PSY2005: APPLIED RESEARCH METHODS & ETHICS IN PSYCHOLOGYLab Class 6: Using a Repeated Measures ANOVA to conduct a Time Series Analysis

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AIMS & OUTCOMES

Provide an overview of research focusing on drug treatments over time

Conduct a repeated measures one-way ANOVA on time series data

Explain the key features of a repeated measures ANOVA

Complete Workbook 6

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TYPES OF TREATMENT

Low threshold: drop-in services, needle exchange, targeted delivery of health care, outreach services, and drug consumption rooms

Detoxification : drugs that block the effects of the to-be-withdrawn drug (naltrexone) may be combined with anaesthetics

Pharmacotherapies : substitute drugs (e.g. Methadone) Talking therapies: therapeutic communities; structured

prevention programmes (e.g. cognitive behavioural therapy, motivational interviewing, community reinforcement and contingency contracting)

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Stevens, Hallam, and Trace (2006)

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DRUG TREATMENTS IN CURRENT STUDY

Time of Measurement Time 1: After 1 month Time 2: After 6 months Time 3: After 1 year

Outcome Measures Self-monitored logbooks: drugs taken Recordings taken over a 28 day period prior to

measurement

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EXAMPLE TREATMENT OUTCOME MEASURE

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PARTICIPANTS & THERAPISTS

Participants: Prolific and other Priority Offender status and tested

positive for cocaine or heroin during their arrest. Randomly allocated to one of the three groups.

Therapists: Twelve therapists ran the sessions. All were qualified to degree standard and had a minimum

of three years experience

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PROCEDURE

Participants took part as part of a voluntary rehabilitation procedure

Participants had either: 90 minute weekly closed (nobody was allowed to join

after the first session) meetings in groups of 4-8 people with two Counsellors.

45 minute weekly individual sessions with one Counsellor Participants attended the sessions for 1 year.

Treatment outcomes were measured at 1 month, 6 months & 12 months.

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ABOUT THE EXPERIMENT! Today’s ingredients Hypotheses:

H0: That there is no significant difference in self-reported drug use across the three periods of drug treatment

H1: That there is a significant difference in self-reported drug use across the three periods of drug treatment

Teasing apart the repeated measures design Independent variable: Length of drug treatment

3 Levels: 1 month, 6 months, 1 year Dependent variable

Self-reported drug use

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SPSS DATA FILES Open Psy2005 folder Open Week 6 Drag Lab Week 6 PPT file to desktop Drag on to desktop and click on ‘drug treatments2.sav’ Fundamental principle

Each participant has their own row Each different bit of data must go in a separate column / variable

Data view vs. Variable View Change via ‘tabs’ at bottom of window

or keyboard combination T⌘ Data view for viewing / editing data Variable view for details of variables

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Self-reported drug use at time: 1 month

Self-reported drug use at time: 6 months

Self-reported drug use at time: 1 Year

Type of session:Group Vs Individual therapy Situation. More on this later!

Type of therapy:12 StepCBT with MIStandard care.

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CREATING A BAR CHART FOR THE TIME SERIES ANALYSIS

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CREATING A BAR CHART FOR THE TIME SERIES ANALYSIS

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CREATING A BAR CHART FOR THE TIME SERIES ANALYSIS

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INCLUDING ERROR BARS

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What is a 95% confidence interval? An inferentialstatistic through which a range of scores is calculatedwith a confidence (95%) that a population value lies within it.

What is a 95% confidence interval? An inferentialstatistic through which a range of scores is calculatedwith a confidence (95%) that a population value lies within it.

THAT’S IT!

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A BAR CHART FOR THE TIME SERIES ANALYSIS

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Comment: Shows a Reduction in drug use From Time 1 to Time 2But less of a reductionFrom Time 2 to Time 3

Comment: Shows a Reduction in drug use From Time 1 to Time 2But less of a reductionFrom Time 2 to Time 3

HOW CAN WE ANALYZE THIS? We could carry out a series of t-tests

1 month Vs 6 months 1 month Vs 1 year 6 months Vs 1 year

Is there a problem with this? Type 1 error: rejecting the null hypothesis when it is true What is the standard probability of doing this? 5% Probability for each t-test of not making a type 1 error is

95%For three tests (.95 x .95 x .95 = .857)Therefore the risk of making a type 1 error across 3 tests is

14.3%17

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REPEATED MEASURES ONE-WAY ANALYSIS OF VARIANCE Testing the Null Hypothesis

Aim of the t-test: find out whether two samples have the same mean: Ho: X1 = X2 H1: X1 ≠ X2

Aim of an ANOVA: to test whether more than two samples have the same mean Ho: X1 = X2 = X3

H1: X1 ≠ X2 ≠ X3

or H1: X1 = X2 ≠ X3

or H1: X1 ≠ X2 = X3

or H1: X1 = X3 ≠ X2

A one-way repeated measures ANOVA tells us whether the treatments had a different effect on the dependent variable across the three time periods

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Where:1.1 month2.6 months3.1 year

Where:1.1 month2.6 months3.1 year

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Type I and Type II Errors•Let us suppose that a person is judged because he or she has commited a crime.

