, that is a between-subjects variable. However, I have the same groups of people looking across type of car (hybrid and electric) so this is within-subjects. Thus, my overall design is a mixed design.
Within subjects ANOVAs
Referred to repeated measures ANOVAs Sample subject is doing multiple tests or measures Main diff is how we handle the within group variance in the F statistic Look at sum of squared deviations within each group and within each subject, and then account of the latter
Two-way ANOVA model
Sum of sq total = SS variable a + SS variable b + SS (variable a and b) + SS within SS (a and b) = SS between - SS (a) - SS (b)
One-way ANOVA model
Sum of sq total = sum of sq between + sum of sq within SS total = SS between + SS within
I test pen type (ball point vs. ink) and pen color (blue and yellow) on legibility of writing. After conducting my factorial ANOVA, I find that there is an interaction between pen type and pen color! Which of the following options gives us an explanation of an interaction effect (instead of a main effect)? Yellow ball point pens and yellow ink pens are harder to read than blue pens of each type. Yellow ink pens are much easier to read than yellow ball point pens, but blue pens of each type are pretty much the same as each other. Ball point pens are easier to read than ink pens. Blue ball point pens are easiest to read.
Yellow ink pens are much easier to read than yellow ball point pens, but blue pens of each type are pretty much the same as each other. Explanation This is tricky one! Answers 1 and 3 are examples of main effects. The first says that yellow pens are worse than blue pens, the third says that ball points are better than ink pens. The final option is automatically true if the other two things are true, and it gives us no information about how these two variables relate to one another. The second answer, though, tells us about some differences in how ink and pen type interact with each other. Try graphing these out to see what they look like!
I am helping a friend with their ANOVA homework and I've noticed they have added together the partial eta squared values to get a sense of the fit of the model? What should I tell them: This looks correct, nice job! This will give us an approximate R-squared value You should use the p-values instead - adding them together gives us a sense of the overall model fit You should use the eta squared values instead of the partial eta squared values, since the eta squared values squared values account for the total model You don't want to add them all together but find the range of the largest and smallest partial eta squared values
You should use the eta squared values instead of the partial eta squared values, since the eta squared values squared values account for the total model Explanation The partial eta squares only look at the contributions of each individual effect on the model as if no other effect existed. Thus, they will not give you a sense of the model fit. Adding together the pure eta squared values will tell you how much that effect contributes to the total model, so adding them will give us a model fit.
Adv and Disadv of Between subject and Within subject factorial
between -sbuject one group answers all questions/ does al ltests Could be bias Less ppl Within subject- 5 ppl for this, 5ppl for that Requires much more ppl Less bias
what's the simplest versions of factorial anova?
between subject, 2 levels ex. people's ratings of food type if food is hot or cold food item and food temp
Which of these scenarios is a good candidate for a factorial ANOVA? a. We want to see if age and height affect weight b. We want to see if amount of light affects how high plants grow c. We want to see whether type of mattress and type of pillow influence quality of sleep d. We want to see if chapstick sales are affected by flavor of chapstick
c. We want to see whether type of mattress and type of pillow influence quality of sleep Explanation The only example with 2 or more predictor variables that are both nominal and one outcome is the third answer here.
Eta squared (n^2)
dependent on sum of squares Sum of squares of effect/ total Eta squared is generally smaller, can add them together to get fit of the full model (R^2 =1)
interactions
key reason to use factorial ANOVA Does the effect of predictor variable 1 on the outcome change based on level of predictor 2 Ex. do ppl's ratings of food items change based on food temperature? If it does change, the effect of how much you look the food item changes based on the food temperatures ex. hot ice cream, hot pancake, cold ice cream, cold pancake
No interaction effect
no post hoc test
Repeated measures ANOVAs (or within-subjects ANOVAs) additionally account for which of the following: variance changes over time variance across multiple predictors variance from that we cannot explain variance within an individual's answers
variance within an individual's answers Explanation We have to account for individual variance because each person is doing multiple tests. Differences between people could really change the data in this case, so we make sure we include that in our equations!
