Intermediate Quantitative Methods for Accounting†MyAssignmenthelp

Question: Discuss about the Intermediate Quantitative Methods for Accounting. Answer: Introduction This paper discusses the use of statistical analysis techniques in business reporting. The International Union of Accountants belongs to a body of accounting firms all over the globe that seeks to improving corporate governance. This paper seeks to report on the environmental accounting compliance of different accounting firms across the globe. The accounting firms are under the control of the Accounting Director of International Union of Accountants and therefore the data is readily available. The variables under investigation in this paper include environmental accounting compliance scores for this year, last year, and a year before last year, percentage of accountants in the selected firms with at least an accounting degree and type of country for each accounting firm. The environmental accounting scores are represented as an average, this is because average is the best measure in descriptive analysis to represent quantitative data, percentage of accountants in different accounting firms is represented as categorical variable where 1 = less than 50% of accountants have an accounting degree and 2 = at least 50% of the accountants have an accounting degree, and the type of country is presented as ordinal variable where 1 = first word countries, 2 = second world countries, and 3 = third world countries(Bhat 2010). The statistical analysis involved in this paper are inferential statistics. Statistical inference is a process which information is acquired about populations from the samples(Cameron 2013). Hypothesis testing and estimation are the two major procedures in making inferences. In estimation, the main objective is determining the value of population parameter based on sample statistic(Carlberg 2014). The process involved in estimation include identification of parameter being estimated, specification of the parameters estimator and the sampling distribution, and construction of interval estimator. In hypothesis testing the main purpose is determining whether there is significant evidence favoring a certain belief about parameters(Chatterjee 2013). Under hypothesis testing we have null and alternative hypothesis and the main objective is reject or not to reject the null hypothesis. Rejecting the null hypothesis refers to that there is substantial or significant evidence to conclude the alternative hypothesis is true. Failing to reject the null hypothesis we conclude there is no significant evidence to support the alternative hypothesis(Cramer 2007). The steps involved in testing hypothesis are as follows: Setting up the null and alternative hypothesis denoted as H0 and H1 Determination of the test statistic and the sampling distribution. Specification of the significance level, usually set as 1%, 5%, or 10% Definition of the decision rule Calculating value of the test statistic Conclusion from the results. Finally from the results that will be obtained, a conclusion will be reached on specific research questions that the Director wished to address, summarizing and discussion of the limitations will also be addressed. Is the percentage of accountants in each firm who has at least one university degree in accounting related to country type? The test statistic to be used in this research question is the Chi-Square test of independence and the Cramers V value(Elliott 2007). The Chi-Square test of independence is a statistical test that is used in determining with there is a significant relationship between two nominal or categorical variables(Heckard 2012). In our case the variables under investigation are country type and percentage of accountants with at least one accounting degree and both are categorical variables. The population of interest in this research question is the percentage of accountants with at least one university degree in accounting and the type of country an accountant is from(Connor n.d.). Following the steps in testing hypothesis, Setting up the null and alternative hypothesis denoted as H0 and H1 respectively. H0: The percentage of accountants with at least one accounting degree and the type of country an accountant is from are independent or there is no significant relationship between percentage of accountants with at least one accounting degree and the type of country an accountant is from. H1: The percentage of accountants with at least one accounting degree and the type of country an accountant is from are dependent or there is a significant relationship between percentage of accountants with at least one accounting degree and the type of country an accountant is from. Determination of the test statistic and the sampling distribution. The test statistic to be used is the Chi-Square test of independence. This the most appropriate test statistic to use because the variables under investigation are both nominal(Epsetein n.d.). Specification of the significance level, usually set as 1%, 5%, or 10% The test will be tested at both 1% and 5% level of significance. Definition of the decision rule The decision rule used in this test is should the p-value ( defined as the smallest value of that leads to rejection of the null hypothesis) be less than the level of significance the null hypothesis will be rejected(Cramer, Advanced Quantitative Data Analysis 2007). Calculating value of the test statistic Table 1 Case Processing Summary Cases Valid Missing Total N Percent N Percent N Percent Acc-Dgr% at time t * Country classification 60 100.0% 0 .0% 60 100.0% Table 1 above represents the total number of firms under study. Therefore, from the results above, we had 60 firms and none of the firms had a missing data. Acc-Dgr% at time t * Country classification Crosstabulation Count Country classification Total First World Countries Second World Countries Third World Countries Acc-Dgr% at time t Less than 50% 2 7 21 30 At least 50% 13 12 5 30 Total 15 19 26 60 Table 2 above summarizes both variables under study. Firms with less than 50% of accountants who had an accounting degree and those with at least 50% were at par with 30 each. Chi-Square Tests Value df Asymp. Sig. (2-sided) Pearson Chi-Square 19.229a 2 .000 Likelihood Ratio 20.933 2 .000 Linear-by-Linear Association 18.389 1 .000 N of Valid Cases 60 a. 0 cells (.0%) have expected count less than 5. The minimum expected