Week 2: Tuesday4 th August, 2015.

Dr Kirsten Challinor.

3RD YEAR VISION SCIENCEEBP AND REVIEW OF STATISTICAL METHODS

http://www.mcescher.com

http://www.mcescher.com

LECTURE OUTLINE• Concept of course

• EBP

• Stats review

• Social media connection

Maurits Cornelis Escher] (17 June 1898 – 27 March 1972)

COURSE CONCEPT• The goal of a vision scientist is to understand how vision works.

• You will learn about vision science from a psychological perspective-

• Social psychology

• Cognition and reading

• Neuropsychology

• Individual differences

• Research methods

• ANOVAs

• Clinical stats

• Qual research – interviews and surveys

• All of these methods will be very useful for your 5 th year projects as well as general lifelong learning as a vision scientist

HOW’S YOUR EBP GOING?

What is EBP?

Examples of learning EBP (5 steps) over your degree

What are the 5 steps in the EBP process?

EVIDENCE BASED PRACTICE

EBP

(Hoffman, 2010)

EBP is the combination of the best available evidence from research, the patient’s preferences/circumstances, the clinical environment and the practitioner’s expertise.

HOW’S YOUR EBP GOING?

What is EBP?

Examples of learning EBP (5 steps) over your degree

What are the 5 steps in the EBP process?

FIVE STEPS IN EBP

Asking clinical questions

Translation of uncertainty to an answerable question 

Acquiring information

Systematic retrieval of best evidence available 

Appraising information

Critical appraisal of evidence for validity, clinical relevance, and applicability 

Applying information

Application of results in practice 

Auditing practice

Evaluation of performance 

Dawes et al, 2005

HOW’S YOUR EBP GOING?

What is EBP?

List 2 or 3 examples of learning EBP (5 steps) over your degree so far

What are the 5 steps in the EBP process?

http://www.eboptometry.com

EBP IN THIS COURSE

Asking clinical questions

Translation of uncertainty to an answerable question 

Acquiring information

Systematic retrieval of best evidence available 

Appraising information

Critical appraisal of evidence for validity, clinical relevance, and applicability 

Applying information

Application of results in practice 

Auditing practice

Evaluation of performance

REMEMBER THAT APPRAISAL IS

• Evaluating the relevant research evidence, to find the highest quality (most reliable, or valid) evidence available relevant to your question.

Critical appraisal is the process of assessing and interpreting evidence by systematically considering its validity and its relevance to the question. • Internal validity: the extent to which the research is

reliable.

• External validity: is an indication of the generalisability of the findings.

10

CRITICAL APPRAISAL TABLEQuestion Yes No Comments

Is the aim of the study clear?

Were the subjects randomized?

Was there a control condition?

Were subjects and experimenters masked?

Is the sample size adequate?

 Power calcs

Are the analysis methods appropriate?

 stats

Are there logical flaws in the paper?

 

Are the conclusions supported by the data?

 Stats

Are there conflicts of interest?

• Use the scale (1 to 5) above to answer the following questions

• I understand regression (as a general linear model)

• I can perform (and interpret) regression in SPSS

• I understand t-tests (both independent and paired)

• I can conduct a t-test in SPSS and also report the results

• I understand Type I and Type II errors

• I understand that all we are talking about is a general linear model

QUIZ5) Yes, I feel good about

this

1) Nope, no idea

2) Um.. Not sure

4) Okay3) Maybe with help

STATS REVIEWDo you know what you did last year?

REVIEW OF 2ND YEAR STATS• Correlation

• Regression

• T-tests

• Independent

• Dependent

• Chi Squared

• Non parametric tests

(aka what to do when assumptions are broken)

• Why do we need stats?• Evidence based practice- Appraisal

• Statistical models• The mean as a model• Sums of squares/fit/Variance

• Correlation• Graphs• Assumptions• Measuring Relationships

• Pearson r• R squared

• Non-parametric

Correlation Lecture outline

What is a Correlation?• It is a way of measuring the

extent to which two variables are related.• It measures the pattern of

responses across variables.• Observing what naturally goes on

in the world without directly interfering with it.

Things to know about the Correlation

It varies between -1 and +1• 0 = no relationshipIt is an effect size• ±.1 = small effect• ±.3 = medium effect• ±.5 = large effectCoefficient of determination, r2

• By squaring the value of r you get the proportion of variance in one variable shared by the other.

• There was no significant relationship between the number of adverts watched and the number of packets of toffee purchased, r = .87, p = .054.

• r = .87 is a large effect.• The sign of r is positive. As one variable increases, so

too does the other. Note that this doesn’t imply causation.

SPSS output

When interpreting a correlation coefficient there are 3 important things to consider.• The significance of r• The magnitude of r• The +/– sign of r

• Lets measure the number of friends that lecturers have.

