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Steps to Conduct Unit Analysis to Determine the Consequences of Marijuana Criminalization in the United States Assignment Solution


Research Question:

The consequences of marijuana criminalization in the United States

Time period: 2010-2018

Operationalized Hypothesis- With the legalization of marijuana, it would eliminate the unfair race and community-targeted enforcement of marijuana criminal laws. Thus with the legalization of marijuana in states increasing, a African American arrest charge decreases.

Unit analysis- marijuana possession arrest

● Independent Variable: Marijuana legalization

● Dependent Variable: # of arrest made

● Control Variables: Sex, Age, and Race

● Sample Size: 100,000

The national marijuana possession arrest rate in 2018 was 203.88 per 100,000. State arrest rates ranged from 707.34 arrests per 100,000, in South Dakota, to 4.52 arrests per 100,000 people, in Massachusetts (see Appendix, Table A for data for all states). Not only did South Dakota have the highest arrest rate in 2018 (see Figure 5), it also had the greatest growth, with a 176% increase in marijuana possession arrests from 2010. Although nationally there was a decline in marijuana possession arrests, arrest rates actually increased in 17 states (see Table 2).

Unit analysis for marijuana possession arrest
Unit analysis for marijuana possession arrest1

Rates of Black and White Marijuana Possession Arrests per 100k people

Unit analysis for marijuana possession arrest2
Unit analysis for marijuana possession arrest3


Descriptive Statistics

Provide a “Descriptive Statistics Table” of variables showing

mean, standard error, ..., sum, and count

Provide a paragraph of explanation about descriptive

statistics of your data


Scatterplot: Visualization and Bivariate Analysis

Create a scatterplot using the dependent variable and

independent variable

Provide a scatterplot with a trend line, a regression

equation, and R-squared

Provide an interpretation of the scatterplot. In other words,

provide an explanation about the effect of the independent

variable on the dependent variable in terms of...

Existence, magnitude, and direction of the effect


Inference Statistics: Multivariate Analysis

Provide a multivariate regression result table

Write a regression equation based on the regression result

Provide explanations about the result

What is your level of significance (i.e. alpha)? “0.05 (5%)”

What is your explanatory power of regression equation as

a whole

Interpret both R-sq. and Adjusted R-sq.

Is your overall regression model statistically significant?

Test the overall model significance by comparing the P-value of F (i.e., Significant F) and alpha

Provide explanations about a result(s) (cont.)

Interpret y-intercept

Interpret the regression coefficient on the independent

variable. Also, explain its statistical significance by

comparing a P-value and alpha


Test (accept or reject) your alternative hypotheses (i.e.

your hypothesis = your tentative answer for your

research question)

Interpret regression coefficients on each control variable.

Also, explain their statistical significance by comparing P-

values and alpha



(Appendix I)

Complete the data spreadsheet (i.e. your raw data table)

Write appropriate

variable labels

of each variable

Table need to show


of each variable


/enter data properly, especially a dummy variable

(0 or 1)


final “Data Set Table”

Copy an Excel spreadsheet of raw data and paste it on

MS-Word your assignment


Statistical Diagnosis

(Appendix II)

If you use a cross-sectional data, then check:


using “Variance Influence Factor (VIF)”

If you use a time-series data or panel data, then check:




using “Durbin-Watson statistic”

Provide each diagnostics processes and outputs and interpret

those results

So to clarify, we are looking at data between 2010-2018 of marijuana arrest rates and marijuana arrest rates between blacks and whites. Looking at a sample size of 100,000

Assignment Solution

1. Descriptive Statistics Table

Count Sum Range Min. Max. Mean Variance Skewness Kurtosis
# Arrests 49 12358 740 13 753 252.21 34130.399 0.871 0.568

The dataset used for the analysis has 49 observations with 13 as the least number of marijuana arrests and 753 as the highest. The data for the Marijuana arrests case is positively skewed and this means that its mean value of 252.21 is greater than the median of the data point. A standard deviation of 184.744 indicates a greater spread in the observations, that is, most of the observations are spread within 92 standard deviations on each side of the mean. The data has a leptokurtic distribution because the distribution has heavier tails.

2. Scatterplot: Visualization and Bivariate Analysis

Unit analysis for marijuana possession arrest4

The shape of the scatterplot between the number of arrests across 49 states in the United States of America indicates a non-linear negative relationship between the dependent variable (Number of arrests) and the independent variable (Marijuana legalization). The scatterplot also portrays the regression equation, trendline, and R-squared. In summary, Marijuana legalization has a non-linear negative impact on a number of arrests and cases related to marijuana.

3. Inferential Statistics

Regression Statistics
Multiple R 0.479266109
R Square 0.229696003
Adjusted R Square 0.213306557
Standard Error 163.8601872
Observations 49
df SS MS F Significance F
Regression 1 376301.6 376301.6 14.01487 0.000494
Residual 47 1261958 26850.16
Total 48 1638259
Coefficients S. Error t Stat P-value
Intercept 328.1032 30.96666 10.59537 4.79E-14
Code -177.083 47.30236 -3.74364 0.000494
The regression equation based on the regression result is given below as
The regression equation above indicates that states that legalized the possession of marijuana has 177.083 fewer arrest cases than states that had not legalized the possession of marijuana.
The test was conducted at 0.05 level of significance. The R-squared value of 0.2297 indicates that the proportion of variance in the dependent variable that can be explained by the independent variable is 23%. While the adjusted R-squared value of 0.2133 indicates that the percentage of variation explained by only the independent variables that actually affect the dependent variable is 21%.
The p-value of F gotten as 0.000494 implies that the model is statistically significant at the stated level of significance since it is smaller than 0.05.
Test for significance of slope and intercept:
H_0: β_0=0
H_1: β_0≠0
The p-value for the slope (0.000494) is less than 0.05 and this implies that we do not have enough evidence to accept the null hypothesis and hence conclude that the regression slope is significant at 0.05 alpha level.
H_0: β_1=0
H_1: β_1≠0
The p-value for the intercept (4.79E-14) is less than 0.05 and this implies that we do not have enough evidence to accept the null hypothesis and hence conclude that the intercept of the regression model is significant at 0.05 alpha level.

4. Appendix 1: Raw Data
State Code Arrests
Alabama 0 63.06
Alaska 1 57.72
Arizona 0 220.01
Arkansas 0 358.79
California 1 13.79
Colorado 1 91
Connecticut 1 64.77
Delaware 1 118.9
Georgia 0 499.68
Hawai‘i 0 59.18
Idaho 0 351.37
Illinois 1 76.17
Indiana 0 286.73
Iowa 0 147.8
Kansas 0 99.8
Kentucky 0 170.07
Louisiana 0 459.82
Maine 1 61.64
Maryland 1 317.86
Massachusetts 1 13.13
Michigan 0 156.98
Minnesota 1 158.83
Mississippi 1 348.68
Missouri 1 359.93
Montana 0 135.19
Nebraska 1 453.58
Nevada 1 95.6
New Hampshire 1 219.2
New Jersey 0 404.67
New Mexico 0 249.93
New York 0 300.26
North Carolina 1 256.4
North Dakota 0 354.04
Ohio 1 272.79
Oklahoma 0 229.69
Oregon 1 77
Pennsylvania 0 264.87
Rhode Island 1 49.93
South Carolina 0 753.11
South Dakota 0 746.68
Tennessee 0 387.44
Texas 0 259.08
Utah 0 372.71
Vermont 1 33.56
Virginia 0 344.02
Washington 1 30.94
West Virginia 0 496.32
Wisconsin 0 360.59
Wyoming 0 655