Introduction
In this paper the basics of statistical data analysis are shown. To explore the association between two variables chosen we use correlation analysis.
Correlation is a relationship between two variables. Calculations similar two criteria relationship based on the formation of paired values that are formed from the considered dependent samples.
Statistics shows the correlation between the two variables and indicates the strength of connection by means of a correlation criterion, called the correlation coefficient. This coefficient is always referred to a Latin letter r, can take values between -1 and +1, moreover if the value is closer to 1, it means that there is strong coupling, and if it is closer to 0, then weak.
If the correlation coefficient is negative, it means that there is an opposite relation: the higher the value of one variable, the lower the value of another. The strength of the connection is also characterized by the absolute value of the correlation coefficient. For a verbal description of the magnitude of the correlation coefficient, the following gradation is being used:
There are two variables are considered in this research: Average household income in the United States and Consumer Price Index in the United States. Each variable is considered by year and over the time period between 1977 and 2013. The data of household income level is given below:
The data is divided by five groups of population and the top 5% of population with the highest income. Source: The United States National Bureau of Statistics (http://www.census.gov/hhes/www/income/data/historical/household/index.html , Table H-3).
The data for the Consumer Price Index for all urban consumers is given in a table below:
The base year is between 1982 and 1984. Source: The Federal Reserve Bank in Minneapolis (http://www.minneapolisfed.org/community_education/teacher/calc/hist1913.cfm).
First of all let’s represent the data on graphs. The average household income level is described below (for all 5 groups):
Now, the same graph for CPI:
In this research we want to check two hypotheses:
- There is an association between all 5 groups of income level by year
- There is a significant correlation between average third fifth income level and CPI
Check the first claim:
H0: ρ=0Ha: ρ≠0
Set level of significance alpha at 5%
Perform correlation analysis using MS Excel:
All correlations are very close to 1. This means that there is very strong positive linear association between the variables. From economic point of view this means that the dynamics of households’ income changes are similar to all five groups of population.
The significance of these correlations is also very high because the number of observations is large.
Now we want to test the second claim:
H0: ρ=0Ha: ρ≠0
Set level of significance alpha at 5%
Perform correlation analysis using MS Excel:
The similar result is for CPI and third fifth of household income level. This means that there is very strong positive linear association between the variables. From economic point of view this means that with CPI increasing the level of income is also increases. And it is natural.
Works Cited
U.S. Census Bureau-Income and Poverty in the United States-September 2014
Tcherneva, Pavlina R. (August 2014). "This Chart Shows Just How (Un)Equal Things Are During A ‘Champion’ Of The 99%’s Administration". Independent Journal Review. Retrieved 13 September 2014.
Binyamin, Appelbaum (September 4, 2014). "Fed Says Growth Lifts the Affluent, Leaving Behind Everyone Else". New York Times. Retrieved 13 September 2014.
W.E. Diewert, 1993. The early history of price index research. Chapter 2 of Essays in Index Number Theory, Volume I, W.E. Diewert and A.O. Nakamura, editors. Elsevier Science Publishers, B.V.
Boskin, Michael J. (2008). "Consumer Price Indexes". In David R. Henderson (ed.). Concise Encyclopedia of Economics (2nd ed.). Indianapolis: Library of Economics and Liberty. ISBN 978-0865976658. OCLC 237794267.
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