• Mean doesn’t have to be a value that is actually observed in the data set. (e.g. 2.67 friends is not real)

The mean as a modelLecturer Number of

Friends

Kirsten 1

Sieu 3

Juno 4

Mean 8/3 = 2.67

Number of Friends (Kirsten) = Mean + Error related to (Kirsten)

1 = 2.6 + E

Slide 22

The Only Equation You Will Ever Need

ii errorModelOutcome The data we observe can be predicted from the model we

choose to fit to the data, plus some amount of error.

Number of Friends (Kirsten) = Mean + Error related to (Kirsten)

1 = 2.6 + E

Understand linear regression with one predictorUnderstand how we assess the fit of a regression model• Total Sum of Squares•Model Sum of Squares• Residual Sum of Squares• F• R2

Know how to do Regression on IBM SPSSInterpret a regression modelSlide 23

Linear Regression Aims

Artic Monkeys

Slide 24

b1• Regression coefficient for the

predictor• Gradient (slope) of the regression

line• Direction/Strength of Relationshipb0

• Intercept (value of Y when X = 0)• Point at which the regression line

crosses the Y-axis (ordinate)

iii XbbY 10

Describing a Straight Liney = mx + by = b + mx

So the model is ‘b + mx’y = model + error

Outcome: Album salesPredictor: $ spent on advertisingAlbum salesi = b0 + b1 advertising budget + Errori

Estimate the value of bs so that we can make a prediction about album sales based on advertising.Album salesi = 50 + (100 x advertising budget) + Errori

How much money do you want to spend on advertising per album? Say $5? Album salesi = 50 + (100 x 5) + Errori

= 550 + Errori

Predicted album sales is 550. This predicted value is not perfect.

Example of simple regression

Summary of Linear Regression• Simple regression is a way of predicting one variable from

another.• We do this by fitting a statistical model to the data in the

form of a straight line.• This line is the line that best summarises the pattern of

data.• We have to assess how well the line fits the data using:• R squared which tells us how much variance is explained by the

model compared to how much variance there is to explain in the first place. It is a proportion of variance in the outcome variable that is shared by the predictor variable.

• F, which tells us how much variability the model can explain relative to how much it can’t explain (i.e., it’s the ratio of how good the model is compared to how bad the model is).

• The b-value, which tells us the gradient of the regression line and the strength of the relationship between a predictor and the outcome variable. If its significant (Sig. < 0.05 in the SPSS table) then the predictor variable significantly predicts the outcome variable.

https://www.youtube.com/watch?v=ocGEhiLwDVc

Video

Comparing Means Lecture Outline• Hypothesis testing• Categorical predictors in the linear model.• Comparing means from a linear model perspectiveComparing Means. Rationale for the testsT-tests: Interpretation & Reporting results• Independent• Dependent (aka paired, matched)Calculating an Effect Size• Assumptions

Research hypothesis & Statistical hypotheses

Research hypothesis

Null hypothesis

Experimental

hypothesis

Do ‘great’ supervisors

produce better students?

No difference between students

Students with highly rated

supervisors will be rated better than students

with lower rated supervisors

Slide 30

The Only Equation You Will Ever Need

ii errorModelOutcome The data we observe can be predicted from the model we

choose to fit to the data, plus some amount of error.

Remember this…

Invisible cloak expAndy Field textbook

• In this case the outcome is membership of one of two groups.

• We are predicting the number of mischievous acts from whether or not someone was wearing a cloak.

• This is regression with one dichotomous predictor.• The b for the model will reflect the the differences between

the mean levels of mischief between the two groups.• The resulting t-test will tell us if the difference between the

means is zero.

Compare the differences between the means of two groups… a kind of regression

Outcome = Model + errorWe can use a linear model to compare means (Cohen, 1968).Yi = (b0 + b1X1i) + ErrorIMischiefi = (b0 + b1Cloaki) + ErrorI

Use dummy variable, 0 and 1 to represent cloak condition. No cloak is coded as 0.Wearing cloak is coded as 1.Ignoring the error (also called the residual)Mischiefi = (b0 + b1Cloaki)

For no cloakMeanNoCloak = b0 + (b1 x 0)b0 = 3.75.The intercept is equal to the mean of the no cloak group.

Mischiefi = (b0 + b1Cloaki)For cloak groupMeanCloak = b0 + (b1 x 1)MeanCloak = MeanNoCloak + b1b1 = MeanCloak - MeanNoCloak

Therefore b1 represents the difference between group means. We have seen that when you run a regression a t-test is used to ascertain the whether the b1 value is equal to zero. In this context it will be testing if the difference between group means is zero.

