DISS-700 Homework #7Ezana D. Aimero An assignment submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy In Information Systems Graduate School of Computer and Information Sciences Nova Southeastern University DISS-700 – Research Methodology April 2012 Instructor: Prof. Ling Wang Interpret the information contained in each of the tables in as much detail as possible b. and employs a total sales force of about 500. and advertising.7 Per capita income (in 1000s of $) Advertisement (in 1000s of $) Table 12A provides data about the sales of the company. as a rule of thumb.3 Std.2 5 2.Exercise 12. Summarize the results for the CEO of the company c.1 25 5. it appears that the sample size of 150 may be too small. summarizing the results of data analyses of research conducted in a sales organization that operates in 50 different cities of the country. In analyzing the statistics provided for the DV sales.3 10. the sample size should be over 260.1 6. The number of salespersons sampled for the study was 150. Make recommendations based on your interpretation of the results TABLE 12 A Variable Sales (in 1000s of $) No. standard deviations. with a population of 500. The dependent variable (DV) is the company sales. the independent and dependent variables will need to be labeled.366) Below are Tables 12A to 12D.6 6 0.8 20. According to Roscoe (1975). of salespersons Population (in 100. While the sampling method was not disclose d.12 75. Mean 75.000s) Means.10 (p. per capita income.1 20. population.9 15. In reviewing the data provided by the company.1 Maximum 97.78 10. minimum. and maximum. the range in company sales was from 2 . The independent variables (IVs) are number of salespersons. deviation 8. a.3 50 7.1 5.2 Minimum 45. in conjunction with the mean. the data contained in Table 12A indicates the following: sales could be 3 . However. 3. The mean and standard deviation are the most descriptive statistics for interval and ratio scaled data.5 and $83. The IV of number of salespersons could also be a normal distribution. This would to the believe that there is a normal distribution and therefore each city (the unit of analysis) is producing sales of between $66. More than half of the observations are within one standard deviations of the mean. Even though there is a high range the mean of the minimum and maximum come close to the overall mean. More than 90% ofthe observations are within two standard deviations of the mean. The SD is also close to the mean.2 which represent a wide spread. there is a tremendous variance in the wealth of the cities that must be taken into consideration in the proportion of sales by city. The mean of company sales was 75. In summar y. Per capita income has a very high range and the SD is not close at all to the mean.8. is a very useful tool because of the following statistical rules.1 which appear reasonable in these circumstances when considering that the mean of the minimum and maximum is 71. Practically all observations fall within three standard deviations of the average or the mean.6.6. In other words. the SD varies a great deal indicating that this is a disproportionate relationship. As for advertising. the IVs of per capita income and advertising are skewed. Sekaran and Bougie (2009) stated that the standard deviation offers an index of the spread of a distribution or the variability in the data and it is used as measure of dispersion and is the square root of the variance. in a normal distribution (Sekaran & Bougie.3 to 45. As for the IVs. 2009): 1. 2.1 hundred thousand individuals and a SD of 0.97.25 and the standard deviation (SD) is 8. population appears to be normally distributed with a mean of 5. while the range would appear reasonable.7 thousand based on the standard deviation of 8. The SD. 05 All figures above 0.0 indicating perfect positive correlation at the +1. 2011).0 All figures above 0. Also. Salespersons Population Income Advertisement 1. In Table 12B.68 Correlations among the variables.15 are significant at p = 0. The stronger the correlation the better the independent variable predicts the dependent variable. and there is only 5% chance that the relationship does not exist (Sekaran & Bougie. 2009).001 Table 12B contains the data of the correlation between the different variables in the study.76 0.0.06 0.16 1. 2009). Simply put. a significance ofp=0. This indicates that 95 times out of 100. correlation measures the strength of the linear relationship between the variables. Correlation values range from -1.0 to +1.21 0. Expenditure 1. the company should focus on cities with high per capit a income.56 0. As we know. 2009).35 are significant atp::.36 1.0 0.62 0.15 have a 95% confidence that the correlation between the variables exists. These changes will be beneficial to the company.0 0.0 level to perfect negative correlation at -1. we know that all figures above 0.0 0.05 is the generally accepted conventional level of social research (Sekaran & Bougie. 