In an effort to determineif the whether or not new sales software is affecting the performance of salespeoplein four regions in which the company operates, the Northeast, Southeast,Central, and West regions, I have created breakdown of the available sales datasince software implementation using the Chi-Square statistics and hypothesistesting methods. The sales data I will be using reflects salespeople, totaling500, who were divided in half, with half of them being provided with the salessoftware and half of them not over the period of three months.
Part of this study is todetermine possible null and alternative hypotheses for a nonparametric test onthis data using chi-square distribution. To better describe these types ofhypotheses I refer to Dr. Tom Pierce of Raddford University (2010) who definesthem as “The null hypothesis is that the researcher’s prediction is not true.The alternative hypothesis is that the researcher’s predicted difference istrue. So, the two-sample t-test gives us a way to decide between a nullhypothesis and an alternative hypothesis.” This study will use thenonparametric qualitive data category of region. Elaborating, nonparametric datais used on qualitive or categorical data such and gender, color, or the aforementionedcategory of region.
The null hypothesis inthis study is that sales software does not make a difference in the performanceof salespeople in their duty to sell a certain number of products and thereforethat there is no statistical significance between the variable of having salessoftware and an increase in sales. The alternative hypothesis in this study isthat there is a statistically significant relationship between the performanceof the sales people and whether or not they were provided with the new salessoftware. The chi-square test “isintended to test how likely it is that an observed distribution is due tochance. It is also called a “goodness of fit” statistic, because itmeasures how well the observed distribution of data fits with the distributionthat is expected if the variables are independent.” (Dept. of Linguistics, PennState University, 2008) In this study I will use chi-square to analyze thecategorical data which has been provided.
Using the chi-square testI have used the data to calculate the expected distribution. The estimatedvalue for each cell is the total for its row multiplied by the total for itscolumn, then divided by the total for the table: that is,(RowTotal*ColTotal)/GridTotal (Dept. of Linguistics, Penn State University,2008).
The second table (below) now shows the distribution of the totals whichis based on the null hypothesis that the sales software will not have an impacton the sales of salespeople in each region. In contrast you will see the firsttable which reflects the actual data. The third table is the expected data. Thefinal table is the chi-square calculations. Region Software No-Software Totals Actual Data Northeast 165 100 265 Southeast 200 125 325 Central 175 125 300 West 180 130 310 Total 720 480 1200 Region Software No-Software Totals Null Hypothesis Northeast 132.5 132.5 265 Southeast 162.
5 162.5 325 Central 150 150 300 West 155 155 310 Total 600 600 1200 Region Software No-Software Totals Expected Northeast 159.00 106.00 265.00 Southeast 195.00 130.00 325.
00 Central 180.00 120.00 300.00 West 186.00 124.00 310.00 Total 720.00 480.
00 1200.00 In order to complete the following table the cv and degrees of freedom were calculated. Observed Expected (O-E) (O-E)2 (O-E)2/E 165 132.5 32.5 1056.
25 7.97 200 162.5 37.5 1406.25 8.65 175 150 25 625 4.16 180 155 25 625 4.
03 100 132.5 -32.5 1056.25 7.97 125 162.
5 -37.5 1406.25 8.65 125 150 -25 625 4.16 130 155 -25 625 4.03 49.62 CV 7.814 ( 3df and .
05% Based on the findingshere using the chi-square method, the null hypothesis must be rejected. Theobserved chi-square of 49.62 is far higher than the 7.814 CV chi-square whichindicates that there is indeed a correlation between the amount of sales that asalesperson makes and whether or not they are utilizing the new sales softwarewhich also proves that we must accept the alternative hypothesis. As StephanieGlen (2013) of Statistics How To said, “A small chi-square value means thatthere is very little relationship between your two variables. A larger valuemeans that there is a greater relationship between your two variables.
“Clearly, there is a strong relationship between our variable of use of salessoftware and salesperson sales.