due on 02/02/16 - STATISTICS - DATA ANALYSIS assignment - follow the sample
allisky
chapter_10_indices.pdf
Chapter 10: Creating Standardized Indicators for Indices
Index Set of variables used as a measure for an abstract concept: each variable is called an item or indicator Commonly used indices:
o Consumer Price Index (CPI): Measures price of goods purchased by consumers o National Association of Security Dealers Automatic Quotations (NASDAQ)
Value of an index is determined by an equation More operationally valid and reliable measure is obtained if several components of an attribute are used Scale: combines indicators according to rules that are designed to reflect a single dimension of a concept
o Assigns a number to a case based on how that case fits into a previously identified pattern of indicators
Before constructing a new index, an attempt should be made to locate/review existing indices
Issues in Developing Indices 1. Defining the concept
Researcher needs to explain what the concept means, and what its components are Review literature to find definitions used by others Operational definition details how the concept will be measured Conceptual definition determines the appropriateness of each possible measure included in the
operational definition Operational and conceptual definitions should be close
2. Selecting Items Four areas to be considered:
o Use the right items o Include enough items to distinguish among all gradations of a dimension and to improve reliability o Determine if every item represents part of or the entire dimension of interest o Keep costs down and reduce complexity by excluding items that provide no additional information
Researcher’s knowledge of the subject area is critical in selecting items o Items selected should be theoretically or conceptually related to what is being measured
Methods for selecting o Researcher can rely on his/her own judgment o Researcher can talk to those knowledgeable in the area and to potential users of the index to
determine what is important o Analysts may prefer methods that allow them to assess how well a set of items ‘hangs together’ o Validity of a measure is dependent on the items selected
3. Combining Items in Index Simplest way is to add the values or rankings for the separate measures into an index The average of the values can be used Item values can be multiplied or divided by one another Values of individual items my need to be transformed before combining
4. Weighting the Separate Items Each item should contribute to the index relative to its importance Weighting is used so that items will have different influence on the index In an ‘unweighted’ index, all items are weighted equally
o Caution must be taken when the scales or ranges of the individual items are very different o An item may unintentionally dominate the index due to the different scale/range
Creating Standardized Indicators for Indices Separate items may need to be standardized so that each is based on the same scale and items measured
in different units can be combined Transforming items will reduce the risk that any one item has undue influence on the index If one item should be weighted more, we can multiply the values by a factor before combining
Chapter 10: Creating Standardized Indicators for Indices
Transforming and weighting should be addressed separately Standardization: where x = standardized value y= value on measure
ya= least need yb = greatest need
Likert Scaling Common method for building indices using summated rating scales Analyst selects a set of statements, each which reflects favorably/unfavorably on some aspect of the
characteristic to be measured o Rating form provided for each item with several ranked responses o Dimension is rated on each item according to the responses o Numerical value assigned to each response, values are summed or averaged to obtain a single value
Used to measure opinions or attitudes of individuals: In survey or interview, respondents are asked to indicate on the rating scale the degree to which they agree/disagree with each statement
Several types of agreement scales: odd number of categories is preferable Selection of Items
o Understand concept to be measured and for each item, explain how it relates to the concept o Similar to writing questions for questionnaires: statements selected must be pretested o Examine relationship of each item to total score: Items should be highly associated with the total
score o Items do not need to be equally weighted o Likert scale items do not measure quantities, but can we be used to rank cases
Factor Analysis Technique used to investigate the relationship between theoretical concepts and empirical indicators Developed to help construct indicators of abstract concepts Reduces a large number of items to smaller, more manageable number of indices Resulting composite should have greater reliability and operational validity Calculates how closely a large number of variables, assumed to be associated with each other, are related
to a common dimension or factor Based on concept of association Associations among variables are assumed to reflect the extent to which the variables measure the same
trait or factor Methodology
o Begins by calculating association measures between each pair of variables o A factor that maximizes the associations among the variables is created mathematically o Factor loadings calculated; these are the coefficients measuring the association between the factor
and each variable o Factor loadings vary between 0 and 1; the closer to 1, the more closely the variable is associated with
the factor
Index Numbers Express the relationship between two figures, one of which is the base, and are used to describe changes
over time CPI measures cost of living and describes changes in economic variables over time Index produces a summary statistic called an index number
100
ab
a
yy
yy x
