6 How to Identify and Change the Level of Measurement of Variables What is the Problem? AH variables can be classified as having a particular level of measurement. Many statistical techniques require that variables are measured at a particular level, so knowing the level or measurement of a variable is crucial when working out how to analyse (he variable. Failing to correctly match the statistical method to a variable's level or measurement leads either to nonsense results or to potentially misleading results. Tliere are three key questions to resolve in relation Pi the level of measurement or variables: " How can we work out the level of measurement of any variable? • Which level of measurement is best? • How fixed are the rules regarding level of measurement? What does level of Measurement" Mean? The level of measurement of a variable refers to how the categories or values of the variable are arranged In relation to each other. There Aie four main levels of measurement: ratio, interval, ordinal and nominal. However, for the purpose of the statistical methods discussed in this book we do not need to distinguish between the ratio and interval levels. Accordingly I will use the term 'interval' level to include ratio-level variables. The level of measurement of a variable depends on whether • there are different categories; • the categories can be rank-ordered; • the differences or intervals between each category can be specified in a meaningful numerical sense. How to identify and ctiunge the level of measurement ul variables Interval Level An interval-level variable has all tliree characteristics and is therefore regarded as being at the highest level of measurement. An interval variable consists of valuei that can be expressed in numerically meaningful terms. For example, age, weight, height, income, and number of children in a family are all interval variables for which the numbers that represent the values of the variable are numerically meaningful (compared with codes of 1 and 2 to represent gender, where the codes have no numeric meaning). The numerical values of an interval level variable are organizťd in order - from the lowest to the highest value or vice versa. Finally, since the values of interval variables are numerically meaningful we can specify the amount of difference (or the interval) between cases with different values. Thus we can say that (he difference between a person with a value of 20 and a person with a value of 15 on the age variable is 5 years. Otdinal Level An ordinal variable is one where we can rank-order categories from low to high. However, v-'C cannot specify numerically how much difference there is between the categories. For example, when age has the categories 'child', 'adolescent', 'young adult', 'middle-aged' and 'elderly' it is measured at the ordinal level. The categories can be ordered from youngest to oldest, but we cannot specify precisely the age gap between people in different categories. Nominal Level A nominal variable is one where the different categories have no set rank order. For example, religious affiliation is a nominal variable where we can distinguish between categories of affiliation (e.g. Jewish, Roman Catholic, Orthodox, Protestant, Islamic, no religion) but eannot rank these categories as having an obvious order. How to Work out a Variable's Level of Measurement Figure 6.1 provides a summary of the distinction between levels of measurement. To work out the level of measurement of a variable, ask yourself how many of the cliaracteristics in the first column of the figure your variable has. Analysing social science data N »man c a IV m o» niti U liti Mámil IrJÍMVAl CaierjOffoiJvolues can ba rank-ordered OROINAL Different caiegaiiei/values NOMINAL lO.VUSl Inval Figuro B. I Dilliřfůncos hatwaoa lovols oimoastiiuiiivnf H.flhůU l liolotürf Torms 'ľhete can be some confusion when reading lexis and selecting statistics since some authors use terms other than nominal, ordinal and interval, while others use other sets of terms interchangeably with level-of-measurement terminology {see Table 6.1). • Qualitative and quantitative. Qualitative variables are those where the codes have no inherent numerical meaning (as with nominal variables), while quantitative variables are those when; the codes do have a numerical meaning (interval variables). Tliis distinction does not recognize ordinal variables and thus makes it unclear how they aru to be analysed. • Categorical and mimetic. This is equivalent to the qualitative—quantitative distinction. • Discrete and continuous. A discrete variable is one with distinct categories, while a continuous variable will have a potentially unbroken set of values between the low and high values. Nominal and ordinal variables will normally havediscrele categories and interval variables will frequently Inj continuous. Unfortunately this is not always the case, as some interval variables can be thought of as discrete variables. For example, the number of children a person has is an interval variable that is also discrete - the number of children a person lias must be one of ihe discrete 42 How to identify and change ihe level m measurement of variables Toblu B.l Synonyms tot ttífíetont tevols o!moasufonioiil Level Other terms M.i n i. r Categorical; qualitative, di-mclc Ordinal Qualitative, dlHMM Interval /ml in Numerical, conUnuou», qn.-mliUlivc values 0, 1, 2, 3, ... ; it cannot be, for example, 1.23543. Dichotomous variables can also be regarded as discrete interval-level variables (see below). low and High Levels of Measurement Nominal-level variables are regarded as having the lowest level of measurement. The codes of the variable contain the least information - they only indicate the existence of difference. Interval variables are regarded as being at the highest level of measurement since the codes contain at least three types of information about cases - existence of difference, order and Ihe aniounl of difference between cases. What is Iho Boat Lovol of Moasuromont? From a statistical pcrspecUve interval-level variables arc (he most desirable. • An interval-level variable conveys much more information about cases and their relation to one another than does a nominal or ordinal variable. The more we know about cases the more powerful a variable should bc in explaining phenomena. • The most powerful statistical methods assume that variables are measured at the interval level. Using nominal or ordinal variables restricts the available methods of analysis. However, statistical requirements are not the only consideration. Many social science variables simply are not interval and cannot be measured at Ihe interval level (e.g. elhnicity, religious group, gender, family type). Furthermore, while interval-level measurements result in more precise data, these measurements are not necessarily more aeeumtt. For example, if we ask people how many limes they attended religious services in the lasl 12 months they may provide a precise number of times but this will not necessarily be correct. Sometimes Ihe more precision we seek the greater the cliance of obtaining inaccurate answers. :.:■