Economic Methods Essay, Research Paper
The majority of the info that we found was form the website of The U.S. Department of Commerce Bureau of Economic Analysis (www.bea.gov). Tables A-1 thru A-5 give the per capita income from 1995 until 1999, respectively.
The data in Tables A-1 thru A-5 were reorganized to form an RCBD structure as shown in Table A-6. The RCBD in Table A-6 contains four rows and five columns. The rows a sample of four states:****************
They represent the primary ?state? factor. The columns are four years that represent the secondary ?year? factor. The RCBD was chosen as the design in the investigation because it allows us to account for and remove the influence of the blocks that affect comparisons among the pf*************************** levels of the primary factor.
To analyze the RCBD, the correct steps must be executed (Kvanli)*******************
The first step is to write a null hypothesis and an alternate hypothesis for each of the primary factor and the block factor
To determine whether or not there is significant difference in the per capita income among the four states, we test the hypothesis.
Null hypothesis Ho: There is no difference per capita income among states
Alternate hypothesis Ha: There is a significant difference in per capita income
among the years
To determine whether or not there is a difference in per capita
income years, we test the hypothesis
Null hypothesis: Ho: There is no difference in per capita income among years.
Alternate hypothesis: Ha: There is difference in per capita income years
The second step requires calculations of the primary totals ( ), and block totals
( ). We then need to calculate the grand total
The third step requires the calculations of the sum of squares (SS):
SS(total), SS(factor), SS(blocks), and SS(error).
SS(total) measures the amount o
SS(factor) measures the variation due to differences among the among the levels of the
primary factor: This equation is:
SS(blocks) measures the variation amount due to block differences. This can be
computed by the below equation:
SS(error) measures the variation amount due to all sources not accounted for. This can
be found by using the equation:
SS(error) = SS(total) – SS(factor) – SS(blocks)
The fourth step in the analysis requires the calculating the following mean squares (MS):
MS(factor), SS(blocks), and MS(error) according to the following formulas:
Step five requires calculating an F-ratio statistic for the F(factor) and another F-ratio
statistic for the F(block). The formulas are:
When the null hypothesis is true, F(factor) has an F-distribution with (k-1, (b-1)(k-1)) degrees of freedom.
When the null hypothesis is true, F(blocks) has an F-distribution with (b-1, (b-1)(k-1)) degrees of freedom
Step six determines the rules for rejection or non-rejection of the null hypothesis for states and years. There are two approaches to choose from.
By using a level of significance one can make a determination of rejection regions by reading the statistical tables (F-distribution tables) to get the critical value. The critical values can be found in Table A.7 in the Kvanli statistics book. A .005 significance level was used for testing procedures in the paper.
In this approach there is no need to refer to statistical tables. All that needs to be done is to read the p-value on the Two-way ANOVA test on Microsoft Excel. We must reject the null hypothesis based on how small the p-value is. This is called the P-Value rule of thumb. (Kvanli)
The null hypothesis must be rejected if the P-value is less than .05. The test fails to reject if the p-value is greater than .5 it is inconclusive.
The required calculations were done with a Two-Factor ANOVA without replication analysis on Microsoft Excel. This test calculated the Sum of Squares, the Mean squares, and the F-ratio. This is seen in the two-way ANOVA table. (Table 1)
Table 1 Anova table for the Randomized Complete Block Design
Anova: Two-Factor Without Replication
SUMMARY Count Sum Average Variance
Row 1 5 93660 18732 1195972
Row 2 5 119119 23823.8 845923.2
Row 3 5 99507 19901.4 2024195
Row 4 5 89860 17972 1409053
Column 1 4 75073 18768.25 7980981
Column 2 4 77123 19280.75 6627569
Column 3 4 80042 20010.5 6944182
Column 4 4 83463 20865.75 6478120
Column 5 4 86445 21611.25 6015248
Source of Variation SS Df MS F P-value F crit
Rows 1.02E+08 3 33842872 666.1089 1.32E-13 3.4903
Columns 21290888 4 5322722 104.7639 3.18E-09 3.25916
Error 609681.8 12 50806.82
Total 1.23E+08 19
Block 1 2 … k Total
1 x x … x
… … … … … …
B x x … x