basic statistics

Statistics Homework Assignment 6 – ANOVA Instructions Place your answer within the box or on the line. For questions involving calculations and numbers only a number goes in the box. Round all answers to 2 decimal places. DO NOT put a formula in the box, only put ONE number in the box. Each response worth 1 point unless otherwise noted. Worth a total of 87.2 points. WARNING. If you do not complete the worksheets at the end the corresponding question will be given a score of 0. Part 1 A common belief among many is that guns cause crime. Hence, many states have enacted strict gun control laws thinking that this will curb violence and crime. A researcher wanted to determine if there was a relationship between crime and gun laws. Based on common belief, the hypothesis was that states with stricter laws should have lower rates of violent crime. Hence, he chose 10 states with the strictest gun control laws, 10 states with moderate gun control laws, and 10 states with more lax gun control laws. The researcher then used the Crime In The United States report from the Federal Bureau of Investigation for 2012 to find the murder rate per 100,000 people in each of these states. The data are presented below. Conduct an ANOVA to investigate the hypothesis, with α = .05. Round to two decimal places. Strict Moderate Low California 5 Colorado 3.1 Alabama 7.1 Connecticut 4.1 Indiana 4.7 Kansas 2.9 New Jersey 4.4 Minnesota 1.8 Kentucky 4.5 Maryland 6.3 Virginia 3.8 Missouri 6.5 New York 3.5 Washington 3 Idaho 1.8 Massachusetts 1.8 Wisconsin 3 S Carolina 6.9 Illinois 5.8 Iowa 1.5 Vermont 1.3 Rhode Island 3.2 Michigan 7 West Virginia 3.9 Delaware 6.2 Nebraska 2.9 Alaska 4.1 D.C. 13.9 N Carolina 4.9 Georgia 5.9 What is the mean for the Strict states? X̄g1 = What is the mean for the Moderate states? X̄g2 = What is the mean for the Low states? X̄g3 = What is the overall Grand mean? X̄G = Using the formula below calculate the total sum of squares. Complete the page titled Part 1 Total Sum of Squares Calculation to help answer this question. Σ(X – X̄ G)2 SSTotal =

5.42

3.57

4.49

4.49

160.79

Using the formula below calculate the within groups sum of squares. Complete the page titled Part 1 Within Groups Sum of Squares Calculation to help answer this question. Σ(X - X̄ g)2 SSWithin = Using the formula below calculate the between groups sum of squares. Complete the page titled Part 1 Between Groups Sum of Squares Calculation to help answer this question. Σ[(X̄ g – X̄ G)2n] SSBetween = What is the total degrees of freedom? dfTotal = What is the within groups degrees of freedom? dfWithin = What is the between groups degrees of freedom? dfBetween = Enter the above information in the ANOVA source table below and then calculate the MSBetween and the MSWithin. Then calculate the F-ratio. Source df SS MS F Between Within Total What is the critical value for F for this experiment? Fcrv = Was the hypothesis supported? Explain how you know in the space provided below. What can the researcher conclude based on the findings?

Part 2 A researcher was interested in determining whether differences exist between liberals, conservatives, and libertarians in their adherence to the U.S. Constitution, including the preservation of state’s rights. A series of legal vignettes were presented to individuals who describe themselves as liberal, conservative, or libertarian and adherence to the U.S. Constitution was rated in their legal decisions. A low score (1) indicates loose adherence and a higher score (10) indicates strict adherence to the U.S. Constitution. The researcher predicted that conservatives would more strictly adhere to the U.S. Constitution in making decision and that liberals would be more loose. It was also predicted that libertarians would fall in between the conservatives and the liberals. The data for 20 individuals is presented below. Conduct an ANOVA to investigate the hypotheses, with α = .05. Round to two decimal places. Conservative Libertarian Liberal 8 9 5 10 9 4 9 10 6 7 7 2 8 6 7 10 8 3 9 9 4 7 10 7 6 9 6 10 5 7 9 6 9 8 8 3 What is the mean for the Conservatives? X̄g1 = What is the mean for the Libertarians? X̄g2 = What is the mean for the Liberals? X̄g3 = What is the overall Grand mean? X̄G = Using the formula below calculate the total sum of squares. Complete the page titled Part 2 Total Sum of Squares Calculation to help answer this question. Σ(X – X̄ G)2 SSTotal = Using the formula below calculate the within groups sum of squares. Complete the page titled Part 2 Within Groups Sum of Squares Calculation to help answer this question. Σ(X - X̄ g)2 SSWithin =

8.42

8

5.25

7.22

98.47

Using the formula below calculate the between groups sum of squares. Complete the page titled Part 2 Between Groups Sum of Squares Calculation to help answer this question. Σ[(X̄ g – X̄ G)2n] SSBetween = What is the total degrees of freedom? dfTotal = What is the within groups degrees of freedom? dfWithin = What is the between groups degrees of freedom? dfBetween = Enter the above information in the ANOVA source table below and then calculate the MSBetween and the MSWithin. Then calculate the F-ratio. Source df SS MS F Between Within Total What is the critical value for F for this experiment? Fcrv = Was the hypothesis supported? Explain how you know in the space provided below. What can the researcher conclude based on the findings? Would this study involve post-hoc or a-priori multiple comparisons? Using the formula below, calculate the effect size. SSBetween η2 = η2 = η2 = SSTotal

If the result is significant, use Tukey’s to explore the data and determine which groups are significantly different from each other. Using the formula below, calculate the critical value for Tukey’s HSD.

