ebd1 lecture 8 2010

General Studies 1

(Community dentistry 1)

Lecture 8

Correlation & RegressionCorrelation & Regression

Dr. Nizam AbdullaDr. Nizam Abdulla

© The University of Adelaide, School of Dentistry

What is Correlation?

• Correlation is a measure of association between two continuous variables

• Eg: To measure/describe relationship between 2 numerical variables (cholestrol and mean blood pressure)– Are the two variables associated?– In which direction does the relationship ~

positive or negative– What is the strength of the association


Direction of correlation

• Positive correlation– If X increases Y will increases

• Negative correlation– If X increases Y will decreases


What is Correlation?

Eg. We want to measure the association between

1. age and knowledge score 2. Cholestrol level and mean blood

pressure

It estimates both the direction and the strength of the relationship between variables.


Is there a Correlation ?


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r = 0.98 r = 0.78

r = 0.62 r = 0.32 r = 0.08

‘r’ = Pearson’s Correlation Coefficient (i.e. a measure of strength of correlation)


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r = + 0.98 r = - 0.94

r = 0

Therefore, r can be –1 to +1

r = 0 means “no correlation.


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r = + 0.98 r = - 0.94

r = 0

If …… r > 0.75V.good-perfect correlation r > 0.50 – < 0.75Moderate-good correlation r > 0.25 - < 0.50Fair correlation r < 0.25little or no correlation

Colton T: Statistics in Medicine. Little, Brown, 1974.


Eg: We want to measure association between age and knowledge score

What hypothesis ?Ho: ρ = 0 (there is no correlation between age and knowledge score); Ha: ρ ≠ 0 (There is correlation between age and knowledge score)

(‘ρ’) = Population


The correlation (Pearson’s) between age and knowledge score is significantly different from zero (P<.001). In other words, there is significant (linear) correlation between age and knowledge score.

The observed correlation coefficient (r) is -.719, which suggests negative and moderate to good correlation (Colton, 1974).


Correlation..summary

Correlation

Strength of association

Direction of association

Any association? P-value

Scatter plotNegative or

positive

Correlation Coefficient (r)

Correlation


Correlation and Regression• Two most common methods used to describe

the linear relationship between two quantitative (numerical) variables (x and y) are correlation and linear regression

• The correlation coefficient is the statistic that measures the strength of the linear relationship between two variables

• The regression line is a prediction equation that estimates the value of y for any given x


• Application depends upon research question; For example– Is there a linear relationship between the

two variables?• Both correlation and regression

– What is the strength of linear relationship?• Correlation

– What will be the increase in the GPA by increasing the average study hours----Prediction

• We use the regression analysis (y= ßo+ß1x)

Difference between Correlation and Regression


Regression equation

A linear regression line has an equation of the form Y = a + bx, where x is the explanatory variable and Y is the dependent variable.

The slope of the line is b, and a represent the y intercept

0,0 1 2 3x

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y = a + (b * x)Dependent = Constant + (slope*Independent)

y = 5 + (2.5 * x)


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Simple Linear Regression

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Slope, b isRegression Coefficient

Slope, b isRegression Coefficient

e.g. b = 1.5 means:mean knowledge score will be1.5 points more, when age is a year older.

e.g. b = 1.5 means:mean knowledge score will be1.5 points more, when age is a year older.


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b = + 15 b = - 15

b = 0

Therefore, b can be –α , 0, +α

b = 0 means “no relationship. b = + means “upward trend” b = - “downward”


Regression (cont.)

If we fit a straight line to our height and weight data we end up with the following equation:

height = 136.898 + 0.519 weight

This straight line will allow us to predict any person's height from a knowledge of that person's weight.Example: We can predict the height of EBD1 students who weigh 55kg: The prediction is height = 136.898 + (0.519 x 55kg) = 165.44cm

The most interesting parameter in a linear model is usually the slope. If the slope is zero, the line is flat, so there's no relationship between the variables.

In this example, the slope is about 0.519 cm per kg (an increase in height of 0.519cm for each kg increase in weight).


Regression (cont.)

Simple linear regression and multiple linear regression are appropriate when the dependent variable is continuous.

Logistic regression is appropriate when the dependent variable is categorical (or dichotomous).


The effectiveness of fissure sealants in preventing caries has been well established in randomised clinical trials. However, there is less consistent evidence of fissure sealant effectiveness from community dental programs. In addition, there are unequivocal findings on the relationship between the effectiveness of fissure sealants and exposure to fluoridated water.

Methods:

The current cohort study examined 4–15 yr-old children across a period of between 6 mths and 3.5 yrs (mean=2 yrs). Oral health data were obtained as part of regular examinations and questionnaire data on residential and water consumption history was provided by parents or guardians.

Results:

A sub-group of 791 people (mean age=10.5 yrs) was selected with one contralateral pair of permanent first molars at baseline where the occlusal surface of one molar had been fissure sealed while the paired surface was diagnosed as sound. The caries incidence of the fissure sealed occlusal surfaces was 5.6% compared to 11.1% for sound surfaces (p<.001), demonstrating a 50% reduction in caries incidence for sealed vs non-sealed surfaces.

An example of a research finding


Children were divided into 3 categories of per cent lifetime exposure to optimally fluoridated water, 0%, 1–99% and 100%. Per cent reduction in caries increment attributable to fissure sealing increased across fluoridated water exposure categories - a 36.2% reduction was found for children with 0% exposure (p>.05), a 44.8% reduction for children with intermediate exposure (p<.01), and an 82.4% reduction for children with 100% lifetime exposure to fluoridated water (p<.001).

Conclusion:

The effectiveness of fissure sealants in community-based programs may be further improved when coupled with increased lifetime exposure to optimally fluoridated water.


Townsend GC. Biostatistics - The foundation of evidence-based dentistry. A self-instructional teaching manual available from the ICC

Bulman JS, Osborn JF (1989) Statistics in dentistry, British Dental Association, London.

Moore DS, McCabe GP (1998) Introduction to the practice of statistics, W.H. Freeman, New York.

Burt BA, Eklund SA (2005) Dentistry, dental practice, and the community, 6th ed. Elsevier Saunders, St. Louis.

Suggested reading

THE END

ebd1 lecture 8 2010

Health & Medicine