Repeated anova measures ppt
-
Upload
aamna-haneef -
Category
Education
-
view
1.708 -
download
3
description
Transcript of Repeated anova measures ppt
![Page 1: Repeated anova measures ppt](https://reader033.fdocuments.in/reader033/viewer/2022050815/547c6dc5b4af9fdd2f8b47c7/html5/thumbnails/1.jpg)
Presented toMs Maryium Gul
Presented by Aamna Haneef
Roll no: 05MS (2012-2014)
Lahore College for Women University
![Page 2: Repeated anova measures ppt](https://reader033.fdocuments.in/reader033/viewer/2022050815/547c6dc5b4af9fdd2f8b47c7/html5/thumbnails/2.jpg)
Repeated Measures ANOVA
![Page 3: Repeated anova measures ppt](https://reader033.fdocuments.in/reader033/viewer/2022050815/547c6dc5b4af9fdd2f8b47c7/html5/thumbnails/3.jpg)
![Page 4: Repeated anova measures ppt](https://reader033.fdocuments.in/reader033/viewer/2022050815/547c6dc5b4af9fdd2f8b47c7/html5/thumbnails/4.jpg)
Repeated measures ANOVA is also referred to as a • “within-subjects ANOVA”,• “Dependent groups” or • “ANOVA for correlated
samples”
Other Names
![Page 5: Repeated anova measures ppt](https://reader033.fdocuments.in/reader033/viewer/2022050815/547c6dc5b4af9fdd2f8b47c7/html5/thumbnails/5.jpg)
Why the repeated factor is called a “within” subjects factor?
Because comparisons are made multiple times ("repeated") “within” the same subject rather than across ("between") different subjects
![Page 6: Repeated anova measures ppt](https://reader033.fdocuments.in/reader033/viewer/2022050815/547c6dc5b4af9fdd2f8b47c7/html5/thumbnails/6.jpg)
In within subject design
• Each participant is measured more than once
• Same subjects across the levels of the IV
• Levels can be ordered like time or treatment
• Or levels can be un-ordered (e.g. cases take three different types of depression inventories)
![Page 7: Repeated anova measures ppt](https://reader033.fdocuments.in/reader033/viewer/2022050815/547c6dc5b4af9fdd2f8b47c7/html5/thumbnails/7.jpg)
What RM ANOVA does?Like T-Tests, repeated measures ANOVA gives the statistic tools to determine whether or not change has occurred over timeT-Tests compare average scores at two different time periods
RM ANOVA compared the average score at multiple time periods
![Page 8: Repeated anova measures ppt](https://reader033.fdocuments.in/reader033/viewer/2022050815/547c6dc5b4af9fdd2f8b47c7/html5/thumbnails/8.jpg)
The logic of RM ANOVA
Any differences that are found between treatments can be explained by only two factors:1. Treatment effect2. Error or Chance
![Page 9: Repeated anova measures ppt](https://reader033.fdocuments.in/reader033/viewer/2022050815/547c6dc5b4af9fdd2f8b47c7/html5/thumbnails/9.jpg)
Cont…
A particular subject’s scores will be more alike than scores collected from multiple subjects
Less variability decrease in sampling error
![Page 10: Repeated anova measures ppt](https://reader033.fdocuments.in/reader033/viewer/2022050815/547c6dc5b4af9fdd2f8b47c7/html5/thumbnails/10.jpg)
Cont…
Subject A B C
Each row
represents
one
subject
measured
under
each of k
conditions.
