Analysis Bob Feehan What are you talking about Repeated Measures Measurements that are taken at two or more points in time on the same set of experimental units ie subjects Longitudinal Data ID: 760113
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Slide1
Repeated Measures/Longitudinal Analysis
-
Bob Feehan
Slide2What are you talking about?
Repeated Measures
Measurements that are
taken
at two or more points in time on the same set of experimental units
.
(
i.e. subjects)
Longitudinal Data
Longitudinal data are a common form of
repeated
measures
in which measurements are recorded on individual subjects
over a period of time
.
Slide3Example
Researchers want to see if high school students and college students have different levels of anxiety as they progress through the semester. They measure the anxiety of 12 participants three times: Week 1, Week 2, and Week 3. Participants are either high school students, or college students. Anxiety is rated on a scale of 1-10, with 10 being “high anxiety” and 1 being “low anxiety”.
Repeated Measurement?AnxietyLongitudinal Measurement?3 WeeksAny other comparisons?High School vs College OverallRate (interaction)
-
http://statisticslectures.com/topics/
factorialtwomixed
/
Slide4Clarifications
Repeated Measures/Longitudinal Design:
Need at least one
Factor
with two
Levels
.
The Levels have to be
dependent
upon the Factor
Example Continued …
Factor
:
Subjects (12)
Levels
:
3
(measured each week from SAME person)
Slide5Example
Researchers want to see if high school students and college students have different levels of anxiety as they progress through the semester. They measure the anxiety of 12 participants three times: Week 1, Week 2, and Week 3. Participants are either high school students, or college students. Anxiety is rated on a scale of 1-10, with 10 being “high anxiety” and 1 being “low anxiety”.
Before we even take any Data:What is our Hypothesis going in? (CRITICAL!!!)
College Students Anxiety (Null
Week1 = Week2 = Week3)
High School Students Anxiety (Null
Week1 = Week2 = Week3)
High School
vs
College Overall (Null
High School = College Overall)
High School
vs
College Trend (Null No Interaction or “Parallel Lines”)
Slide6Data
Why not just do multiple
Paired/Independent
T – Tests?
Takes Time (Time is precious)
Only can look at one Factor at a time. (
ie
Week)
Factor can only be two levels (
ie
no repeated measures > 2)
Cannot look at over-all
interactions
Why use ANOVA?
Saves time
Can look at multiple Factors
Factors can have multiple levels
Can look at differences between separate groups (
ie
College/High school)
Slide7Minitab Tricks – “Stacked” Data
7
8
9
10
1112
Slide8Minitab Tricks - “Stacked” Data
Slide9Minitab Tricks - “Stacked” Data
Slide10Minitab Tricks – “Subset” Data
Slide11Minitab Tricks – “Subset” Data
Slide12Data ANOVA
ANOVA General Linear Mode:
Responses:
Model:
Random Factors:
Response
Week
Subject
Subject
*Note: Without Subjects as Random our N of 6 would be N of 18. It would count each measurement of a subject as
INDEPENDENT
!
Slide13College Student Results
Results for: College Students
General Linear Model: Response versus Week, Subject Factor Type Levels ValuesWeek fixed 3 Week 1, Week 2, Week 3Subject random 6 1, 2, 3, 4, 5, 6Analysis of Variance for Response, using Adjusted SS for TestsSource DF Seq SS Adj SS Adj MS F PWeek 2 148.0000 148.0000 74.0000 111.00 0.000Subject 5 1.3333 1.3333 0.2667 0.40 0.838Week*Subject 10 6.6667 6.6667 0.6667 **Error 0 * * *Total 17 156.0000** Denominator of F-test is zero or undefined.
College Students Anxiety (Null Week1 = Week2 = Week3)High School Students Anxiety (Null Week1 = Week2 = Week3)High School vs College Overall (Null High School = College Overall)High School vs College Trend (Null No Interaction or “Parallel Lines”)
Slide14High School Student Results
Results for:
High School General Linear Model: Response versus Week, Subject Factor Type Levels ValuesWeek fixed 3 Week 1, Week 2, Week 3Subject random 6 1, 2, 3, 4, 5, 6Analysis of Variance for Response, using Adjusted SS for TestsSource DF Seq SS Adj SS Adj MS F PWeek 2 44.3333 44.3333 22.1667 28.91 0.000Subject 5 0.5000 0.5000 0.1000 0.13 0.982Week*Subject 10 7.6667 7.6667 0.7667 **Error 0 * * *Total 17 52.5000** Denominator of F-test is zero or undefined.
College Students Anxiety (Null Week1 = Week2 = Week3)High School Students Anxiety (Null Week1 = Week2 = Week3)High School vs College Overall (Null High School = College Overall)High School vs College Trend (Null No Interaction or “Parallel Lines”)
Slide15Combined Analysis
College Students Anxiety (Null Week1 = Week2 = Week3)High School Students Anxiety (Null Week1 = Week2 = Week3)High School vs College Overall (Null High School = College Overall)High School vs College Trend (Null No Interaction or “Parallel Lines”)
High School / College Comparisons
-Problems?
