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==Correlation coefficients==

==Correlation coefficients==

Correlation coefficients are used when comparing two [[Data types#Quantitative data|quantitative variables]], and are based upon the '''covariance''' between these variables amongst the individuals in the study population. The covariance can be viewed as how the two variables of interest differ in individuals in relation to their mean values in the whole population, but put more simply, is a measure of how two different variables change in relation ''to each other''. As the magnitude of this variable will depend upon the magnitudes of the variables in question, this value is 'standardised' in order to give a correlation coefficient, which lies between -1 (indicating a perfect negative correlation) and +1 (indicating a perfect positive correlation), with a coefficient of 0 indicating no correlation. Therefore, correlation coefficients measure how closely associated the two variables of interest are to each other.

Correlation coefficients are used when comparing two [[Data types#Quantitative data|quantitative variables]], and are based upon the '''covariance''' between these variables amongst the individuals in the study population. Strictly speaking, the covariance is a measure of how two variables differ in individuals in relation to their mean values in the whole population - or put more simply, it is a measure of how the variables change in relation ''to each other''. As the magnitude of the covariance will depend upon the magnitudes of the variables in question, this value is 'standardised' in order to give a correlation coefficient, which lies between -1 (indicating a perfect negative correlation) and +1 (indicating a perfect positive correlation). A coefficient of 0 indicates no correlation, and therefore correlation coefficients are a useful measure of the strength of association between quantitative variables.

==Ratio measures==

==Ratio measures==

Although correlation coefficients are commonly used in statistical studies, epidemiological investigations often deal with binary exposures and outcomes (such as presence or absence of a proposed risk factor for disease, and presence or absence of disease itself). Therefore, '''ratio measures''' such as the '''prevalence ratio''', the '''risk ratio''', the '''rate ratio''' and the '''odds ratio''' are commonly used as measures of strength of association in epidemiological studies.<br>

Although correlation coefficients are commonly used in statistical studies, epidemiological investigations often deal with binary exposures and outcomes (such as presence or absence of a proposed risk factor for disease, and presence or absence of disease itself). Therefore, '''ratio measures''' such as the '''prevalence ratio''', the '''risk ratio''', the '''rate ratio''' and the '''odds ratio''' are commonly used as measures of strength of association in epidemiological studies.<br>

Understanding how these measures are calculated is best approached using a contingency table (also known as a cross tabulation), as shown below. In the columns, the individuals are divided into exposed and unexposed, whilst in the rows, individuals are divided into those who are diseased and those who are not diseased. Therefore, cell 'm₁' represents all diseased individuals, cell 'n₁' represents all exposed individuals, and cell 'a₁' represents exposed individuals who are also diseased.

Understanding how these measures are calculated is best approached using a '''contingency table''' (also known as a '''cross tabulation'''), as shown below. In this table, the columns divide all individuals into ''exposed'' and ''unexposed'', whilst the rows divide individuals into those who are ''diseased'' and those who are ''not diseased''. Therefore, cell 'm₁' represents all diseased individuals, cell 'n₁' represents all exposed individuals, and cell 'a₁' represents exposed individuals who are also diseased.

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The measures of disease frequency which could be extracted from this table will depend on the [[Study design|study design]] used, which will be [[Study design#Analytic studies|analytic]] in nature, as data regarding exposure has been collected.<br>

The measures of disease frequency which can be extracted from this table will depend on the [[Study design|study design]] used, which will be [[Study design#Analytic studies|analytic]] in nature, as data regarding exposure have been collected.<br>

In the case of a [[Study design#Cross sectional studies|cross sectional study]], the '''[[Measures of disease frequency#Prevalence|prevalence]]''' can be estimated amongst exposed individuals as (a₁/n₁), and amongst unexposed individuals as (a₀/n₀).<br>

In the case of a [[Study design#Cross sectional studies|cross sectional study]], the '''[[Measures of disease frequency#Prevalence|prevalence]]''' can be estimated amongst exposed individuals as (a₁/n₁), and amongst unexposed individuals as (a₀/n₀).<br>

In the case of a [[Study design#Cohort studies|cohort study]], the '''[[Measures of disease frequency#Incidence risk|incidence risk]]''' can be estimated amongst exposed individuals as (a₁/n₁), and amongst unexposed individuals as (a₀/n₀). Alternatively, the [[Measures of disease frequency#Incidence rate|incidence rate]] can be estimated as (a₁/[total number of animal-time units in exposed group]) amongst exposed animals and (a₁/[total number of animal-time units in unexposed group]) amongst unexposed animals.<br>

In the case of a [[Study design#Cohort studies|cohort study]] or a [[Study design#Experimental studies|randomised controlled trial]], and assuming that the disease status relates only to ''new'' cases of disease, the '''[[Measures of disease frequency#Incidence risk|incidence risk]]''' can be estimated amongst exposed individuals as (a₁/n₁), and amongst unexposed individuals as (a₀/n₀). Alternatively, the [[Measures of disease frequency#Incidence rate|incidence rate]] can be estimated, if the total animal-time for each exposure group is known, as (a₁/[total number of animal-time units in exposed group]) amongst exposed animals and (a₁/[total number of animal-time units in unexposed group]) amongst unexposed animals.<br>

In the case of a [[Study design#Case control studies|case control study]], no [[Measures of disease frequency|measures of disease frequency]] can be calculated. However, the '''odds of exposure''' can be estimated amongst diseased individuals as (a₁/a₀), and amongst nondiseased individuals as (b₁/b₀).<br>

In the case of a [[Study design#Case control studies|case control study]], no [[Measures of disease frequency|measures of disease frequency]] can be calculated, as selection of individuals was based upon their disease status. However, the '''odds of exposure''' can be estimated amongst diseased individuals as (a₁/a₀), and amongst nondiseased individuals as (b₁/b₀).<br>