1subj1 under
condition A
subj1 under
condition B
subj1 under
condition C
2subj2 under
condition A
subj2 under
condition B
subj2 under
condition C
3subj3 under
condition A
subj3 under
condition B
subj3 under
condition C
And so on…
![Page 11: Repeated anova measures ppt](https://reader033.fdocuments.in/reader033/viewer/2022050815/547c6dc5b4af9fdd2f8b47c7/html5/thumbnails/11.jpg)
Assumptions
Dependent variableIt should be measured at the interval or ratio level (continuous), such as • revision time • Intelligence• exam performance • weight
![Page 12: Repeated anova measures ppt](https://reader033.fdocuments.in/reader033/viewer/2022050815/547c6dc5b4af9fdd2f8b47c7/html5/thumbnails/12.jpg)
Assumptions Cont…
Independent variable It should consist of at least two categorical, "related groups" or "matched pairs“• 10 individuals' performance in a
spelling test before and after new form of computerized teaching method
• measuring changes in blood pressure due to an exercise-training program
![Page 13: Repeated anova measures ppt](https://reader033.fdocuments.in/reader033/viewer/2022050815/547c6dc5b4af9fdd2f8b47c7/html5/thumbnails/13.jpg)
Assumptions Cont…
No significant outliers differencesData values that are "far away" from the main group of data• Distorting the differences between the related groups• Reduces the accuracy of results
![Page 14: Repeated anova measures ppt](https://reader033.fdocuments.in/reader033/viewer/2022050815/547c6dc5b4af9fdd2f8b47c7/html5/thumbnails/14.jpg)
Assumptions Cont…Normally distributed Dependent
variable• The dependent variable between the
two or more related groups should be approximately normally distributed
• It is quite "robust" to violations of normality
• The Shapiro-Wilk test of normality can test for normality
![Page 15: Repeated anova measures ppt](https://reader033.fdocuments.in/reader033/viewer/2022050815/547c6dc5b4af9fdd2f8b47c7/html5/thumbnails/15.jpg)
Assumptions Cont…
Sphericity• Refers to differences between
variances in levels of the repeated-measures factor (Time)
• Violation of the assumption of sphericity, causes the test to become too liberal (leads to an increase in the Type I error)
• Mauchly's Test of Sphericity can help to test for its violation
![Page 16: Repeated anova measures ppt](https://reader033.fdocuments.in/reader033/viewer/2022050815/547c6dc5b4af9fdd2f8b47c7/html5/thumbnails/16.jpg)
Hypothesis for RM ANOVA
The repeated measures ANOVA tests for whether there are any differences between related population means
H0: µ1 = µ2 = µ3 = … = µk
H0: There are no differences between population means.HA: At least one treatment or observation mean is significantly different
![Page 17: Repeated anova measures ppt](https://reader033.fdocuments.in/reader033/viewer/2022050815/547c6dc5b4af9fdd2f8b47c7/html5/thumbnails/17.jpg)
Sources of Variability• In repeated measure ANOVA, there are
three potential sources of variability: 1. Treatment variability: between columns, 2. Within subjects variability: between
rows, and 3. Random variability: residual(chance
factor or experimental error beyond the control of a researcher) .
• A repeated measure design is powerful, as it controls for all potential sources of variability.
![Page 18: Repeated anova measures ppt](https://reader033.fdocuments.in/reader033/viewer/2022050815/547c6dc5b4af9fdd2f8b47c7/html5/thumbnails/18.jpg)
FORMULA
variance between treatmentsF = ------------------------------------------
Error variance • A large F value indicates that the
differences between treatments/observations are greater than would be expected by chance or error alone.
![Page 19: Repeated anova measures ppt](https://reader033.fdocuments.in/reader033/viewer/2022050815/547c6dc5b4af9fdd2f8b47c7/html5/thumbnails/19.jpg)
Approaches to RM ANOVA
SPSS conducts 3 types of tests if the within-subject factor has more than 2 levels• The standard univariate ANOVA test• The alternative univariate tests• The multivariate test
![Page 20: Repeated anova measures ppt](https://reader033.fdocuments.in/reader033/viewer/2022050815/547c6dc5b4af9fdd2f8b47c7/html5/thumbnails/20.jpg)
Advantages • Using the same participants in
different experimental manipulations • Exclude the effects of individual
differences • This design is also very economical • Removing variance due to differences
between subjects from the error variance greatly increases the power (probability of correctly rejecting a false null hypothesis)
![Page 21: Repeated anova measures ppt](https://reader033.fdocuments.in/reader033/viewer/2022050815/547c6dc5b4af9fdd2f8b47c7/html5/thumbnails/21.jpg)
Disadvantages
• Practice effects causing participants’ results to improve • Carry-over effects (bias)• Demand characteristics (more
exposure, more time to think about meaning of the experiment).• Boredom and lack of concentration
![Page 22: Repeated anova measures ppt](https://reader033.fdocuments.in/reader033/viewer/2022050815/547c6dc5b4af9fdd2f8b47c7/html5/thumbnails/22.jpg)
Tidbits
Why it is always called F statistic?
The F statistic was named after Ronald A. Fisher, who mainly developed ANOVA
![Page 23: Repeated anova measures ppt](https://reader033.fdocuments.in/reader033/viewer/2022050815/547c6dc5b4af9fdd2f8b47c7/html5/thumbnails/23.jpg)