If more than two groups of data, Estimating the difference in a quantitative/ continuous parameter between more than 2 independent groups - ANOVA TEST

1. ANALYSIS OF
CONTINUOUS
VARIABLES
(ANOVA test & Correlation)
Dr Lipilekha Patnaik
Professor, Community Medicine
Institute of Medical Sciences & SUM Hospital
Siksha ‘O’Anusandhan deemed to be University
Bhubaneswar, Odisha, India
Email: drlipilekha@yahoo.co.in

2. Session Objectives
• ANOVA test
• Correlation
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3. Which parametric test to use
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Outcome/
dependent
variable
Exposure/
independent
variable
Continuous
variable
Normally
Distributed
2 related group
..
One group
…..
2 independent
group
Continuous
variable
Normal dist.
Categorical
variable
> 2 independent
group
One sample ..
t test
Paired sample
t test
Unpaired
sample t test
ANOVA Test
…..
Pearson
correlation test

4. • If more than two groups of data
• Estimating the difference in a quantitative/ continuous parameter
between more than 2 independent groups.
- ANOVA TEST
How many groups and between whom we are comparing?
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5. If means are significantly different:
• The independent variable has an effect on the
dependent variable
• Compare the blood sugar of Heavy Smokers, mild
smokers and Non-smokers.
• Independent groups,>2 groups
• Quantitative/Continuousvariable
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6. When to choose ANOVA?
• Criterion 1: Comparison between groups
Eg: Compare the birth weight of children born to mothers in different BMI
groups (Under weight, Normal, Over weight/Obese)
• Criterion 2: More than 2 groups
Eg.- Comparison between 3 BMI groups
• Criterion 3: The groups are independent
Eg.- Subjects can only belong to either one of the BMI groups i.e.:
(Under weight, Normal, Over weight/Obese)
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7. Cont.
• Criterion 4: Dependent variable is continuous/quantitative
(in other words one should be able to compute the mean of the
measured variable)
eg.: The variable to be compared (birth weight) measured in grams is a
continuous variable
• Criterion 5: The data should follow normal distribution in each group
of the sampled population.
Eg: Birth weight data follows normal distribution in Under weight,
Normal, Over weight/Obese
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8. Additional assumption for ANOVA
• The population variances should be equal
Eg: The amount of variation of birth weight in Under weight, Normal,
Over weight/Obese.
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11. Post-hoc tests
• Further analysis to understand how the groups differ.
• If the F-test is significant, you have a difference in population
means. But you don’t know where.
• We need a test to tell which means are different.
• Bonferroni/ Tukey HSD should be done.
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13. • Used to predict the association between two continuous variables.
• Eg. Correlation between systolic blood pressure and cholesterol
levels
• We estimate correlation coefficient (Pearson Product Moment
Correlation coefficient).
Correlation analysis
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14. • The sample correlation coefficient, denoted by r
• This quantifies the direction and strength of correlation.
• Direction may be
• Positive:Positivechangein one producespositivechangein the other
• Negative: Positivechange in one producesnegativechangein the other
• Ranges between +1 and -1
Correlation coefficient
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15. r value Nature of correlation
(Negative correlation)
r value Nature of correlation
(Positivecorrelation)
-1 Absolute correlation +1 Absolute correlation
-0.9 to -1 Very high correlation +0.9 to +1 Very high correlation
-0.7 to -0.9 High correlation +0.7 to +0.9 High correlation
-0.5 to -0.7 Moderate correlation +0.5 to +0.7 Moderate correlation
-0.3 to -0.5 Low correlation +0.3 to +0.5 Low correlation
0 to -0.3 Negligible correlation 0 to +0.3 Negligible correlation
Degree of correlation
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Magnitude of ‘r’ determines the strength of association
Usually scatter plot is used to determine if any relation exists.
r value‘0’- No correlation

16. Correlation table
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20. Scatter plot
The pattern of data is indicative of the type of relationship between
two variables:
Øpositive relationship
Ønegative relationship
Øno relationship
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21. Scatter plot
• No Correlation (r = 0)
• Random or circular assortment of dots
• Positive Correlation (r > 0)
• ellipse leaning to right
• Age of children and height
• Age and SBP
• Negative Correlation (r < 0)
• ellipse learning to left
• Depression & Self-esteem
• Hours of studying & test errors
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27. • Failure to consider a third variable related to both and responsible for
the results of correlation can be omitted (Confounders).
• Can not establish causation.
• Non-linear relationship, though may exist, may not become visible in
correlation analysis.
Limitations of correlation
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28. Take Home Messages
• Difference in a quantitative/ continuous parameter between 2
independent groups -Unpaired T-test/ Independent samples T –test
• Difference in a quantitative/ continuous parameter between paired
data from one sample - Paired T-test
• Difference in a quantitative/ continuous parameter between more than
2 groups – ANOVA
• Association between two continuous variables – Correlation
• Predict the value of one variable corresponding to a given value of
other variable - Regression
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