BUS501 Business Analytics and Statistics

1. What are the top/worst selling products in terms of sales
   1. Is there a difference in payments methods
2. Are the differences in sales performance based on where the product is located in the shop How does this effect both profits and revenue
3. Is there a difference in sales and gross profits between different months of the year
4. Are their differences in sales performance between different seasons
   1. How does this relate to rainfall and profits.

This report will use longitudinal and cross-sectional data collected from a small health food shop on the Sunshine Coast. The main area of emphasized is the sales and profit yield. It is thought that there is a profit difference by the area of sale, the season of the year and month of the year. Therefore, the data will help determine whether the profit, and net sale made during different times of the year, and places significantly differ. Among other objectives, the research pointed out business performance, which can help make business decisions. Among others, the research computed descriptive statistics for the shop to give an overview of the business performance. Second, several statistical tests were carried out to determine which product is the best performing; which location is returning the highest revenue/sales, whether profit by month/season significantly differs. The data were refined, where the data measurement scales for Location of product in the shop, Product Class (number), Product Class and Product Name were changed from the ordinal scale to nominal scale. Similar changes were made for the Season of the year, Month of the year, and Weekday.

Business performance

1. The total sales by the product class

The summary of the descriptive statistics of the total sales by the product class. It indicates that the water has the highest average sales of $1,866.88 (SD = $2,541.63). The second best performing product class is fruit (M= $1,048.68, SD = $2,469.41). The product class that is not performing well (worst performing) is juicing with an average sale of $5.00, and second worse performing product class is $17.96 (SD = $24.37).

1. The total profit by the product class

The summary of the descriptive statistics is as follows. 

The product class with the highest average profit is water (M = $884.25, SD = $1,188.12), and second-best performing is fruit (M = $530.73, SD = $1,247.33). The worse performing product is the Juicing ($3.00).

Business performance by product location in the shop

1. Total Profit by location of product in the shop

Summary statistics are in the following table.

The best performing location of the product is outside front (M= $3,384.37, SD = $4,719.35) and the second best performing location is the front with an average total sale of $572.75 (SD = $1,430.66). The worse performing shop location is the right with an average of $218.22 (SD = $427.61). The assessment was carried out to determine whether there is a significant difference in the average total sales by the location of the product in the shop. The summary of the Analysis is as summarized below.

There is sufficient evidence that at least one of the average total sales is significantly different (F (4, 1029) = 37.176, p < .05) (Gelman, et al., 2014). Further assessment was carried out to determine which location(s) had a significant difference with the help of error bar chart. 

The chart shows that the outside front total sales average 95% confidence interval does not overlap with the total sales of the left and right position confidence interval/ this implies that the sales in this position are significantly different (Barton, Yeatts, Henson, & Martin, 2016).

Total profit by location of product in the shop

The summary of the total profit by location of the product in the shop.

The location that has the highest average total profit is $1,809.63 (SD = $2,343.36), and the least performing location of the product in the shop is the left side with an average of $99.55 (SD = $195.85).

An assessment was carried out to determine whether the average total profit was significantly different by the location of the product in the shop. The summary of the test is as follows.

The summary indicates that there is a significant difference in the average total profit each location in the shop yield (F (4,1029) = 46.211, p-value < .05) (Gelman, et al., 2014). It is important to determine which places have a different average total profit. The error bar was plotted, and it is as illustrated below. 

The 95% confidence interval of the outside front does not overlap with any of the other confidence intervals, which implies that it has a different average total profit (Barton, Yeatts, Henson, & Martin, 2016). However, rear and front; right and left do not have a different average total profit since their error bars confidence interval overlaps.

Business payment performance 

The research tested and analyzed whether the performance of each mode of payment in the shop was statistically different. First, the descriptive statistics were computed, and they are as summarized below.

The credit card seems to be performing better with the highest average (M = $584.80, SD = $228.86). The Visa is the second best performing mode of payment with an average of $555.85 (SD = $244.87). The method that seems to be performing poorly is the Mastercard with the lowest average of $22.09 (SD = $67.82). However, although there seem to a difference in the average, it is imperative to test the hypothesis. Therefore, the hypothesis at the level .05, whether the methods of payment were performing differently.

