ANOVA test and correlation
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The document discusses statistical methods for analyzing continuous variables, specifically focusing on the ANOVA test and correlation analysis. It outlines the criteria for using ANOVA, including comparisons between independent groups and assumptions such as normal distribution and equal population variances. Additionally, it addresses correlation analysis, emphasizing the interpretation of the correlation coefficient and the limitations of correlation in establishing causation.
ANOVA test and correlation
- 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 2
- 3. Which parametric test to use 3 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? 4
- 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 5
- 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) 6
- 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 7
- 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. 8
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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. 11
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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 13
- 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 14
- 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 15 Magnitude of ‘r’ determines the strength of association Usually scatter plot is used to determine if any relation exists. r value‘0’- No correlation
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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 20
- 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 21
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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 27
- 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 28
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