Interval Scale

Abstract: The Likert scale is widely used in social work research, and is commonly constructed with four to seven points. It is usually treated as an interval scale, but strictly speaking it is an ordinal sc...

Abstract: The ease of likert scale on its contruction as a measurement scale of individual traits must be cautioned to prevent some errors in the data analysis. Some researchers consider likert scale as an interval scale, while the others mention likert scale as an ordinal scale. After reviewing some papers from some different authors, we argue that a likert scale using total score of all items is an interval scale. On the other hand, items using likert format is an ordinal scale. The number of responses in the likert scale suggested is 7 based on responden’s preference that of they like it the most. Moreover, the 7 response format has a good reliability, validity, discriminating power, and test-retest (stability) index. Keywords : interval , likert , measurement, ordinal, scale

Abstract: Many statistical procedures used in educational research are described as requiring that dependent variables follow a normal distribution, implying an interval scale of measurement. Despite the desirability of interval scales, many dependent variables possess an ordinal scale of measurement in which the differences among values composing the scale are unequal in terms of what is being measured, permitting only a rank ordering of scores. This means that data possessing an ordinal scale will not satisfy the assumption of normality needed in many statistical procedures and may produce biased statistical results that threaten the validity of inferences. This article shows how the measurement technique known as item response theory can be used to rescale ordinal data to an interval scale. The authors provide examples of rescaling using student performance data and argue that educational researchers should routinely consider rescaling ordinal data using item response theory.

Abstract: A special type of ordinal scale comprising a number of intervals of known numeric ranges can be used when estimating severity of a plant disease. The interval ranges are most often based on the percent area with symptoms [e.g. the Horsfall–Barratt (H–B) scale]. Studies in plant pathology and plant breeding often use this type of ordinal scale. The disease severity is estimated by a rater as a value on the scale and has been used to determine a disease severity index (DSI) on a percentage basis, where DSI (%) = [sum (class frequency × score of rating class)]/[(total number of plants) × (maximal disease index)] × 100. However, very few studies have investigated the effects of different scales on accuracy of the DSI. Therefore, the objectives of this study were to investigate the process of calculating a DSI on a percentage basis from ordinal scale data, and to use simulation approaches to explore the effect of using different methods for calculation of the interval range and the nature of the ordinal scales used on the DSI estimates (%). We found that the DSI is particularly prone to overestimation when using the above formula if the midpoint values of the rating class are not considered. Moreover, the results of the simulation studies show that, if rater estimates are unbiased, compared with other methods tested in this study, the most accurate method for estimation of a DSI is to use the midpoint of the severity range for each class with an amended 10% ordinal scale (an ordinal scale based on a 10% linear scale emphasising severities ≤50% disease, with additional grades at low severities). As for biased conditions, the accuracy for calculating DSI estimates (%) will depend mainly on the degree and direction of the rater bias relative to the actual mean value.