A recent survey asked business people about the concern of hiring and maintaining employees during the current harsh economic climate. It was reported that 85 percent of respondents were concerned about recruiting employees and 81 percent said they were concerned about retaining employees. When the economy is uncertain, as in 2008-2009. turnover is rapid. Generally speaking, if an organization wants to retain its employees, it must learn why people leave their jobs and why others stay and are satisfied with their jobs. Discriminant analysis was used to determine what factors explained the differences between salespeople who left a large computer manufacturing company and those who stayed. The independent variables were company rating. job security, seven job-satisfaction dimensions, four role-conflict dimensions, four role-ambiguity dimensions, and nine measures of sales performance. The dependent variable was the dichotomy between those who stayed and those who left. The canonical correlation, an index of discrimination (R = 0.4572), was significant (Wilks’ A = 0.7909, F26•173 = 1.7588, p = 0.0180). This result indicated that the variables discriminated between those who \eft and those who stayed.
The results from simultaneously entering all variables in discriminant analysis are presented in the accompanying table. The rank. order of importance, as determined by the relative magnitude of the structure correlations, is presented in the first column. Satisfaction with the job and promotional opportunities were the two most important discriminators, followed by job security. Those who stayed in the company found the job to be more exciting, satisfying, challenging, and interesting than those who left,?
Note that in this example, promotion was identified as the second most important variable based on the structure correlations. However, it is not the second most important variable based on the absolute magnitude of the standardized discriminant function coefficients. This anomaly results from multi col linearity.
Assess Validity of Discriminant Analysis
Many computer programs, such as SPSS, offer a leave-one-out cross-validation option. In this option, the discriminant model is reestimated as many times as there are respondents in the sample. Each reestimated model leaves out one respondent and the model is used to predict for that respondent. When a large holdout sample is not possible, this gives a sense of the robustness of the estimate using each respondent, in turn, as a holdout.
It is helpful to compare the percentage of cases correctly classified by discriminant analysis to the percentage that would be obtained by chance. When the groups are equal in size, the percentage of chance classification is I divided by the number of groups. How much improvement should be expected over chance? No general guidelines are available, although some authors have suggested that classification accuracy achieved by discriminant analysis should be at least 25 percent greater than that obtained by chance.?
Home Bodies and Couch Potatoes
Two-group discriminant analysis was used to assess the strength of each of five dimensions used in classifying individuals as TV users or nonusers. The procedure was appropriate for this use because of
the nature of the predefined categorical groups (users and nonusers) and the interval scales used to generate individual factor scores.
The canonical correlation for the discriminant function was 0.4291, significant at the p < 0.0001 level. The eigenvalue was 0.2257. The accompanying table summarizes the standardized canonical discriminant coefficients. A substantial portion of the variance is explained by the discriminant function. In addition, as the table shows, the home orientation dimension made a fairly strong contribution to classifying individuals as users or nonusers of television. Morale, security and health, and respect also contributed significantly. The social factor appeared to make little contribution
The cross-validation procedure using the discriminant function from the analysis sample gave support to the contention that the dimensions aided researchers in discriminating between users and nonusers of television. As the table shows, the discriminant function was successful in classifying 75.76 percent of the cases. This suggests that consideration of the identified dimensions will help marketers understand the elderly market. Although it is very important for marketers to know and understand the elderly market the born between 1961 and 1981) are also a group that should not be overlooked by to technological advances with the Internet and television, a revolutionary form of interactive TV CITY) has been created. As of 2009, ITV services were fully deployed and .operational and combiMd Internet and broadcasting with software programs and hardware components to give consumers Internet access, online shopping, music downloads, and an interactive broadcast program, all through their television. Willi a prosperous-looking forecast for ITV, who better to target this revolutionary form of television than Generation Xers? Discriminant-analysis can again be used to determine who among Generation Xers are users or nonusers of !TV and to market !TV services successfully
Standard Canonical Discriminant Function Coefficients
Standard Canonical Discriminant Function Coefficients
Security and health 0.39850
Home orientation 0.77496
Social -0.0 1996
Classification Results for Cases Selected for Use In the Analysis
Multiple Discriminant Analysis
Formulate the Problem
The data presented in Tables 18.2 and 18.3 can also be used to illustrate three-group analysis. In the last column of these tables, the households are classified into three categories, based on the amount spent on family vacation (high, medium, or low). Ten households fan in each category. The question of interest is whether the households that spend high, medium, or low amounts on their vacations (AMOUNT) can be differentiated in terms of annual family income (INCOME), attitude toward travel (TRAVEL), importance attached to family vacation (VACATION), household size (HSIZE), and age of the head of household (AGE).”
Estimate the Discriminant Function Coefficients,
Table 18.5 presents the results of estimating three-group discriminant analysis. An examination of group means indicates that income appears to separate the groups more widely than any other
variable. There is some separation on travel and vacation. Groups I and 2 arc very close in terms of household size and age. Age has a large standard deviation relative to the separation between the groups. The pooled within-groups correlation matrix indicates some correlation of vacation and household size with income. Age has some negative correlation with travel. Yet these correlations arc on the lower side, indicating that although multi col linearity may be of some concern, it is not likely to be a serious problem. The significance attached to the univariate F ratios indicates that when the predictors arc considered individually, only income and travel arc significant in differentiating between the two groups
In multiple discriminant analysis,lf there arc G groups, G – I discriminant functions can be estimated if the number of prcdictors is larger than this quantity. In general, with G groups and k -predictors, it is possible to estimate up to the smaller of G – I or k discriminant functions.
The first function has the highest ratio of between-groups to within-groups sum of squares. The second function, uncorrelated with the first, has the second highest ratio, and so on. However, not all the functions may be statistically significant
Because there arc three groups, a maximum of two functions can be extracted. The eigenvalue associated with the first function is 3.8190, and this function accounts for 93.93 percent of the explained variance. Because the eigenvalue is large, the first function is likely to be superior. The second function has a small eigenvalue of 0.2469 and accounts for only 6.07 percent of the explained variance
Determine the Significance of the Discriminant Function
To test the null hypothesis of equal group centro ids, both the functions must be considered simultaneously. It is possible to test the means of the functions successively by first testing all means simultaneously. Then one function is excluded at a time, and the means of the remaining functions arc tested at each step. In Table 18.5, the 0 below “After Fen (after functions removed)” indicates that no functions have been removed. The value of Wilks’ A is 0.1664. This transforms to a Chi-square of 44.831, with 10 degrees of freedom, which is significant beyond the 0.05 level.
Thus, the two functions together significantly discriminate among the three groups, However, when the first function is removed, the Wilks’ A associated with the second function is 0.8020, which is not significant at the 0.05 level. Therefore, the second function does not contribute significantly to group differences.