Procedures for statistically adjusting the data consist of weighting. variable respecification, and scale transformations. These adjustments are not always necessary but can enhance the quality of data analysis.

**Weighting **

In weighting, each case or respondent the database is assigned a weight to reflect its importance relative to other cases or respondents. The value 1.0 represents the un weighted case. The effect of weighting is to increase or decrease the number of cases in the sample that possess certain characteristics.

Weighting is most widely used to make the sample data more representative of a target population on specific characteristics. For example, it may be used to give greater importance to cases or respondents with higher quality data. Yet another use of weighting is to adjust the sample so that greater importance is attached to respondents with certain characteristics. If a study is conducted to determine what modifications should be made to an existing product. the researcher might want to attach greater weight to the opinions of heavy ‘users of the product. This could be accomplished by assigning weights of 3.0 to heavy users. 2.0 10 medium users. and 1.0 to light users and nonusers. Weighting should be applied with caution. because it destroys the self-weighting nature of the sample design.

**Determining the Weight of Fast-Food Customers
**

A mail survey was conducted in the Los Angeles-Long Beach area to determine consumer patronage of fast-food restaurants. The resulting sample composition differed in educational level from the area population distribution as compiled from recent census data. Therefore. the sample was weighted to make it representative in terms of educational level. The weights applied were determined by dividing the population percentage by the corresponding sample percentage. The distribution of education for the sample and population. as well as the weights applied. are given in the following table.

Categories underrepresented in the sample received higher weights. whereas overrepresented categories received lower weights. Thus. the data for a respondent with I to 3 years of college education should be overweighted by multiplying by (29.42/22.33 =) 1.32.whereasthedataforarespondent with 7or more years of college education should be underweighted by multiplying by (6.90112.18=) 0.57.

If used. the weighting procedure should be documented and made a part of the project report.

**Variable Respecification **

Variable respecification involves the transformation of data to create new variables or modify existing variables. The purpose of respecification is to create variables that are consistent with the objectives of the study. For example, suppose the original variable was product usage. with 10 response categories, These might be collapsed into four categories: heavy, medium. light. and nonuser. Or the researcher may create new variables that are composites of several other variables. For example. the researcher may create an Index oflnformation Search (liS). which is the sum of information customers seek from dealers, promotional materials. the Internet. and other independent sources. Likewise, one may take the ratio of variables. I{ the- amount of purchases at department stores (XI) and the amount of purchases charged (X2) have been measured. the proportion of purchases charged can be a new variable created by taking the ratio of the two (X/XI)’ Other respecifications of variables include square root and log transformations. v hich are often applied to improve the fit of the model being estimated,

An important respecification procedure involves the use of dummy variables for respecifying categorical variables. Dummy variables are also called binary, dichotomous, instrumental. or qualitative variables. They are variables that may take on only two values. such as 0 or I. The general rule is that to respecify a categorical variable with K categories variables are needed. The reason for having K – I. rather than K. dummy variables is that only categories are independent. Given the sample data. information about the Kth category can be derived from information about the other K – I categories. Consider sex, a variable having categories. Only one dummy variable is needed. lnfonnarion on the number or percentage of males in the sample can be readily derived from the number or percentage of females.

**“Frozen” Consumers Treated as Dummies**

Ina study of consumer preferences for frozen foods.therespondents were classified as heavy.medium. light. and nonusers and originally assigned codes of 4.3.2. and I. respectively.This coding was not meaningful for several statistical analyses. In order to conduct these analyses. product usage was represented b) three dummy variables, XI’ Xl’ and X3 as shown.

Note that XI = I for nonusers and 0 for all others. Likewise. X2 = I for light users and 0 for all others. and X3 = I for medium users and 0 for all others. In analyzing the data. XI’ X2 and X3 are used to represent all user/nonuser groups.

**Scale Transformation**

Scale transformation involves a manipulation of scale values to ensure comparability with other scales or otherwise make the data suitable for analysis. Frequently. different scales are employed for measuring different variables. For example, image variables may be measured on a 7-point semantic differential scale. altitude variables on a continuous rating scale, and lifestyle variables on a 5-point Likert scale. Therefore, it would not be meaningful to make comparisons across the measurement scales for any respondent. To compare attitudinal scores with lifestyle or image scores. it would be necessary to transform the various scales. Even if the same scale is employed for all the variables, different respondents may use the scale differently. For example. some respondents consistently use the upper end of a rating scale. whereas others consistently use the lower end. These differences can be corrected by appropriately transforming the data.

**Health Care Services-Transforming Consumers
**

In a study examining preference segmentation of health care services. respondents were asked to rate the importance of 18 factors affecting preferences for hospitals on a 3-point scale (very somewhat or not important). Before analyzing the data. each individual’s ratings were transformed. For each individual. preference responses were averaged across all 18 items. Then this mean was subtracted from each item rating and a constant was added to the difference. Thus. the transformed data. X1 were obtained by:

Subtraction of the mean value corrected for uneven use of the importance scale. The constant C was added to make all the transformed values positive, because negative importance ratings a not meaningful conceptually. This transformation was desirable because some respondents. especially those with low incomes. had rated almost all the preference items as very important. Others. high-income respondents in particular. had assigned the very important rating to only a few preference limb Thus. subtraction of the mean value provided a more accurate idea of the relative importance of the factors.

In this example. the scale transformation IS corrected only for the mean response. A more common transformation procedure is standardization. To standardize a scale X. we first subtract the mean. X. fmm each score and then divide by the standard deviation. Thus the standardized scale will have a mean of zero and a standard dev ration of I. This is essentially the same as the calculation of : scores (see Chapter 12). Standardization allows the researcher to compare variables that have been measured using different types of scak,.11 Mathematically. standardized ‘cores may be obtained as:

**ACTIVE RESEARCH**

**lexus: The Treatment of luxury
**Visit www.themarketingresearch.com and conduct an Internet search using a search engine and your library’s online database to obtain information on the criteria buyers use in selecting a luxury car brand. Demographic and psychographic data were obtained in a survey designed to explain the choice of a luxury car brand. What kind of consistency checks, treatment of missing responses, and variable respecification should be conducted?

As the marketing manager for Lexus, what information would you like to have to formulate marketing strategies to increase your market share?