If observations are given a qualitative value then the data are said to be categorical (i.e. they have been assigned to categories). There are many occasions when it is not possible to express data in any other way (such as when scoring flower colors or species). There will be other circumstances when the categories are for convenience only Authentic T.Y. Hilton Jersey , and are achieved by imposing a set of categories on a continuous scale. This can either be an arbitrary scale (e.g. the effect of an illness from ‘well’ through ‘showing symptoms’ to ‘dead’) or a scale that could be measured. However, if the observations are assigned to categories in this way there are several tests that can be applied to determine whether the division of the observations into classes is independent or not. In other words ‘are the observations for two categorical variables associated?’
• Phi coefficient of association
This is a special case of the Cramer coefficient for 2×2 tables (i.e. there are only two categories for each of the two variables). It is used in combination with the chi-square test as it generates a value (rφ) that ranges from 0 to 1, indicating a range from no association through to perfect association. It can be calculated directly after a chi-square test has been carried out as it is equal to the square root of the value of X2 after it has been divided by the number of observations. If each individual observation is assigned a meaningful numerical value in two variables there are several tests that may be applied to determine whether the two sets of observations are associated or correlated Authentic Andrew Luck Jersey , the strength of the correlation and whether it is significant or not.