0.9% 4 .affected by the placement of salespersons in cities.0 0. of salespersons Population Income Ad. The correlation is derived by assessing the variations in one variable as another variable also vari es (Sekaran & Bougie.35 have a 99. TABLE 12 B Sales Sales No.11 0. we know that all figures above 0. and the company should invest advertising funding into those cities with the least sales. with zero indicating no correlation (Investopedia. we can be sure that there is a true or significant correlation between the two variables.23 1. 9% confidence interval. The relationship between population and amount of sales is also based on a confidence interval of99. There is no significant relationship between population and number of salespersons based on a correlation of . This relationship suggests that as the number of salespersons increas e.11 out of 1.76 out of 1. As expected. suggesting that sales are better with a somewhat larger population as potential customers.62 out of 1. so does the amount of sales increase which indicated a strong correlation between the variables. per capita income and advertising dollars.00 with a 95% confidence interval. The correlations for advertising dollars and other variables are mixed. population. there is a strongly significant relationship between number of salespersons and amount of sales.9%.00 with a 99.00.00. The relationship between per capita income and amount of sales is moderately significant at . The correlation between number of salespersons and amount of sales is significant at . There is no significant relationship between per capita income and population at . There is a medium correlation between population and amount of sales that is significant at .16 out of 1.00 with a confidence interval of 99.00 with a confidence interval of99. The independent variables are number of salespersons. There is a mild but significant correlation between advertising dollars and population at 5 .9%. We can say with 95% confidenc e. The dependent variable is amount of sales.confidence that the correlation between the variables exists. The correlation is low but still significant between per capita income and number of salespersons at .00.21 out of 1.56 out of 1.06 out of 1. 68 out of 1. This is not surprising and suggests that advertising is a definite contributor to sales. that there is a slightly significant relationship between advertising dollars and number of salespersons (.9%. There is a somewhat strong and significant relationship between advertising dollars and amount of sales at .00). To determine the values it is necessary to compute the sum of squares for each source of variability between groups. Sums of squares 50. In other word s. The statistics also reveal a low but significant correlation between advertising dollars and per capital income at .01 Table 12C provided the results by using a one-way ANOVA test to study sales by level of education. The ANOVA formula (which is a ratio) compares the amount of variability between groups (which is due to the grouping factor) to the amount of varia bili ty within groups (which is due to chance). the within group difference is equal to the amount of variability due to between group differences and any difference between groups will not be significant.00 with a 95% confidence interval. which is then squared.7 3. The ANOVA examines significant mean differenc es among more than two groups on an interval DV.00 with a confidence interval of 95%.6 Significant of F 0. and the total.36 out of 1. TABLE 12 C Source of variation Between groups Within groups Total Results of one-way ANOVA: sales by level of education..5 F 3. The DV in this study was sales and the IV was level of education.7 501. The within group sum of squares is equal to the sum of differences between each individual score in a group and the mean of each group. which is then squared. The F ratio is the ratio of variability between groups to variability within groups. The total sum of squares is equal to the sum of the between group and the 6 .23 out of 1. The between groups sum of squares equals the sum of differences between the mean of all scores and the mean of each groups scor e. We would like to point out that table 12C needs to be updated to resolve a calculatio n error on the total degrees of freedom which should be 149 not 150. within groups.5 Degree of Freedom 4 145 150 Mean squares 12.8 552. 54 Sig. The obtained value or F statistic of 3.47 Value 2 Value 3 t 2.6 is then compared to the critical value (CV) which is the value needed for rejection of the null hypothesis. Model Summary Value 1 Multiple R 0.000 Variable Beta Training of salespersons 0. of Salespersons 0.467 0. Since there are four degrees of freedom (df) between groups.144) F 5.01.7 by the within group of 3. 2005 ).09 Per capita income 0. Computi ng the F statistic requires dividing each sum of squares by the degrees of freedom (which are in approximation to the sample or group size).200 4. The F statistic can be thought of as a measure of how different the means are relative to the variability within each sample (Levin & Stephan. the number of groups would be five as follows: 4dfs= [5 groups (or levels of education) -1] x [3 categories of interest -1].within group sum of squares (Mertler & Vannatt a. and then dividing the resulting mean sum of squares due to between group differences by the mean sum of squares due to within group differences (Salkin d.55 0. The F statistic for table 12C was obtained by the dividing the between group of 12.35225 Standard error 0. TABLE 12 D Results of regression analysis. We can say this with 99% confidence since the significance of F is listed as .32 as determined from the appropriate table.34 Population 0.28 No.97 1.768 3.278 Sig 0.00001 7 . 