Economic Methods Essay, Research Paper

Methods

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.

Procedures

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:****************

? Alabama

? Alaska

? Arizona

? Arkansas

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(total) =

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.

1st Approach

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.

2nd Approach

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)

P-Value rule

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.

Calculations

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

ANOVA

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

Appendix

Table A-1

Table A-2

Table A-3

Table A-4

Table A-5

Table A-6

Factor Levels

Block 1 2 … k Total

1 x x … x

… … … … … …

B x x … x

Total …

327

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