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# BUSINESS STATISTICS: ANOVA, CORRELATION ANALYSIS AND KRUSKAL-WALLIS TEST (Essay Sample)

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Exports are said to be important to development of any country in that they are part of revenue, through foreign exchange, that a country gets in any financial year. Exports represent the total value of all goods and marketable services provided to other countries who need them. Exports include the value of merchandise, insurance, freight, license fees travel, royalties, financial services, transport & logistics, and other services, such as business, personal services, construction, information, communication and government services. These exclude transfer payments, investment income and compensation of employees (factor services).
The volume or contribution of exports to other countries is affected by several factors such as exchange rates, inflation, cost of goods and services, marketing strategies used, working population compared to dependency ratio among others. In this paper, we will evaluate the relationship between exports, inflation rates and dependency ratio. Analysis of variance, both one and two way, will be used together with correlation and non-parametric test (Kruskal-Wallis test.
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BUSINESS STATISTICS: ANOVA, CORRELATION ANALYSIS AND KRUSKAL-WALLIS TEST
Name
Course
Institution
Task
1 Introduction
Exports are said to be important to development of any country in that they are part of revenue, through foreign exchange, that a country gets in any financial year. Exports represent the total value of all goods and marketable services provided to other countries who need them. Exports include the value of merchandise, insurance, freight, license fees travel, royalties, financial services, transport & logistics, and other services, such as business, personal services, construction, information, communication and government services. These exclude transfer payments, investment income and compensation of employees (factor services).
The volume or contribution of exports to other countries is affected by several factors such as exchange rates, inflation, cost of goods and services, marketing strategies used, working population compared to dependency ratio among others. In this paper, we will evaluate the relationship between exports, inflation rates and dependency ratio. Analysis of variance, both one and two way, will be used together with correlation and non-parametric test (Kruskal-Wallis test.
* Sample size
In this research, a sample of 264 countries will be used in the analysis and they are from all continents of the world.
* Dependent variablesThe dependent variable in this case is exports and it is represented as a percentage of Gross domestic product (GDP) of a country. This variable, exports, is said to be affected by several factors as discussed above.
* Factors used
Factors used in this case are ordinal data with least 3 categories each. The two factors are;
Inflation rate
Inflation, as measured by the consumer price index (CPI) reflects the annual change (in %) in the cost to the consumer of acquiring a basket of goods or services that may be fixed or that varies at specified intervals, such as quarterly or yearly. The Laspeyres formula is mostly used in this case. The inflation rates of these countries have been categorized into three main groups; Low inflation, average inflation and High inflation. Low inflation countries, in this case have been assumed to be those with rates less than 3 while average inflation is assumed to be those between 3 and 7%. High inflation countries are those with a rate of more than 7%. The data has been recorded using SPSS and the file is provided.
Dependency ratio
Age dependency ratio, according to world bank statistics, is the ratio of dependents-people less than 15 years or older than 64 years-to the working-age population-those between ages 15 and 64 years. Data for this variable are shown as the proportion of dependents per 100 working-age population and it is further assumed to have three main categories; Low dependency, average dependency and high dependency. Low dependency is assumed to be countries with proportions less than 45, average dependency being those with proportions between 45 and 60. Above the proportion of 60, the country is assumed to be having a higher rate of dependency.
* Source and period of the data used
The source of this data is world bank database which as a wide range of information on several indicators for different countries. The database is believed to have accurate information and it is updated. For this analysis, only year 2016 data was used since it had complete data. For 2017, the data for some indicators was missing hence the decision to choose year 2016.
2 Analysis of Variance-ANOVA
* One-way ANOVA
* Dependent variable and factor A
Testing the null hypothesis that the dependent variable means are the same for all categories in Factor A amongst the population of countries.
Hypothesis testing
Ї Formulating the null and alternative hypotheses
Ho: The means for exports are the same for all categories in Factor A (Inflation groups) amongst the population of countries
HA: The means for exports are not the same for all categories in Factor A (Inflation groups) amongst the population of countries
Ї Statistical decision using significant value (рќ›ј) of 5% for the test.
We reject the null hypothesis (Ho) because p-value <0.05 hence conclude that the means for exports are not the same for all categories in Factor A (Inflation groups) amongst the population of countries.