2011).65924 R square 0. The CV in this case is 3.089 0.41173 df (5.43459 Adjusted R square 0. t 0.5 which provided the result of 3. 2004).12 Advertisement 0.6.0092 0. We may therefore conclude that the null hypothesis may be rejected and that sales are indeed affected by level of education.00001 0. It should 8 .55). different degrees of change among the IVs.65924 indicates that the combination of IVs predicts the DV of sales and shows a good fit between the predicted and actual scores of the DV. the multiple correlation or R of . The t and p values are used to indicate the significance of the beta weights applied. The squared multiple correlation (R squared) of . The results should be in the range of20. For instance. population. The ANOVA generated an F test of 5.0. in order to see if that IV is significantly affecting the DV in the regression model.Table 12D is the results of a regression analysis. and advertising were all significant to different degrees. indicating that there is a positive change in the DV when the IV increases.43459 tells us that the percentage of variance of over 43% gives us a degree of "goodnes s of fit" that indicates that it is likely that there are more IVs that could contribute to the research study. number of salespersons (t value of3. population and per capita income have low Beta test results.5.768. the IVs of training of salespersons (t value of2. When interpreting the regression analysis. This is much lower than would be expected in a linear relationship.278 assuming a level of significance of 0. however. the Beta test was run and a t value generated. The results of the t tests showed that for a sample size of 150 and a t score threshold of2. In running the Beta test.01 and therefore showing no significant difference from the 0. On the other hand.2 were below the threshold for error. and advertisement (t value of 4. each IV had a positive value. the t value results for population of . There is evidence of bias possibly caused by the small sample size.97 and per capita income of 1.54) were above the t value threshold required to be compliant with the probability of error which is approximately p < . The adjusted squared multiple correlation (R squared adjusted) of . per capita income.35225 indicates that there was an overestimate of the Rand R squared populat ion.768 ). The IVs of salespersons. There are. For each ind ividual IV.5 to 22. The evidence for this is demonstrated across three different statistical tests: correlation. Recommendations The research team recommends that the company invest in number of salespersons and training of salespersons and also review and increase advertising dollars in those areas that are lacking. per capita income was measured in 1O O O s dollars. Executive Summary The consulting team collected sales data across 50 cities and sampled 150 salespersons from the 500 member sales force.O O O s people. References 9 . education levels of salespersons . Finally. Education level and training of salespersons was also of evaluat ed. The overall results indicate that number of salespersons.be noted that even though the significant t value for population was higher at . advertising of of was measured in 1O O O s dollars. and regression analysis. the t value remained below the required threshold and this difference was therefore significant. it would be useful to create additional regression models to find a better fit model and increase understanding of the factors that best contribute and in what proportion to positively affect amount of sales. Not surprisingly. Sales was measured in 1O O O s dollars. and advertising dollars are the biggest contributors to amount of sales. populations was of measured in 1O O . training of salespersons. I t is also recommended that further analysis is done regarding education levels of salespersons to better understand the educational threshold. correlation tests indicate there is some evidence that a larger population provides more potential for larger sales but income does not appear to play a major part based on the current analysis. analysis of variance.467. (8th edition.com Levin. D.K.. Advanced Multivariate Statistical Methods: Practical Application and Interpretation. Salkind. D.Neil J. Uma Sekaran & Roger Bougie. (2005). (2004). Even You Can Learn Statistics: A Guide for Everyone Who Has Ever Been Afraid of Statistics. Glendale. C. A. U. Upper Saddle River.: Prentice Hall. Mertler. (2011). West Sussex. Investopedia. 10 .S.investopedia.A.. Exploring Research. 2011). & Stephan. A. NJ: Pearson Prentice Hall. N. Research Methods for Business: A Skill Building Approach. (5th edition.. & Vannatta. U. Upper Saddle River. CA: Pyrczak Publishing. R.J.: John Wiley & Sons. 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