Week 11 Flashcards
Repeated Measures
- Within- Subjects
- When each participant is exposed to all the treatments
One-way ANOVA
- Tells whether there are differences in mean scores on the DV across 3 or more groups
- Invented by Sir Ronadl Fisher - F statistic
- Post-hoc tests can be used to find out where the differences are
Null Hypothesis
- Usually denoted by letter H with subscript ‘0’
- There is no significant difference between the means of various groups
Alternative Hypothesis
At least one of the means is different from the rest
Factor
The Independent Variable
One-way = single-factor = One independent variable
e.g. the type of treatment
Between-Subjects
- Independent groups
- Each group is different to the other groups
- e.g. comparing male and female & intersex
Within Subjects Group
- Dependent Groups
- One group of participants exposed to all levels of Individual Variable
Examine and Compare
- Indicates there will be a t-test or an ANOVA
- Two groups = t-test
- 3 or more groups = ANOVA
Familywise Error
- The more t-tests we do the greater the risk of error
- ANOVAs guard against familywise errors
Repeated-measures ANOVA
10:49 Part 1
- Can analyse differences between means from same group of participants
- If overall F is significant then run post-hoc analyses
Statistical Question
- Is there a statistically significant difference among the averages of the means
- Different treatments completed by the same group of subjects
Benefits of Repeated Measures
- Sensitivity
- Economy
Repeated Measure - Sensitivity
- A source of error is removed
- No individual differences when same subjects are in each group
- By removing variance data becomes more powerful in identifying experimental effects
Repeated Measure - Economy
- Research often constrained by time and budget
- Fewer subjects required to get the same data
Problems with Repeated Measures
- Drop-out
- Practice/Order/Carry-over Effects
Repeated Measures Drop Out
- Participants may withdraw for many differnt reasons
- If we miss even one score all data for that subject has to be removed
Repeated Measures Drop Out
- Participants may withdraw for many differnt reasons
- If we miss even one score all data for that subject has to be removed
- Researchers should state what the drop out rate is
Repeated Measures Practice/Order/Carry-Over Effects
- Receiving one type of treatment can make subsequent treatments easier
- May cause varied performance
- What happens at beginning might affect what happens at the end of research
- We can use counterbalancing to get around this
Assumptions - Tests for Sphericity
- With t-tests and Between-subjects ANOVAs we look for homogeneity of variance
- With paired samples t-tests and Within-subjects ANOVAs we want Differences to be equal
- Mauchly’s Test for sphericity
- Equality in variances of differences
Mauchly’s Test for Sphericity
- Equality in variances of differences
- Tested using Mauchly’s Test
- p < .05, assumption of sphericity has been violated
- p > .05, assumption of sphericity has been met
Looking at Dataset
Each row is a participant and each column is the IV Condition
SPSS - Repeated Measures Within ANOVA
1. Analyse
2. General Linear Model
3. Repeated Measures
4. Type the factor (IV) name (Recovery_Methods) and number of levels (3)
5. Add
6. Define
SPSS Within-subjects ANOVA
- Replace ? marks!
* One at a time drag each group to Within-Subjects Variables window
* Place them in order
* Click EM Means
EM Means
8. EM Means
* Drag IV (recovery method) into “Display Means For” Window(recovery Method)
9. Continue
10. OK
Descriptive Statistics - Within Subjects Anova
- Sample Sizes for each of the conditions
- Standard Deviations
- Means
Tests for Sphericity
Part 4 - 5:46
- Mauchly’s Test of Sphericity
- don’t need df or others
- Only state the test used and p-value
- Say whether assumption was violated or not
- p < .05 Assumption has been met
Interpret Within-Subjects Effects
- If spericity has been met we use first row
- If sphericity is violated we can use Greenhous-Geisser or Huynh-Feldt Corrections
Within-Subjects ANOVA Degrees of Freedom
- k = the number of conditions (3)
- N = the sample size (40)
Formula = dfwithinfactor = k - 1 = 2
dferror = (k-1)(N-1) = 2 x 39 x = 78
Multivariate Test
- This is to get around the Sphericity Assumption
- Wilks Lambda
- Non Parametric Test
- is less powerful but is another option
Post-Hoc Tests
1. Analyse
2. General Linear Model
3. Repeated Measures
4. EM Means
5. Tick compare main effects
6. Select Bonferroni under “CI adjustment”
7. Continue
8. Ok
Pairwise Comparisons - Bonferroni
- Inspect the p-values to see which treatments are significantly different
*
APA Write up for Within-subjects ANOVA
- A one-way within-subjects ANOVA revealed that ther was an overall sidnificant difference between the ream recover rates of athletes across the three recovery methods, F(2, 78 = 12.38, p < .001. The assumpthion of sphericity was met, p = .75. Post-hoc analyses using Bonferroni adjustment showed the combined method resulted in significantly higher recovery rates than both the carbohydrates (p = .03) and the rehydration (p < .001) methods. There was however, no significant difference between the carbohydrates and rehydration techniques (p = .09)
Write up APA Format if Sphericity is violated
Use Wilks Lambda instead and the df are different, and the F value is different
Part 4 - 15:20
Activity and Non-Parametric Tests