Ї Conclusion
At 5% level of significance, the sample evidence does not support the null hypothesis that the means for exports are the same for all categories in Factor A (Inflation groups) amongst the population of countries. Therefore, there is at least one difference in the means for exports for all categories in Factor A (Inflation groups) amongst the population of countries.
Test for homogeneity of variances
* Hypothesis statements:
Ho: Homogeneity of variances has not been violated.
H1: Homogeneity of variances has been violated.
* Statistical decision using significant value (рќ›ј) of 5% for the test.
Do not reject Ho because p-value (0.067) is greater than significance value of 0.05.
* Conclusion
At 5% level of significance, the sample evidence supports the null hypothesis that the homogeneity of variances has not been violated. In post-hoc analysis, we can use Tukey method.
Post Hoc Tests
Hypothesis testing
* Formulating the hypothesis
Ho: There is no significant difference between high inflation and low inflation categories
HA: There is a significant difference between high inflation and low inflation categories
* Statistical decision using significant value (рќ›ј) of 5% for the test.
We therefore reject our null hypothesis that there is a significant difference between high inflation and low inflation categories in favor of alternative hypothesis (HA).
* Conclusion
At 5% level of significance, the sample evidence does not support the null hypothesis that there is a significant difference between high inflation and low inflation categories. Therefore, there is at least one difference in the means for high inflation and low inflation categories amongst the population of countries.
There is a significant difference between high inflation and low inflation categories because p-value <0.05. The observed p-value, from the table above is 0.033 for the Tukey HSD test and 0.001 and both are less than our p-value of 0.05.
* Dependent Variable and factor B
Testing the null hypothesis that the dependent variable means are the same for all categories in Factor A amongst the population of countries.
Hypothesis testing
* Formulating the null and alternative hypotheses.
Ho: The means for exports are the same for all categories in Factor B (dependency groups) amongst the population of countries
HA: The means for exports are not the same for all categories in Factor B (dependency groups) amongst the population of countries,
* Statistical decision using significant value (рќ›ј) of 5% for the test.
We reject the null hypothesis (Ho) because p-value <0.05 hence conclude that the means for exports are not the same for all categories in Factor B (Dependency groups) amongst the population of countries.
* Conclusion
At 5% level of significance, the sample evidence does not support the null hypothesis that the means for exports are the same for all categories in Factor B (dependency groups) amongst the population of countries. Therefore, there is at least one difference in the means for exports for all categories in Factor B (Dependency groups) amongst the population of countries.
Test for homogeneity of variances
* Hypothesis statements:
Ho: Homogeneity of variances has not been violated.
H1: Homogeneity of variances has been violated.
* Statistical decision using significant value (рќ›ј) of 5% for the test.
We reject Ho because p-value (0.00) is less than significance value of 0.05.
* Conclusion
At 5% level of significance, the sample evidence does not support the null hypothesis that the homogeneity of variances has not been violated. In post-hoc analysis, we can use Tukey method.
Post Hoc Tests
* Tukey and Games-Howell confidence intervals is to be done to test for the mean difference between pair of Factor B (Dependency group) categories
Hypothesis testing
* Formulating the hypothesis
Ho: There is no significant difference between high dependency and low dependency categories for factor B (Dependency groups)
HA: There is a significant difference between high dependency and low dependency categories for factor B (Dependency groups)
* Statistical decision using significant value (рќ›ј) of 5% for the test.
* Conclusion
There is a significant difference between high dependency and low dependency categories because p-value <0.05. The observed p-value, from the table above is 0.000 for the Tukey HSD test and 0.000 and both are less than our p-value of 0.05. we therefore reject our null hypothesis that there is a significant difference between high dependency and low dependency categories in favor of alternative hypothesis (HA).
* Two-way ANOVA
* 2-way ANOVA to test the null hypothesis that dependent variable means are the same for all categories in Factor A and Factor B amongst the population of countries.
Hypothesis testing
* Formulating the null and alternative hypotheses
Ho: Dependent variable (Exports) means are the same for all categories in Factor A (Inflation groups) and Factor B (Dependency groups) amongst the population of countries
H1: Dependent variable (Exports) means are different for all categories in Factor A (Inflation groups) and Factor B (Dependency groups) amongst the population of countries
* Statistical decision using significant value (рќ›ј) of 5% for the test.
We reject the null hypothesis that means are the same for all categories in Factor A (Inflation groups) and Factor B (Dependency groups) amongst the population of countries.
* Conclusion
At 5% level of significance, t...

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