Slide16Combined Analysis
“Crossed” Factors vs “Nested” Factors for arbitrary Factors “A” & “B”
Nested: Factor "A" is nested within another factor "B" if the levels or values of "A" are different for every level or value of "B".Crossed: Two factors A and B are crossed if every level of A occurs with every level of B.
Our Factors: Subjects, School, & Week
Crossed?School & WeekSubjects & Week
Nested?
Subject is nested within School
i
e
.
Each subject has a measurement in High School
or
College not High school
and
College
Therefore; any comparisons between them are
independent
(Not paired!)
Slide17Combined Analysis
Setting up the ANOVA GLM with only Crossed Factors:(Pretend “Highschool” = Freshman year of College & “College” = Senior year)
ANOVA General Linear Mode:
Responses:
Model:
Random Factors:
Response
Week Year Subject Week*Year Week*Subject Year*Subject
Subject
Slide18Combined Analysis
General Linear Model: Response versus Week, Year, Subject Factor Type Levels ValuesWeek fixed 3 Week 1, Week 2, Week 3Year fixed 2 Freshman, SeniorSubject random 6 1, 2, 3, 4, 5, 6Analysis of Variance for Response, using Adjusted SS for TestsSource DF Seq SS Adj SS Adj MS F PWeek 2 175.1667 175.1667 87.5833 99.15 0.000Year 1 2.2500 2.2500 2.2500 19.29 0.007Subject 5 1.2500 1.2500 0.2500 0.56 0.744 xWeek*Year 2 17.1667 17.1667 8.5833 15.61 0.001Week*Subject 10 8.8333 8.8333 0.8833 1.61 0.234Year*Subject 5 0.5833 0.5833 0.1167 0.21 0.950Error 10 5.5000 5.5000 0.5500Total 35 210.7500
Slide19Combined Analysis
Setting up the ANOVA GLM with Nested Factors:(Reminder – Subjects are nested within School)
ANOVA General Linear Mode:
Responses:
Model:
Random Factors:
Response
School Subject(School) Week School*Week
Subject
Note: No Subject*Week interactions as School*Week included Subject*Week
Slide20General Linear Model: Response versus School, Week, Subject Factor Type Levels ValuesSchool fixed 2 College, High SchoolSubject(School) random 12 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12Week fixed 3 Week 1, Week 2, Week 3Analysis of Variance for Response, using Adjusted SS for TestsSource DF Seq SS Adj SS Adj MS F PSchool 1 2.250 2.250 2.250 12.27 0.006Subject(School) 10 1.833 1.833 0.183 0.26 0.984Week 2 175.167 175.167 87.583 122.21 0.000School*Week 2 17.167 17.167 8.583 11.98 0.000Error 20 14.333 14.333 0.717Total 35 210.750
Combined Analysis
College Students Anxiety (Null
Week1 = Week2 = Week3)High School Students Anxiety (Null Week1 = Week2 = Week3)High School vs College Overall (Null High School = College Overall)High School vs College Trend (Null No Interaction or “Parallel Lines”)
College Students Anxiety (Iffy)High School Students Anxiety (Iffy)High School vs College Overall (P <0.001, Means differ - College less)High School vs College Trend (P <0.001, Rate at which Anxiety changes varies dependent on the week. High schoolers became less anxious as Time went on and college students more anxious)
Slide21My Data
20 Minute Body cooling procedure where measurements (etc. HR, BP, Skin Temperature) are taking at baseline and then ever 2 minutes during cooling all the way to 20 minutes. 11 Total measurements during the cooling procedure.Two Group (Younger and Older) Two Infusions (Saline and Vitamin C) on Both Older and YoungerTwo “Timepoints” (Pre Infusion and Post Infusion) on each injection day.20 Subjects total (10 Older and 10 Younger)
Summary:
Each subject comes for two visits. One visit is Saline, the other is Vitamin C injection
Each visit subjects puts on cold suit and is cooled twice. Once before the infusion and once after
Measurements are taking Before cooling (baseline) and then ever 2 minute
increments up to 20 minutes.
Subjects are splits into two groups, Younger and Older
Slide22My Data
Crossed Factors at total analysis:
Infusion (Saline/Vit C), Timepoint (Pre/Post), Cooling (BL + every 2 minutes), & Subjects (1-20)
Nested Factors at Total Analysis:
Subjects and Group (Subjects are nested within Groups because Subjects have either a Young or Old attached to it, not both.
Repeated Measures and Time:
Each
factor takes a repeated measure but the only longitudinal design in the 20 min cooling that has more then one non random level (it has
11).
Subjects do not count as they are considered random.
Slide23SBP and HR Hypotheses
Hypotheses on Systolic BP Change due to cooling while adding Vitamin C:Young and Older Saline Days should NOT differ (accept Null hypothesis)*Young and Older VitC days could Differ (reject Null Hypothesis)*We can use Change in SBP as a standardization for different starting pointsOlder’s Change in SBP will be blunted compared to Younger’s*
Hypotheses on HR changes due to cooling while adding Vitamin C:Young and Older Saline Days should NOT differ (accept Null hypothesis)*Young and Older VitC days should NOT differ (accept Null hypothesis)*We can use Change in HR as a standardization for different starting pointsOlder’s Change is HR should not change from Younger’s*
*Old published Data supports it