Exam 4 Lecture 4 Flashcards
Independent Variable is Categorical and Dependent Variable is Continuous
t-test
ANOVA
Comparing endurance exercisers to resistance exercisers and sedentary people on daily protein intake
Independent Variable and Dependent Variable are both Categorical
Chi square test
Fischer’s Exact test
Likelihood that endurance exercisers also engage in resistance training
Difference between t-test and ANOVA
T-test and ANOVA have the same assumptions but t is for 2, ANOVA is for more than 2 groups
ANOVA= Analysis of variance= An F test.
If you have 5 groups, you could technically do a series of t-tests
- But, every tine you do a statistical test, you have Type 1 and Type 2 error to consider
- If you keep doing tests over and over, you increase your risk of getting an incorrect result, especially a Type 1 error (False-Positive)
Multiple Testing Problem & Solutions
1 test = 5% risk of Type 1 error (a= .05)
100 tests, each 5% risk… that risk is going to catch up with you.
This problem is one of 3 key problems that has led to the current “reproducibility” crisis in science.
Why is multiple testing a problem?
Say you have a set of hypotheses that you wish to test simultaneously. The first idea that might come to mind is to test each hypothesis separately, using some level of significance a. At first blush, this doesn’t seem like a bad idea. However, consider a case where you have 20 hypotheses to test, and a significance level of 0.05. What’s the probability of observing at least one significant result just due to chance? So, with 20 tests being considered, we have a 64% chance of observing at least one significant result, even if all of the tests are actually not significant.
Statisticians have devised ways to fix this/reduce this risk
IV= still categorical, but >2!
DV= still continuous.
Analysis of Variance (ANOVA)
- IV= group, DV= continuous
You ae comparing groups on how much of something
Compares means of a variable between groups
Asks: Are the groups different from one another, and if so, is that because of chance?
Can be used when there are more than 2 groups (H.S., club, college athlete)
Compares how much variance there is WITHIN a group to how much variance there is BETWEEN the groups
- ‘One-way’ ANOVA- comparing one IV (athlete status)
- ‘Two-way’ ANOVA- comparing 2 IVs (e.g., athlete status & sport type)
Study Design AGAIN!
Between subjects (I am comparing one person to another)
- This phrase means that some people in your study do one thing and other people in your study do a different thing (everyone does not do everything)
- You are comparing Person 1 (or Group 1) to Person 2 (or Group 2)
Comparing heat rate (DV) in runners versus non-runners
Usually considered cross-sectional
Within subjects (I am comparing one person to themselves)
- This phrase means that you have everyone do everything in your study
- You compare Person 1 at time 1 to person 1 at time 2, etc
- This is “stronger” because no one is a better control for you than you .
Comparing heart rate (DV) before versus after a 1-mile run
Time passes= typically longitudinal
A ‘regular’ ANOVA
Used when each group has different people.
Step 1: The omnibus test.
Asks: Are there differences between the groups IN GENERAL? The null is that past month frequency is the same in all groups. Doesn’t compare individual groups!
Step 2: Post-hoc analyses, also called pairwise comparisons
ONLY DONE if the omnibus test is significant!
- This is critical! people cheat and look at these when they shouldn’t!
Asks: Where are the the differences coming from?
(see: if no diffs, then don’t look for their source!)
- No gym vs. CrossFit- obvious difference
- Planet Fitness vs. CrossFit- ????
OMNIBUS= when everything is considered together
Before you can ask:
Is engagement at Rutgers gyms different from Planet Fitness gyms?
You must first ask:
DOES MODALITY AFFECT ENGAGEMENT (This is to reduce Type 1 error)
- Tukey’s test is most common post-hoc analysis
Reported as: F(3,76)=43.36, p<.05
3= Between group
76= Within group
F value= 43.36
ANOVA
Picking the right ANOVA
Independent Variable Considerations
ANOVA- single factor: who you have 1 set of groups (male/female)
ANOVA- two factor: when you have 2 sets of overlapping groups (male/female, athlete/non-athlete)
Dependent Variable (DV) Considerations
Without replication: Comparing 1 thing/sample/subject across multiple conditions (e.g. my stress in Jan, Apr, Jun & Sept when I do or do not have a big project due)
With replication:
When you have multiple samples per group (cross-sectional) or have collected same data at multiple times (longitudinal)
We will stick with Two-way ANOVA “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 chance 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
