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Repeated  Measures/Longitudinal Repeated  Measures/Longitudinal

Repeated Measures/Longitudinal - PowerPoint Presentation

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Repeated Measures/Longitudinal - PPT Presentation

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

high school week college school high college week null students subject anxiety subjects factors data levels factor response random week1 week3 week2

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Slide1

Repeated Measures/Longitudinal Analysis

-

Bob Feehan

Slide2

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

.

(

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

.

Slide3

Example

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

/

Slide4

Clarifications

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)

Slide5

Example

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”)

Slide6

Data

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)

Slide7

Minitab Tricks – “Stacked” Data

7

8

9

10

1112

Slide8

Minitab Tricks - “Stacked” Data

Slide9

Minitab Tricks - “Stacked” Data

Slide10

Minitab Tricks – “Subset” Data

Slide11

Minitab Tricks – “Subset” Data

Slide12

Data 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

!

Slide13

College 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”)

Slide14

High 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”)

Slide15

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”)

High School / College Comparisons

-Problems?

Slide16

Combined 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!)

Slide17

Combined 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

Slide18

Combined 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

Slide19

Combined 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

Slide20

General 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)

Slide21

My 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

Slide22

My 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.

Slide23

SBP 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