count is 7.50. Table 3 above represents the Chi-Square tests results of the variables under study. The p-value 0.0000 is less than the level of significance at both 1% and 5%. Therefore, we fail to accept the null hypothesis and conclude that the percentage of accountants with at least one accounting degree and the type of country an accountant is from are dependent or there is a significant relationship between percentage of accountants with at least one accounting degree and the type of country an accountant is from. Symmetric Measures Value Asymp. Std. Errora Approx. Tb Approx. Sig. Nominal by Nominal Phi .566 .000 Cramer's V .566 .000 Interval by Interval Pearson's R -.558 .097 -5.125 .000c Ordinal by Ordinal Spearman Correlation -.564 .098 -5.200 .000c N of Valid Cases 60 a. Not assuming the null hypothesis. b. Using the asymptotic standard error assuming the null hypothesis. c. Based on normal approximation. Table 4 indicates the measure of association between the percentage of accountants with at least one accounting degree and the type of country an accountant is from, this is represented as Cramers V(Lee n.d.). Conclusion from the results. Results obtained from the Chi-Square test of independence reveal that there is an association between the percentage of accountants with at least one accounting degree and the type of country an accountant is from(Stott 2010). This can be interpreted as at least 50% of accountants from first world countries have an accounting degree while less than 50% of accountants in third world countries have an accounting degree. The relationship between the percentage of accountants with at least one accounting degree and the type of country an accountant is from is strong as this is depicted by the Cramers V of 0.566(Levin 2010). Therefore, we can conclude that the percentage of accountants in each firm who has at least one university degree in accounting is related to country type(Triola, Elementary Statistics using Excel 2010). This is well illustrated in the column chart below Is there evidence of different environmental compliance scores (EAC) over the three-year period The test statistic to be used in this research question is the one-way analysis of variance which is an extension of the two-sample t test(Liu 2012). This test is used when there are several means to be compared. If the ANOVA indicates that the means are not equal, this means that the means are an unequal and a post hoc analysis on the means can be carried out to rank the difference in means(Moy n.d.). The population of interest in this research question is the average of environmental accounting compliance scores of the accounting firms under investigation(Donnelly 2013). Following the steps in testing hypothesis Setting up the null and alternative hypothesis denoted as H0 and H1 respectively. The hypothesis being tested in this research question is as follows: H0: There is no significant difference in means of the environmental accounting compliance scores over the three year period of study. H1: There is a significant difference in means of the environmental accounting compliance scores over the three year period of study. Before deciding on which test statistic to use, it is wise to test for normality of the data in order to know whether the data follows normality or not(Ryan 2012). Data that follows normal distribution allows parametric distribution techniques to be used in data analysis while data that fails to follow a normal distribution assumes non-parametric techniques of analysis. Since the sample size is greater than 20, Shapiro-Wilk test will be used to test for normality, if the sample size was less than 20, Kolmogorov-Smirnov would have been used(Spicer 2005). Tests of Normality Country classification Kolmogorov-Smirnova Shapiro-Wilk Statistic df Sig. Statistic df Sig. EAC-Scrs this year (t) First World Countries .129 15 .200* .923 15 .214 Second World Countries .101 19 .200* .966 19 .694 Third World Countries .110 26 .200* .960 26 .400 EAC-Scrs last year (t-1) First World Countries .129 15 .200* .928 15 .256 Second World Countries .164 19 .191 .922 19 .125 Third World Countries .150 26 .138 .973 26 .689 EAC-Scrs the year before last year (t-2) First World Countries .142 15 .200* .956 15 .628 Second World Countries .131 19 .200* .929 19 .166 Third World Countries .120 26 .200* .978 26 .840 a. Lilliefors Significance Correction *. This is a lower bound of the true significance. Table 1 above represents the results for testing normality, all the p-values for environment accounting compliance scores in all the three years is greater than the level of significance at 1% and 5%. Therefore, we fail to reject the null hypothesis and conclude that the data follows normality(Triola 2010). The test statistic to be used will therefore be a parametric distribution. This is also explained in the histograms below: Determination of the test statistic and the sampling distribution. The test statistic to be used is the Analysis of Variance. This the most appropriate test statistic to use because we have more than two means to compare. Specification of the significance level, usually set as 1%, 5%, or 10% The test will be tested at both 1% and 5% level of significance. Definition of the decision rule The decision rule used in this test is should the p-value ( defined as the smallest value of that leads to rejection of the null hypothesis) be less than the level of significance the null hypothesis will be rejected. Rejecting the null hypothesis is an indication that there is mean from one group that is not equal to the rest of the means. Calculating value of the test statistic Table 2 above indicates the ANOVA results of the environmental accounting compliance scores for the past three years. The p-value in all three years is less than the significance level at 1% and 5%. Therefore, we fail to accept the null hypothesis and conclude that there is a significant difference in means of the environmental accounting compliance scores across the three years. Conclusion from the results. From the results obtained in the ANOVA we can comfortably conclude that there is sufficient evidence of different environmental compliance scores (EAC) over the three-year period. This means that across the three year period different accounting firms had different environmental accounting compliance scores. Is there evidence to suggest that the environmental compliance