The correct answer is C, E, B only.
Key Points
Multicollinearity: Multicollinearity refers to a high degree of correlation between independent variables in a multiple regression model. If such a correlation is found, it makes it difficult to understand the effect of each individual variable. However, multicollinearity is generally a consideration in the model-building step, not in scale selection and construction. Scales are employed to structure responses and don't deal directly with the relationship between multiple predictors.
Data properties: The nature of the data you are working with can greatly influence the choice and construction of scale. Data properties may include characteristics such as distribution (normal or non-normal), type of data (nominal, ordinal, interval, or ratio), range of values, and the presence of outliers. For example, if you're working with ordinal data, certain scaling methods like Likert scales might be more appropriate.
Number of dimensions: The number of dimensions in your data, or in other words, the number of variables or characteristics you are analyzing, can affect your scaling choice. In some instances, a unidimensional scaling is used when measurements reflect a single construct. However, when measurements reflect multiple characteristics, multidimensional scaling techniques are employed. These types of scales help to visualize patterns and relations in multi-attribute data sets.
Level of Significance: The level of significance, often denoted by alpha (α), is a threshold set before the data collection for deciding whether to reject the null hypothesis. It determines the probability of rejecting the null hypothesis when it is true. Mostly used in hypothesis testing, it doesn't fundamentally impact the selection and construction of the scale. In scale selection and construction, the focus is on the properties of the data and research objectives, not testing hypotheses.
Research objectives: The goals of your research or analysis also play a crucial role in the choice of your scaling method. If your objective is to establish a hierarchy or ranking of data points, an ordinal scale would be suitable. On the other hand, if your goal is to establish distances or intervals between data points, an interval or ratio scale might be more appropriate.