14-12-13 1 Magdy Ibrahim Mostafa Prof. Obstetrics & Gynecology, Faculty of Medicine, Cairo University Director; Research, Biostatistics & IT Units, MEDC, Cairo University Management member; EBM Unit, MEDC, Cairo University Scientific Council Member, Egyptian IT Fellowship Board Member, Egyptian Ob/Gyn Fellowship Associate Editor; Kasr Al Aini Journal of Obstetrics and Gynecology Peer Reviewer; Gyn Endocrin J, Gyn Oncol J, Obstet Gynecol Invest Journal Peer Reviewer; Cairo University Medical Journal, Kasr El Aini Medical Journal, MEFS Journal.y
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14-12-13
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Magdy Ibrahim MostafaProf. Obstetrics & Gynecology, Faculty of Medicine, Cairo University
Director; Research, Biostatistics & IT Units, MEDC, Cairo University
Management member; EBM Unit, MEDC, Cairo University
Scientific Council Member, Egyptian IT Fellowship
Board Member, Egyptian Ob/Gyn Fellowship
Associate Editor; Kasr Al Aini Journal of Obstetrics and Gynecology
� Truncation of range: Underestimate strength of relationship if you can’t see full range of x value
� No proof of causation
Testing hypothesis
� Pearson correlation coefficient describes the correlation between the sample observations on two variables in the same way that ρdescribes the relationship in a population
� Thus we need to knowing if we may conclude that ρ # 0
� The hypotheses are:
� H0: ρ = 0 (no correlation in the population)
� Ha: ρ ≠ 0 (there is correlation in the population)
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Testing hypothesis
� The test used is the t test (revise t test uses)
� Statistically significant doesn’t mean clinically important or useful
� If you are examining many correlations coefficients, have to use the Bonferroni adjustment
Coefficient of determination
� The square of Pearson cc, r2, is the proportion of variation in
the values of y that is explained by the regression model with x
� Amount of variance accounted for in y by x
� Percentage increase in accuracy you gain by using the
regression line to make predictions
� 0 ≤ r2 ≤ 1 (100%)
� The larger r2 , the stronger the linear relationship
� The closer r2 is to 1, the more confident we are in our
prediction
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Coefficient of determination
Example
� Topography of adipose tissue (AT) is associated with metabolic complications considered as risk factors for cardiovascular disease
� To measure the amount of intraabdominal AT as part of the evaluation of the cardiovascular-disease risk of an individual. Computed tomography (CT), the only available technique that precisely and reliably measures the amount of deep abdominal AT, however, is costly, exposes the subject to irradiation and is not available to many physicians
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Example
� Despres and his colleagues conducted a study to develop equations to predict the amount of deep abdominal AT from simple anthropometric measurements
� Among the measurements taken on each subject were deep abdominal AT obtained by CT and waist circumference. The question of interest is how well can deep abdominal AT correlates to waist circumference
Spearman Correlation
� It is a measure of the strength and direction of association that exists between two variables measured on at least an ordinal scale
� It is denoted by the symbol rs, R
� The test is used for either ordinal variables or for interval/ratio data that has failed the assumptions necessary for conducting the Pearson's product-moment correlation
� The values of the variables are converted in ranks and then correlated
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Spearman Correlation
Assumptions:
1. Variables are measured on an ordinal, interval or ratio scale
2. Variables need NOT be normally distributed
3. There is a monotonic relationship (either the variables increase in value together or as one variable value increases the other variable value decreases) but linearity is not needed
4. This type of correlation is NOT very sensitive to outliers