scores (EAC) for this year (time t) is greater than two years ago (time t-2) among the 60 selected accounting firms? The test statistic to be used in this research question will be one sample t-test. This is because we are comparing two means of environmental compliance scores for this year (time t) and that of two years ago (time t-2). Since we are not comparing whether the two means are equal but rather whether the environmental compliance scores for this year (time t) is greater than that of two years ago, the test will be one tailed and not two tailed test(Terrell 2012). The population of interest in this research question is the average of environmental accounting compliance scores of the accounting firms under investigation for this year and those of two years ago. Following the steps in testing hypothesis Setting up the null and alternative hypothesis denoted as H0 and H1 respectively. The hypothesis being tested in this research question is as follows: H0: There is no significant difference in means of the environmental accounting compliance scores for this year and those of two years ago. H1: The environmental compliance scores for this year are greater than those of two years ago. This hypothesis can be re-written as H0: 0 = 1 = 0 H1: 0 1 Determination of the test statistic and the sampling distribution. The test statistic to be used is the one sample t-test. This the most appropriate test statistic to use because we are comparing two means. Specification of the significance level, usually set as 1%, 5%, or 10% The test will be tested at both 1% and 5% level of significance. Calculating value of the test statistic One-Sample Test Test Value = 0 t df Sig. (2-tailed) Mean Difference 95% Confidence Interval of the Difference Lower Upper EAC-Scrs this year (t) 55.279 59 .000 62.8717 60.596 65.147 EAC-Scrs the year before last year (t-2) 50.048 59 .000 59.7050 57.318 62.092 Table 1 above represents the results from one sample t-test. The p-value is less than the significance level at both 1% and 5% and indicates a positive t-statistic. Therefore, we fail to accept the null hypothesis and conclude that this years environmental compliance scores is greater than that of two years ago(Topics in Applied Statistics 2016). Conclusion from the results Results from the t-test indicates that this years is environmental compliance scores are greater than those of two years ago. This can be explained in the positive t-test statistic obtained from the results. If the t-test statistic would be negative, we would have concluded that the environmental compliance score for this year is less than that of two years ago. Is there evidence to suggest that this year environmental compliance scores (EAC) of accounting firms which has less than 50% accountants with at least one university degree in accounting is lower than this year environmental compliance scores (EAC) of accounting firms which has at least 50% accountants with at least one university degree in accounting? The test statistic to be used in this research question will be the independent t-test. This is because we are comparing the mean of environmental compliance scores of this year (time t) of accounting firms that have less than 50% accountants with at least one university degree in accounting whether is lower than this years environmental compliance scores of accounting firms which has at least 50% accountants with at least one university degree in accounting(Newbold 2013). Since we are not comparing whether the two means are equal but rather whether the environmental compliance scores for this year (time t) is greater than that of two years ago, the test will be one tailed and not two tailed test. The grouping factor in this test will be accounting degree at time t. The population of interest in this research question is the average of environmental accounting compliance scores of the accounting firms under investigation for this year and the percentage of accountants who have at least one university degree in accounting. Following the steps in testing hypothesis Setting up the null and alternative hypothesis denoted as H0 and H1 respectively. The hypothesis being tested in this research question is as follows: H0: There is no significant difference in the mean of environmental compliance scores of this year (time t) of accounting firms that have less than 50% accountants with at least one university degree in accounting and this years environmental compliance scores of accounting firms which has at least 50% accountants with at least one university degree in accounting. H1: The mean of environmental compliance scores of this year (time t) of accounting firms that have less than 50% accountants with at least one university degree in accounting whether is lower than this years environmental compliance scores of accounting firms which has at least 50% accountants with at least one university degree in accounting. This hypothesis can be re-written as H0: 0 = 1 = 0 H1: 0 1 Determination of the test statistic and the sampling distribution. The test statistic to be used is the independent t-test. This the most appropriate test statistic. Specification of the significance level, usually set as 1%, 5%, or 10%. The test will be tested at both 1% and 5% level of significance. Calculating value of the test statistic Group Statistics Acc-Dgr% at time t N Mean Std. Deviation Std. Error Mean EAC-Scrs this year (t) dimension1 Less than 50% 30 58.750 7.9148 1.4450 At least 50% 30 66.993 7.7532 1.4155 Table 1 represents the descriptive statistics of this years environmental compliance scores grouped by the percentage of accountants who have at least one university degree in accounting. Independent Samples Test Levene's Test for Equality of Variances t-test for Equality of Means F Sig. t df Sig. (2-tailed) Mean Difference Std. Error Difference EAC-Scrs this year (t) Equal variances assumed 0.01 0.9 -4.08 58 0 -8.2433 2.0228 Equal variances not assumed -4.08 57.98 0 -8.2433 2.0228 Table 2 above indicates the t-test statistic between mean difference of environmental compliance scores of this year (time t) of accounting firms that have less than 50% accountants with at least one university degree in accounting and this years environmental compliance scores of accounting firms which has at least 50% accountants with at least one university degree in accounting. 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