The summary of the paired t-test shows that all the methods of payment are significantly different (p-values < .05). Therefore, we are 95% confidence that the performance of the different methods of payment is statistically different. This means that Credit card is the best performing method of payment and Mastercard worst performing.

Average sales by the month of the year

It was important to determine which month makes the highest sales. Two analyses were carried out. First, the descriptive statistics and second the test of whether the averages are significantly different.

The summary shows that November has the highest average with an average net sale of $1,154.40 (SD =$302.65), and June the least average net sale (M = $899.49, SD= $221.12).

The second part of the analysis was to determine whether the averages are significantly different at the level .05. 

The results show that there is no sufficient evidence which indicates that the averages are significantly different (F _{(11, 354)} = 1.303, p-value = 0.221) (Afifi & Azen, 2014). This implies that throughout the years the sales were not significantly different.

Net sales by the season of the year

However, is there is a difference in average net sales by the season of the year. The hypothesis was tested to ascertain this claim The net sales of the Autumn have the highest average (M=1045.64, SD=336.46), closely followed by the Spring with an average sale of 1044.67 (SD =313.80). Winter has the lowest average net sales (M= 956.02, SD =257.435). ANOVA test was carried out to determine whether the average net sale is different in the four seasons.

The ANOVA table shows that there is no significant difference in the average sales (F (3, 362) = 1.658, p = .176) (Gelman, et al., 2014). The 95% error bar was illustrated as shown The chart shows that the averages are not statistically different at the level .05 since the 95% confidence interval error bars are overlapping (Hoekstra, Morey, Rouder, & Wagenmakers, 2014).

Gross profit by month of the year

An assessment was performed to determine whether the gross profit was different in different months of the year. The summary of the analysis is as follows.

The month of September has the highest average profit total (M= 46.26, SD =38.94) (Keller, 2014). An assessment to determine whether the averages were significantly different was carried out at the level .05, and the results are summarized below.

In accordance with Keller, (2014) there is sufficient evidence to support that at least one of the monthly average total profit is significantly different (F (11, 354) = 3.867, p-value < .05). Error bar plot was illustrated to determine which months had a significantly different average profit total.

The 95% confidence interval indicates that some of the months like March-June are significantly different from the averages of September and August. This is because, their intervals do not overlap (Afifi & Azen, 2014).

Association between net sales and month of the year

Notably, the net sales are on an interval scale and the month of the year in nominal scale, hence the most appropriate method of assessing whether there is an association is using Eta. This was carried out, and the results are as follows.

 The Eta value is 0.197, and as a general rule, this shows that there is a small effect of month of the year on net sale (Keller, 2014). This effect is not significant.

Regression model

A model was developed to determine whether there is a significant association between net sales and the rainfall amount. The net sales were considered as the dependent variable and the rainfall as the factor variable.

The coefficient of determination shows that only 0.1% of the variation of net sales can be explained by the rainfall. Further, the Durbin-Watson value is 2.140 which shows that there is no correlation between the residuals (Keller, 2014). The regression model is not significant (F (1, 363) =0.454, p-value = 0.501). Thus, we can conclude that rainfall is not associated with net sales.

Conclusion

The findings of the research are as follows:

• The total profit by the location of the product in the shop is significantly different. This means that different location in the shop has a different return.
• Total profit yield at different location of the product in the shop is significantly different.
• The average of different methods of payment is different.
• The average net sales all months throughout the year were not different.
• At least one of the monthly average total profit is significantly different.
• There is a small effect of month on net sale.
• Rainfall is not associated with net sales.

References

Afifi, A. A., & Azen, S. P. (2014). Statistical analysis: a computer oriented approach. Academic press.

Barton, M., Yeatts, P. E., Henson, R. K., & Martin, S. B. (2016). Moving beyond univariate post-hoc testing in exercise science: A primer on descriptive discriminate analysis. Research quarterly for exercise and sport, 87(4), 365-375.

Chatterjee, S., & Hadi., A. S. (2015). Regression analysis by example. John Wiley & Sons.

Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2014). Bayesian data analysis. 2. Boca Raton, FL: CRC press.

Hoekstra, R., Morey, R. D., Rouder, J. N., & Wagenmakers, E.-J. (2014). Robust misinterpretation of confidence intervals. Psychonomic bulletin & review, 21(5), 1157-1164.

Keller, G. (2014). Statistics for management and economics. Nelson Education.