Details: Research is an integral part of all professional fields. Designing a research study can be a complicated task that can be simplified if the appropriate techniques can be identified. This...

Table of Contents
Literature review    2
Sampling and Experimental Design    2
Data analysis    2
Descriptive    3
Inferential    4
Results    6
Recommendations and further work    6
References    7
Appendix    8
Literature review
The top 10 economies of the world are the United States, China, Japan, Germany, United Kingdom, India, France, Italy, Brazil, and Canada. I want to analyse if there is any significant difference in the average growth rate between the United States, China, Japan, Germany, the United Kingdom, and India. 
According to a recent article by CCN, India and China are surpassing United States Economy by the 2030 year. It is also predicted that the United States will fall to third place. China & India are Surpassing US' Economy By 2030. (2019, January 13).
Sampling and Experimental Design
The data is obtained with the help of secondary research. The source of the data is worldbank.com.  The data is considered for 47 years from 1971 until the year 2017. The method of cluster sampling is used for the purpose of Data Collection. There are numerous clusters in this case corresponding to the country of the United States, China, Japan, Germany, the United Kingdom, and India.
This is a type of matched pair experimental design. An effort is made in order to match the year of each country what is the growth of the gross domestic product.
Data analysis
The dependent variable is the growth of the gross domestic product. This is measured by the ratio scale of measurement and is a continuous variable. The independent variable is the countries. The countries are measured by the nominal scale of measurement. The considered countries are the levels of the independent variable.
Descriptive
The line chart depicting the gross domestic product for the considered 7 countries from the year 1971 until the year 2017 is given below.

The growth of GDP for China has been the highest since 1977 until the current year. An exception is seen in 1999 where the gross domestic product of India was slightly higher in comparison to China. The year of 2015 is also noticeable and the gross domestic product of India was greater than that of China. In the year of 2010 the gross domestic product of India and China approximately equal.
It is also evident that in the recession year of 2008 and 2009 India and China unaffected as the Gross Domestic Product was greater than zero. However, all other countries like United States, Japan, Germany, and the United Kingdom were drastically affected by the recession. It is evident that at the gross domestic product for the country of the United States, Japan, Germany, United Kingdom were in the range of - 3 to - 6%
Inferential
Consider the null hypothesis, there is no significant difference in the average growth of gross domestic product between the seven types of countries. This is tested against an alternative hypothesis, is that at least one of the average growth of gross domestic product between the seven types of countries differ significantly. Girden, E. R. (1992). 
The level of significance is set at 5%. This indicates that I am 95% confident about my results.
    ANOVA: Single Factor
    
    
    
    
    
    
    
    
    
    SUMMARY
    
    
    
    
    Groups
    Count
    Sum
    Average
    Variance
    United States
    47
    131.3615954
    2.794927562
    4.0879
    China
    47
    419.351527
    8.922372915
    10.5755
    Japan
    47
    117.8168518
    2.506741527
    6.6481
    Germany
    47
    94.21806535
    2.004639688
    3.8394
    United Kingdom
    47
    105.5385567
    2.245501206
    4.4415
    India
    47
    265.7702293
    5.654685729
    8.9514
    ANOVA
    
    
    
    
    
    
    Source of Variation
    SS
    df
    MS
    F
    P-value
    F crit
    Between Groups
    1772.2159
    5
    354.4432
    55.1752
    0.0000
    2.2467
    Within Groups
    1773.0127
    276
    6.4240
    
    
    
    
    
    
    
    
    
    
    Total
    3545.2286
    281
    
    
    
    
    
    
    
    Level of significance
    0.05
The decision rule is to reject the null hypothesis if P-value is less than 5%. However if the value is greater than 5%, the null hypothesis is retained and 5% level of significance.
With F=821575.2840, p<5%, I reject the null hypothesis at 5% level of significance. There is sufficient evidence to conclude that at least one of the average growth of the Gross Domestic Product between the seven types of countries significantly. Gu, C. (2013). 
Now to check which pair of countries differ significantly with respect to the average growth of GDP, a turkey crammer t-test is applied.
If P-value is less than 5%, I can say that the specific pair differ significantly with respect to the mean. Wilcox, R. R. (2011). 
    Tukey-Kramer Multiple Comparisons
    
    
    
    
    Sample
    Sample
    Group
    Mean
    Size
    1: United States
    2.794928
    47
    2: China
    8.922373
    47
    3: Japan
    2.506742
    47
    4: Germany
    2.00464
    47
    5: United Kingdom
    2.245501
    47
    6: India
    5.654686
    47
    
    
    
    Other Data
    
    Level of significance
    0.05
    
    Numerator d.f.
    6
    
    Denominator d.f.
    276
    
    MSW
    6.423959
    
    Q Statistic
    4.109
    
    
    Absolute
    Std. Error
    Critical
    
    Comparison
    Difference
    of Difference
    Range
    Results
    Group 1 to Group 2
    6.127445
    0.369702559
    1.519
    Means are different
    Group 1 to Group 3
    0.288186
    0.369702559
    1.519
    Means are not different
    Group 1 to Group 4
    0.790288
    0.369702559
    1.519
    Means are not...