Business Research Project Final: Research Report & Presentation
Discussion and Interpretation of Tables and Figures
We start our interpretation and discussion from the descriptive statistics. The descriptive statistics was calculated by the means of Excel and the results are summarized in the table below:
The average smartphones sales are 877.3647 units sold with a standard deviation of 328.6233 units. The 50th percentile or the middle element of the data is 855.3 units. Most often, the volume of sales was 322.5 units. The coefficients of kurtosis and skewness show that the data is quite close to a normal distribution (values are close to 0). The lowest volume of sales was 304.3 units and the highest volume of sales was 1481.3 units. The distribution of smartphones sales is visualized on the histogram below:
The average tablets sales are 129.4294 units sold with a standard deviation of 15.14854 units. The 50th percentile or the middle element of the data is 128.4 units. Most often, the volume of sales was 124.8 units. The coefficients of kurtosis and skewness show that the data is quite close to a normal distribution (values are close to 0). The lowest volume of sales was 54.3 units and the highest volume of sales was 103 units. The distribution of smartphones sales is visualized on the histogram below:
A special part of the descriptive statistics discussion should be dedicated to the histograms of the distribution. A histogram allows you to analyze the frequency distribution of the number series, and thus makes it possible to identify the most probable number or range. If the observed value is subject to a normal distribution, a histogram of the data set will have a unimodal symmetric form. Normal distribution may be subject to any value which is not influenced by special factors (such as binding or limiting): when it is exposed to a large number of random noise. It is believed that all of the most common distributions are normal.
It is very important to determine whether the distribution of our variables is normal or not, because normality is one of the assumptions of almost all parametric tests. In our case, histograms do not demonstrate a perfect match to a normal distribution shape. However, we can make an assumption that the population (from which the data was drawn) is distributed approximately normally. This assumption is a core requirement for the further inferential statistics and findings discussed below.
In this project, we have examined the correlation between the company’s tablet and smartphone sales. As a rule, a common measure of the linear relationship is Pearson’s correlation coefficient. Its proximity to one indicates a high degree of linear dependence. The correlation coefficient between the company’s tablet and smartphone sales is calculated in Excel. The results are given in the table below:
In our case, the correlation coefficient is equal to 0.999998. This value is extremely close to 1, indicating a very strong positive linear relationship between the variables. Positive coefficient is an indicator of a direct relationship. Based on this result, we can conclude that as the smartphone sales increase, the tablets sales also increase and vice versa. Obviously, this value is higher than the critical value (which can be drawn from the critical tables of Pearson’s product moment correlation). The null hypothesis is rejected and we conclude that the correlation is significant at the 1% level of significance.
The next research questions that was examined is devoted to the comparison of the smartphones and tablets sales. The research question can be formulated as follows: Do the volumes of the sales vary considerably between smartphones and tablets? For this research question, the null hypothesis is: there is no significant difference in the volume of sales between smartphones and tablets. The alternative hypothesis is: there is a significant difference in the volume of sales between smartphones and tablets.
Assuming that the level of significant is the most common (5%), we can test the difference between means using the two-tailed t-test for independent samples. This test can be applied for the mean values of two independent samples, if these samples were drawn from a normally distributed population. It should be noted that none of z-tests can be used in this case, as the population standard deviation is unknown for both smartphones and tablets sales. The t-test for independent samples was conducted in Excel and the following results were obtained:
The t-test indicated a very significant difference in the volume of sales between smartphones and tablets (t=44.61, p<0.001). The null hypothesis should be rejected even at the 1% level of significance. Based on this sample, we conclude that the volumes of sales of smartphones and tablets vary considerably.
Summary of the Results of Testing the Hypotheses
In this paper, we have examined the following two research questions:
Is there a correlation between the company’s tablet and smartphone sales?
Do the volumes of the sales vary considerably between smartphones and tablets?
After a brief discussion of the descriptive statistics, we have made the necessary assumptions for the statistical inference procedures used for hypothesis testing. For the first research question, we have used Pearson’s correlation coefficient. It is appeared that the sales of smartphones and tables are associated very strongly: as the smartphone sales increase, the tablets sales also increase and vice versa. The second research question was examined by two-sample t-test for independent samples. The test indicates a very significant difference in the volume of sales between smartphones and tablets. The comparison of measures of central tendency shows that the volume of smartphone sales is significantly higher that the volume of tablets sales.
The results of this study have a limited application. We can statistically infer about the correlation between the sales, however, it does not mean causation between the two factors. We cannot say that the increase (or decrease) in the smartphone sales causes the corresponding increase (or decrease). There might be some other factors that affect the sales of both gadgets and these factors are not included in the field of our research. The future researches may be devoted to the study of all possible factors affecting the sales of smartphones and tablets.
