Exam 4 Lecture 5 Flashcards
Two-way ANOVA
We will stick with:
“With Replication”
If data are cross-sectional: “with replication” means that there are multiple people in each group.
If data are longitudinal: “with replication” means that people are tested more than once. This type is also called REPEATED MEASURES ANOVA.
How things change in groups over time
Repeated Measures ANOVA
- Same principle as regular ANOVA but math is different. Same person measured repeatedly over time (like a paired t-test)
- Usually participants are grouped into ‘control’ (no change expected) OR ‘experimental’ (change is expected)
- Because the people in each group stay the same, there is less ‘noise’
You are your own best control!
- ‘Classic’ ANOVA assumes independence- there are no overlaps in group participants.
Asking: Are people changing over time/due to an experimental manipulation?
This is a 2-part question!
- Is there CHANGE?
- Is it due to GROUP ASSIGNMENT?
And- you get 3 statistics!
- Within-person (time)
- Between-person (group)
-Time x group interaction
The last statistic- the interaction term- is really the answer to your question!
Do people in one group change differently than people in the other group?
ANOVAs- which one?
DV (what you want to know)- days per week of exercise.
One-way ANOVA- does modality affect days of exercise per week?
(aerobic/resistance/cross-training)
Two-way ANOVA- does modality affect days of exercise per week differently in men versus women?
Factor 1= (aerobic/resistance/cross-training)
Factor 2= (male/female/non-binary)
Two-way ANOVA with TIME as a factor- does modality affect days of exercise per week differently over time?
Factor 1=
(aerobic/resistance/cross-training)
Factor 2=
time (start, 1 month later, 2 months later… 1 year later)
Repeated Measures ANOVA
Do certain types of exercises show more consistent engagement?
Is there change over time? COLUMNS
Are there group differences? ROWS
Do the groups differ in how they change over time? INTERACTION
IV Group: color coded
IV Passage of Time: always on x axis
DV Days of exercise: on y axis
This graph shows the INTERACTION
Interpreting INTERACTIONS
How do you interpret change within a group AND compare change across the groups
* People get this wrong all the time!
“Perfect” data: one group changes, the other group does not.
- Groups start the same
- Green group shows an increased fat intake over time
- Blue group shows no change in fat intake over time
- Groups start the same
- Green group has greater decrease in calories over time
- Blue group shows no change over time
Example: Behavior before and after taking a nutrition course
- Groups start the same
- Groups different after course
- Green group increases protein intake, blue group decreases protein intake over time
Interpretation: The nutrition course improved diet in exercisers but made diet worse for non-exercisers! - Groups start differently, but end the same.
- At stat, green group eats more protein than blue group
- Green group doesn’t change. Blue group increases to level of green!
- Can’t say ‘greater change’ in blue group.
Interpretation: The nutrition course increased protein intake in non-exercisers, who were eating significantly less protein than exercisers before the course.
Drawing Conclusions
A real graph for a real scientific paper that my group published about Rutgers athletes. This is a performance on a cognitive test. There are >2 groups (IV) and the outcome (DV) is continuous= ANOVA
FANCY– bar graph with scatterplot overlaid! IV is categorical! Everyone’s data within each group is shown. RESULT: NO SIGNIFICANT TEAM DIFFERENCES (Look at the bars. Don’t you want to try to say something??)
DON’T DO IT!!
In the absence of ‘significant differences’, you CANNOT interpret differences. Even if you think you see some.
Non-significance means that any perceived differences are probably just due to chance based on the sample you selected.
This is a classic error-> you eyes see something and you forget that the math does not back up your perception.
Independent Variable is Continuous and Dependent Variable is Continuous
Correlation
Regression
Relating daily protein intake to skeletal muscle mass
Independent Variable is Continuous and Dependent Variable is Continuous
Regression, logistic
Likelihood of developing heart disease based on endurance exercise history
What you have vs what you want- correlation/regression
Independent Variable-> Dependent Variable
- Height as toddler-> Height as an adult
- Protein powder intake-> Weight changes
- Cannabis use-> Overall GPA
- Soda consumption-> Blood pressure
One thing leads to another, or do two things co-occur?
Correlation- variables are associated or related.
They co-occur, change together, or co-vary. Both things happen simultaneously or are measured at the same time, so DIRECTIONALITY IS IMPOSSIBLE TO DETERMINE.
A <-> B
Causation- one variable causes/changes in the other.
- More difficult to demonstrate- implies before-> after
- Requires controlled study designs (longitudinal)
A-> B
Correlation (‘classic’, Pearson’s)
- When you aren’t looking for causation
- When you aren’t predicting directionality
- You are simultaneously modeling A-> B and B-> A
- Usually assumed to be linear
- Looking for correlation coefficient (r)
r= -1 -> Completely negatively correlated
r=0 -> Completely uncorrelated
r=+1 -> Completely positively correlated
Are overall GPAs associated with major GPAs?
Is more exercise related to more calorie intake?
Correlation (rank, Spearman’s)
- Same kind of thing except instead of looking at a variable;e’s value, you are looking at its rank
- Math behind it is different but the principle is the same
- This is particularly good when the data are not normally distributed, when there are outliers, or when there is huge dispersion of values (kurtosis)
- It is called non-parametric because it doesn’t have the same assumptions!
Do colleges with winning football teams get more student applications?
The many flavors of regression: LINEAR is #1
- Looking for an association when you want to assess causation, when you know which variable causes which
- Allows us to predict B from A, so ONE DIRECTION ONLY!
- You are creating a regression line that ‘best fits’ the data, that is, where the most variance is explained (least error)
This is y= mx+b
Regression Types
- Linear
- Nonlinear
- Multiple
- Hierarchical
- Logistic
Reported with r^2
Use r^2 to show how much variance in DV is explained by IV. SIGNIFICANCE TESTING!
In real life, nothing is simple.
Interactions:
- When two variables combined have a different effect than expected
- Probably implies a third variable at play (e.g., they affect each other in addition to the outcome, or both affect something unmeasured)
- When both IVs and DVs are continuous, you can compare regression lines
- To each other
- To 0
Diet & exercise affect weight
- Diet reduces weight 1 lb/week
- Exercise reduce eight 0.25 lb/week
- Diet + exercise reduces weight 2.25 lb/week
IN CONCLUSION
Categorical IV and Categorical DV- Chi square test, Fischer’s Exact test- SIGNIFICANT MORE/LESS LIKELY
Categorical IV and Continuous DV- t-test, ANOVA- SIGNIFICANTLY DIFFERENT
Continuous IV and Categorical DV- Regression, logistic- SIGNIFICANTLY MORE/LESS LIKELY
Continuous IV and Continuous DV- Correlation, Regression- SIGNIFICANTLY RELATED