Constant = B0 = 3.75 = same as mean of the no cloak groupRegression co-efficient = B1 = 1.25 = difference between two group meanst-statistic = test of if b1 is sig different from zero. Which is a test of the difference between means.

t = 1.713, p =.101. As p<.05, if is not significant- there is not a meaningful/reliable difference between the two populations.

P363 of text

Dependent t-test• Compares two means based on

related data.• E.g., Data from the same people

measured at different times.• Data from ‘matched’ samples.

Independent t-test• Compares two means based on

independent data• E.g., data from different groups of

people

t-test

Significance testingTesting the significance of Pearson’s correlation coefficientTesting the significance of b in regression.

Rationale to the t-test continued

t =

observed differencebetween sample

means−

expected differencebetween population means(if null hypothesis is true)

estimate of the standard error of the difference between two sample means

We compare • the difference between the sample means that we collected

to• difference between the sample means that we would expect to obtain if there were no

effect (i.e. if the null hypothesis were true). Use the standard error as a gauge of the variability between sample means. If the difference between the samples we have collected is larger than what we would expect based on the standard error then we can assume one of two:• There is no effect and sample means in our population fluctuate a lot and we have, by

chance, collected two samples that are atypical of the population from which they came.• The two samples come from different populations but are typical of their respective parent

population. In this scenario, the difference between samples represents a genuine difference between the samples (and so the null hypothesis is incorrect).

t =

observed difference

between sample means

−expected differencebetween population means(if null hypothesis is true)

estimate of the standard error of the difference between two sample means

Page 365 of text

Compares two means based on independent dataE.g., data from different groups of people

Independent t-testOn average, participants given a cloak of invisibility engaged in more acts of mischief (M = 5, SE = 0.48), than those not given a cloak (M = 3.75, SE = 0.55). This difference, was not significant t(22) = −1.71, p = .101; however, it did represent a medium-sized effect d = .65.

Paired t-test

Cartoon-Guide-Statistics by Larry-Gonick

Type I and Type II ErrorsType I error• occurs when we believe that there is a genuine effect in our

population, when in fact there isn’t.• The probability is the α-level (usually .05)Type II error• occurs when we believe that there is no effect in the population when,

in reality, there is.• The probability is the β-level (often .2)

TYPE I AND II ERRORS

http://www.economistsdoitwithmodels.com/2010/02/17/before-you-go-locking-up-all-of-those-crazy-people/

• https://www.youtube.com/watch?v=y4WyuiWK6lw

THE T STATISTIC AND THE P VALUE

Slide 44

Chi Squared LectureOutlineStatistical• Categorical Data• Contingency Tables• Chi-Square test• Likelihood Ratio Statistic• Odds Ratio

Diagnostic• Sensitivity • Specificity

Likelihood ratios in diagnostic testing.

Slide 45

To Sum Up …We approach categorical data in much the same way as any other kind of data:• we fit a model, we calculate the deviation between our model and the

observed data, and we use that to evaluate the model we’ve fitted.• We fit a linear model.

Two categorical variables• Pearson’s chi-square test• Likelihood ratio test

Effect Sizes• The odds ratio is a useful measure of the size of effect for categorical

data.

We will learn the theory behind and how to analyse in SPSS 3 non-parametric tests.These tests are relevant for comparing 2 means.

When independent t-test assumptions are broken use:The Wilcoxon rank-sum (Ws) test OrMann–Whitney (U) test

When paired t-test assumptions are broken use:Wilcoxon signed-rank (T) test

Non-Parametric testsLecture Outline

END OF STATS REVIEWDo you know what you did last year?

Use the scale (1 to 5) above to answer the following questions• I understand regression (as a general linear model)• I can perform (and interpret) regression in SPSS• I understand t-tests (both independent and paired)• I can conduct a t-test in SPSS and also report the results• I understand Type I and Type II errors• I understand that all we are talking about is a general linear model

Quiz 5) Yes, I feel good about this

1) Nope,

no idea

2) Um.. Not sure

4) Okay3) Maybe with help

http://www.uk.sagepub.com/field4e/main.htm

49

http://www.uk.sagepub.com/field4e/study/default.htm

CONNECTING TO EBP ONLINE1) Spend some time looking at the textbook website. Set up mobile study if you like (10mins) http://www.uk.sagepub.com/field4e/study/default.htm

2) Hook up to EBP social media (10 mins)

Twitter examples

• @EBPoptometry

• @EvidenceMatters

• @EBMOnline

• @cochranecollab

Online examples

• http://www.badscience.net/about-dr-ben-goldacre/

• http://www.facebook.com/evidencebasedoptometry

• http://www.cochrane.org/about-us

• http://evidencebasedmedicine.com.au/

50

YOUR HOMEWORK TO COMPLETE BEFORE NEXT WEEK:

IMPROVE YOUR STATS CONFIDENCE.

Do you have any answers under 4?