Under the assumption that the ordinal variables are derived from the discretization of two unobserved quantitative random variables with a normal distribution, the polychoric correlation coefficient aims to measure the relation between those two unobserved quantitative variables. It is frequently used to analyze survey data with ordinal responses. The polychoric correlation coefficient characterizes the relation between two ordinal variables. The latter is known as being reliable when there are more than eight observations. When the number of observations is lower than 50 and when there are no ties, XLSTAT gives the exact p-value. It can be interpreted in terms of probability - it is the difference between the probabilities that the variables vary in the same direction and the probabilities that the variables vary in the opposite direction. It can be thus be considered as non parametric. It is well suited for ordinal variables as it is based on ranks.
One can interpret this coefficient in terms of explained variability of the ranks. It can be thus be considered as non parametric. This coefficient is adapted to ordinal data. The Spearman coefficient is based on the ranks of the observations and not on their value. However, one needs to be cautious when interpreting these results, as if two variables are independent, their correlation coefficient is zero, but the reciprocal is not true. The p-values that are computed for each coefficient allow testing the null hypothesis that the coefficients are not significantly different from 0.
Note: the squared Pearson correlation coefficient gives an idea of how much of the variability of a variable is explained by the other variable. Its value ranges from -1 to 1, and it measures the degree of linear correlation between two variables. This coefficient is well suited for continuous data. The Pearson coefficient corresponds to the classical linear correlation coefficient. XLSTAT proposes three correlation coefficients to compute the correlation between a set of quantitative variables, whether continuous, discrete or ordinal: Pearson correlation coefficient This tool to compute different kinds of correlation coefficients, between two or more variables, and to determine if the correlations are significant or not.
0 kommentar(er)