•If we approach this case as a hypothesis contrast:

•H0: the person is inoccent wilst the contrary is not proved.

•H1: the person is guilty.

•In order to not accept the H0 we have to find evidence against the H0 and supporting the H1.

•But still, when we are going to make a decision, we might make the following mistakes

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Metodología de la Investigación y Estadística II-UMA

WHAT DOES POWER MEAN?

Type 1 Error: Fail to Accept Null when true

Correct Decision: Retain Null when true

Correct decision: Fail to accept null when false

Type 2 Error: Accept Null when false

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Retain NullFail to Accept Null

Null istrue

Null is False

Power is the probability of correctly rejecting a false null hypothesis. Things that effect Power: Effect size, sample size, significance criterion and the amount of variability in the data set

Power is the probability of correctly rejecting a false null hypothesis. Things that effect Power: Effect size, sample size, significance criterion and the amount of variability in the data set

State ofnature

Decision

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WHY DOES A RM ANOVA HAVE MORE POWER THAN AN IG ANOVA?

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We control forIndividual differencesWe control forIndividual differences

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Sphericity Homogeneity of variance and covariance: The variances are

equal and the variance of the differences between the conditions are equal

The Mauchly’s Sphericity Test Don’t worry if this is hurting your head SPSS conducts a test to

assess whether we are breaking the rules If the test is significant we have broken the rules and we need to

apply a correction (E.g. The Greenhouse-Geiser Correction) For more information read Chapter 13 of Andy Field’s book

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CONDUCTING A ONE-WAY RM ANOVA IN SPSS

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CONDUCTING A ONE-WAY RM ANOVA IN SPSS

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Insert theseInsert these

CONDUCTING A ONE-WAY RM ANOVAIN SPSS

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CONDUCTING A ONE-WAY RM ANOVA IN SPSS

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CONDUCTING A ONE-WAY RM ANOVA IN SPSS

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CONDUCTING A ONE-WAY RM ANOVA IN SPSS

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CONDUCTING A ONE-WAY RM ANOVA IN SPSS

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THE OUTPUT: DESCRIPTIVE STATISTICS

Observations The first box informs us that we entered the correct variables The second provides us with descriptive statistics suggesting

that the biggest decrease in drug use occurred between drugs use 1 month and drugs use 6 months

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THE OUTPUT: MAUCHLY’S SPHERICITY TEST

Observations This test shows that we have not violated the sphericity assumption

(p>0.05); our data set shows homogeneity of the variances of the differences.

In essence these outputs direct us to the correct row in the ANOVA. We will be looking at the top row (Sphericity Assumed)

The word Epsilon is used in statistics as a measure of error. If we did not meet the sphericity assumption we could select one of these measures of error to guide us in the following ANOVA table. 31

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THE OUTPUT: THE MAIN ANOVA

Observations: We are interested in the F-Ratio highlighted. It is a ratio of average

variability explained (Systematic variance: 249.862) to average variability unexplained (Unsystematic Variance: 3.528).

The F-ratio has a probability distribution which can be used to determine significance levels

The F-ratio is written thus: (F(2,282)=70.819,MSe=3.528 p<0.001)32

THE OUTPUT: POST-HOC BONFERRONI TESTS

These test the differences between the treatment outcome times whilst controlling for family wise error (remember t-tests). Remember this is a very conservative test. These tell us that there are significant differences between time 1 (1 month) and time 2 (6 months) and time 1 (1 month) and time 3 (1 year). There are no differences between time 2 (6 months) and time 3 (1 year).

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CONCLUSIONS The bar chart indicated a difference between the three times that

the outcomes were measured The Mauchly’s Test showed us that we did not violate an

important rule for carrying out a repeated measures ANOVA The ANOVA informed us that we can fail to accept:

H0: That there is no significant difference in self-reported drug use across three periods of drug treatment

And accept: H1: That there is a significant difference in self-reported drug use across

three periods of drug treatment The Post-hoc tests tell us that:

There are significant differences between time 1 (1 month) and time 2 (6 months) and time 1 (1 month) and time 3 (1 year). There is no difference between time 2 (6 months) and time 3 (1 year).

These findings show that in this study the participants reported significantly more drug use at time 1 than at time 2 or time 3.

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COMPLETE WORK & SAVE YOUR FILES

Data Set: ‘drug treatment2.sav’ Output: ‘week6workbook.spv’ Cut and paste the graphs in to Workbook (week 6) Upload to Unihub

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