Correlational analysis
Introduction
In nursing research, examining relationships between variables are often of interest and correlation is a common statistical technique employed to perform the task. Correlation refers to how closely two or more variables are related. In correlational analysis, magnitude and direction of linear relationships between variables would be estimated and the statistical significance1 needs to be tested, where the null hypothesis is that there is no relationship between the variables and the alternative hypothesis is that a relationship exists.2 Once a relationship has been established using correlational analysis, a model can be created that allows the researcher to use an explanatory variable to predict an outcome variable, which is a statistical technique known as simple linear regression. A causal relationship can be established using regression. However, correlational analysis is only appropriate to explore relationship between variables and not to infer causal relationship.
Bivariate, partial and multiple correlational analyses are common variants of correlational analysis. Bivariate correlation measures the relationship between two variables. Partial correlation examines the relationship between two variables while taking into consideration the effect of a third variable.3 Multiple correlation examines the correlation between the outcome variable and the combined effect of other predictors.3 Statistical software has become a common tool to compute different correlation statistics. The aim of this paper is to outline different approaches used to examine bivariate relationships of interval/ratio, ordinal and nominal variables4 and demonstrate the use of correlational analysis using examples from published research.
Section snippets
Correlation analysis using interval/ratio variables
Correlational analysis in interval/ratio variables prerequisites confirming a linear relationship and no outlier in the data using Scatterplots. Fig. 1A suggests a positive linear relationship between X and Y, where as X increases, Y also increases. Fig. 1B suggests a negative linear relationship, where as X increases, Y decreases. Fig. 1C shows that the points on the graph are scattered randomly and depicts no apparent linear relationship. No outliers are present in Fig. 1.
The most commonly
Correlation analysis using ordinal variables
The most common test statistic used to examine the association between ordinal variables is the Spearman's rank-order correlation (rs), also referred to as Spearman's rho [ρ].5 Spearman's correlation coefficient is a measure of correlation which uses rank order to determine the magnitude and direction of relationship between two sets of ranked data. Similar to the Pearson's r, values for Spearman's correlation coefficient vary between −1.00 and +1.00 and can be interpreted in a similar fashion.
Association with nominal variables
Relationship between nominal variables can be assessed by cross-tabulating data in a contingency table9 and computing the Pearson's Chi-square statistic (χ2). The computed Chi-square value can be tested for statistical significance where the null hypothesis is no relationship exists between the variables. Most statistical packages produce χ2 along with the p-value. The existence of a relationship between nominal variables can be determined using the χ2 statistic. However, the strength of the
Summary
This paper has presented different approaches used to conduct correlational analysis based on different types of variables. Pearson's correlation is appropriate for interval/ratio variables; Spearman's correlation and Kendall's Tau appropriate for ordinal variables and Pearson's Chi-square with Phi coefficient or Cramer's V appropriate for nominal variables. Correlational analysis is a statistical technique employed in measuring linear relationships between variables. A causal relationship
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