MSWithin HSD.05 = Q(k, dfWithin) n HSD.05 = HSD.05 = Using the value for HSD.05 determine which groups are significantly different from each other and interpret the finding. Difference Significant (Yes or No) Conservative vs. Libertarian Conservative vs. Liberal Libertarian vs. Liberal Your interpretation:

Part 1 Total Sum of Squares Calculation. Each square worth .1 points.

Strict X – X̄ G (X – X̄ G)2 Moderate X – X̄ G (X – X̄ G)2

California 5 Colorado 3.1

Connecticut 4.1 Indiana 4.7

New Jersey 4.4 Minnesota 1.8

Maryland 6.3 Virginia 3.8

New York 3.5 Washington 3

Massachusetts 1.8 Wisconsin 3

Illinois 5.8 Iowa 1.5

Rhode Island 3.2 Michigan 7

Delaware 6.2 Nebraska 2.9

D.C. 13.9 N Carolina 4.9

Low X – X̄ G (X – X̄ G)2

Alabama 7.1

Kansas 2.9

Kentucky 4.5

Missouri 6.5

Idaho 1.8

S Carolina 6.9

Vermont 1.3

West Virginia 3.9

Alaska 4.1

Georgia 5.9

-0.42 0.18

-1.32 1.74

-1.02 1.04

1.05 1.10

-1.75 3.06

-3.45 11.90

0.55 0.30

-2.05 4.20

0.95 0.90

8.65 74.82

2.61 6.81

-1.59 2.53

0.01 0.0004

2.01 4.04

-2.69 7.24

2.41 5.81

-3.19 10.18

-0.59 0.35

-0.39 0.15

1.41 1.99

-0.47 0.22

1.13 1.28

-1.77 3.13

0.23 0.05

-0.57 0.32

-0.57 0.32

-2.07 4.28

3.43 11.76

-0.67 0.45

1.33 1.77

Part 1 Within Groups Sum of Squares Calculation. Each square worth .1 points.

Strict X – X̄ g (X – X̄ g)2 Moderate X – X̄ g (X – X̄ g)2

California 5 Colorado 3.1

Connecticut 4.1 Indiana 4.7

New Jersey 4.4 Minnesota 1.8

Maryland 6.3 Virginia 3.8

New York 3.5 Washington 3

Massachusetts 1.8 Wisconsin 3

Illinois 5.8 Iowa 1.5

Rhode Island 3.2 Michigan 7

Delaware 6.2 Nebraska 2.9

D.C. 13.9 N Carolina 4.9

Low X – X̄ g (X – X̄ g)2

Alabama 7.1

Kansas 2.9

Kentucky 4.5

Missouri 6.5

Idaho 1.8

S Carolina 6.9

Vermont 1.3

West Virginia 3.9

Alaska 4.1

Georgia 5.9

Part 1 Between Groups Sum of Squares Calculation. Each square worth .1 points.

X̄ g – X̄ G (X̄ g – X̄ G)2 (X̄ g – X̄ G)2n

Strict

Moderate

Low

Part 2 Total Sum of Squares Calculation. Each square worth .1 points. Conservative X – X̄ G (X – X̄ G)2 Libertarian X – X̄ G (X – X̄ G)2

8 9

10 9

9 10

7 7

8 6

10 8

9 9

7 10

6 9

10 5

9 6

8 8

Liberal X – X̄ G (X – X̄ G)2

5

4

6

2

7

3

4

7

6

7

9

3

-0.41 0.17

1.59 2.53

0.59 0.35

-1.41 1.99

-0.41 0.17

1.59 2.53

0.59 0.35

-1.41 1.99

-2.41 5.81

1.59 2.53

0.59 0.35

-0.41 0.17

-0.25 0.06

-1.25 1.56

0.75 0.56

-3.25 1.56

1.75 3.06

-2.25 5.06

-1.25 1.56

1.75 3.06

0.75 0.56

1.75 3.06

3.75 14.06

-2.26 5.06

1 1

1 1

2 4

-1 1

-2 4

0 0

1 1

2 4

1 1

-3 9

-2 4

0 0

Part 2 Within Groups Sum of Squares Calculation. Each Square worth .1 points.

Conservative X – X̄ g (X – X̄ g)2 Libertarian X – X̄ g (X – X̄ g)2

8 9

10 9

9 10

7 7

8 6

10 8

9 9

7 10

6 9

10 5

9 6

8 8

Liberal X – X̄ g (X – X̄ g)2

5

4

6

2

7

3

4

7

6

7

9

3

Part 2 Between Groups Sum of Squares Calculation. Each square worth .1 points.

X̄ g – X̄ G (X̄ g – X̄ G)2 (X̄ g – X̄ G)2n

Conservative

Libertarian

Liberal