Monday, January 30, 2012

How to Intrepret SPSS output

Below are Tables 14A to 14D, summarising    the results of data analyses of research conducted in a sales organisation that operates in 50 different cities of the country, with a total sales force of about 500.  The number of salesmen sampled for the study was 150.




Question

You are to: 
  1. Interpret the information contained in each of the tables, in as much detail as  possible.
  2. Summarise the results for the CEO of the company.
  3. Make recommendations based on your interpretation of the results.

                                Table 14A
Means, Standard Deviations, Minimum, and Maximum
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                                                                    Std.
Variable                                Mean      Deviation      Minimum        Maximum
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Sales (in $000s)                      75.1             8.6               45.2                    97.3
No. of salespeople                   25                6                   5                       50
Population (in 000s)                  5.1             0.8                 2.78                    7.12
Per capita income (in 000s      20.3           20.1               10.1                   75.9
Advertising (in $000s)            10.3            5.2                   6.1                   15.7
                     ------------------------------------------------------------------------------------------------------------

 Answer
The average population of the three cities is 5100 and the mean per capita income of the people is $ 20,300. There is a wide variation in the income (std. dev. = 20.1), indicating that some are quite rich while others are poor. For an average advertisement expenditure of $10,300, the mean sales of $ 75,100 gets about $7.5 for each dollar expended on advertisement.


Correlations Among the Variables
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                                     Sales       Salesmen    Population    Income   Advertisement
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Sales                           1.0
No. of salesmen          .76                  1.0
Population                   .62                    .06                   1.0
Income                         .56                   .21                   .11              1.0
Ad. Expenditure          .68                    .16                   .36              .23                 1.0
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All figures above .15 are significant at  p - .05.
                        All figures above .35 are significant at  p < .001.

  Answer
Sales, obviously the dependent variable, is highly significantly positively correlated to the number of salespersons, the population, the income of the people, and the advertisement dollars expended. This makes good sense. High income areas have more salespersons who cover the territory to sell the product, More advertising is aimed at the high income groups, and the more populated areas, which seem to be good strategies for increasing sales and income for the company.

In other words, sales are significantly correlated at p<.001 level with all four of the variables in the study. The number of salesmen and the advertisement expenditure are understandably related to sales (r=.76 and .68, respectively) . 

There are four other significant correlations, but they may not be of much relevance to  our interpretation of sales data.

Table 14C
Results of Oneway ANOVA: Sales by Level of Education
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Source of              Sums of                           Mean                        Significance
Variation               Squares         Df              Square           F               of  F
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Between Groups        50.7             2                 12.7            3.6                  .05
Within Groups          501.8         147                   3.5
Total                        552.5         149
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Answer

The level of education of the salespersons does have an influence on the sales they make, since the F value is significant at the .05 level. If we are to detect where the differences lie, the Duncan Multiple Range test can be performed. 

To put it differently, the one-way ANOVA table indicates that there is a significant difference in the sales made by the three groups of salesmen with different educational levels (F=3.6, p=.05). Further tests such as the Duncan Multiple Range or the Bonferroni test will have to be conducted to know which of the groups are significantly different.

Table 14D
Results of Regression Analysis
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Multiple R                           .65924       
R square                             .43459       
Adjusted R square              .35225       
Standard error                    .41173

DF                                       (5,144)
F                                           5.278
Sig                                          .000     


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          Variable                        BETA                t                Sig  t
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Training of salesmen                 .28                 2.768          .000
No. of salesmen                       .34                  3.55            .000
Population                                 .09                  0.97            .467
Per capita income                    .12                  1.20            .089
Advertisement                          .47                  4.54            .000
                       -----------------------------------------------------------------------------------

Answer
 
The five independent variables, together, explain 43 percent of the variance in Sales. Advertisement seems to have the greatest influence on sales, judged by the Beta weight of .47 (which is the highest), followed by the number of salespersons (Beta of .34). The training of the salespersons also has a significant influence on sales (Beta of .28). The population and per capita income do not individually explain the variance in sales volume significantly. So, if sales are to be increased, spending more advertising dollars, increasing the number of salespersons, and offering good training to them, would help.


Summary of Results for CEO

The sales made by different salespersons vary considerably, depending on many factors. There is also considerable variation in the number of salespersons, the population, and the per capita income of the people in the various areas.

The level of education of the salespersons makes a difference to the sales volume generated by the individuals. Further analysis can be done to see the best level of education for generating more sales.

Advertisements seem to boost sales considerably. The greater the number of salespersons deployed, the more the sales. Better trained salespersons generate more sales than those who are not as well trained. Neither the per capita income nor the population size, seems to make a difference to the sales volume when all the variables are considered simultaneously.


Recommendation 
If the goal of the company is to increase the volume of sales, spend more money on advertising, increase the number of salespersons, and train them better. Recruiting salespersons who have the optimum level of education will also help.

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