Chi-Square Test
Chi-Square
The Chi-Square method of verification shall rely on data provided by the AAA Foundation for Traffic Safety (Tefft et al., 2020) and from Statista accounts. The information incorporated in this study was published in January 2020 and indicates the estimated percentages of fatal road accidents from 2008 to 2017. This is significantly convenient since it accounts for the two relevant time periods of the study, before and after the legalization of marijuana in some states in the U.S. The statistics used are a record for Washington State, which legalized the use of marijuana for recreational use in 2012. The Statista accounts provides the percentage of US adults that have used marijuana from 2008 t0 2017 by states.
The study shall incorporate a Chi-Square, including the computation and analysis of the results. The data used in the AAA Foundation for Traffic Safety site is portrayed in a bar chart. However, to calculate the Pearson Chi-Square value, we shall the analysis in SPSS and obtain the tables of crosstabs, Chi-Square tests and Phi and Cramer’s V. The data retrieved from the AAA Foundation for Traffic Safety and Statista accounts was typed in SPSS to conduct the analysis. The output of the crosstabs will be presented in form of columns and rows. The null and alternative hypotheses for the study will be;
H0: The fatal accidents in Washington state is independent of legalization of marijuana vs
H1: The fatal accidents in Washington state is dependent of legalization of marijuana
| Fatal Accidents * Marijuana Consumption Crosstabulation | |||||
| Marijuana Consumption | Total | ||||
| High consumption of Marijuana | Low Consumption of Marijuana | ||||
| Fatal Accidents | Low percentage of Accidents | Count | 0 | 4 | 4 |
| % within Fatal Accidents | 0.0% | 100.0% | 100.0% | ||
| % within Marijuana Consumption | 0.0% | 80.0% | 40.0% | ||
| % of Total | 0.0% | 40.0% | 40.0% | ||
| High percentage of Accidents | Count | 5 | 1 | 6 | |
| % within Fatal Accidents | 83.3% | 16.7% | 100.0% | ||
| % within Marijuana Consumption | 100.0% | 20.0% | 60.0% | ||
| % of Total | 50.0% | 10.0% | 60.0% | ||
| Total | Count | 5 | 5 | 10 | |
| % within Fatal Accidents | 50.0% | 50.0% | 100.0% | ||
| % within Marijuana Consumption | 100.0% | 100.0% | 100.0% | ||
| % of Total | 50.0% | 50.0% | 100.0% | ||
|
Chi-Square Tests | |||||
| Value | df | Asymptotic Significance (2-sided) | Exact Sig. (2-sided) | Exact Sig. (1-sided) | |
| Pearson Chi-Square | 6.667a | 1 | .010 | ||
| Continuity Correctionb | 3.750 | 1 | .053 | ||
| Likelihood Ratio | 8.456 | 1 | .004 | ||
| Fisher’s Exact Test | .048 | .024 | |||
| Linear-by-Linear Association | 6.000 | 1 | .014 | ||
| N of Valid Cases | 10 | ||||
| a. 4 cells (100.0%) have expected count less than 5. The minimum expected count is 2.00. | |||||
| b. Computed only for a 2×2 table | |||||
| Symmetric Measures | |||
| Value | Approximate Significance | ||
| Nominal by Nominal | Phi | -.816 | .010 |
| Cramer’s V | .816 | .010 | |
| N of Valid Cases | 10 | ||
Interpreting the Chi-square Value
The null and the alternative hypothesis of are;
H0: The fatal accidents in Washington state is independent of legalization of marijuana Vs
H1: There is association between fatal accidents in Washington state and legalization of marijuana
We shall observe the p-value of the Pearson Chi-Square from the Chi-Square table retrieved from the from the SPSS. In order to reject the null hypothesis, the P-value of the Pearson Chi-Square should be less than 0.05 level of significance. The level of significance normally ranges between 0.01 and 0.10. It is used to determine whether there is a significant association between two variables. Most researchers chose 0.01, 0.05, or 0.10. However, any other figure between 0.01 and 0.1 can be used. For this study, we shall use 0.05.
The p-value in the Chi-Square table is indicated by Asymptotic Significance. The Pearson Chi-Square value is 6.667. The p-value corresponding to this number is 0.010. The p-value is less than the α = 0.05 level of significance (0.010 < 0.05). Therefore, we shall reject the null hypothesis and accept the alternative hypothesis. We shall conclude that there is association between fatal accidents in Washington state and legalization of marijuana.
The Phi and Cramer’s V values are -0.816 and 0.816, respectively. The p-values corresponding to these values are 0.010. Phi and Cramer’s V values are used to test if the association between the two variables is weak or strong. If the P-value is less than 0.05, the strength is strong and if the p-value is greater than 0.05, the strength is weak. Therefore, the strength of association between fatal accidents and legalization of marijuana in Washington state is strong.
From the crosstabs above, we can see that the proportion of high consumption of marijuana and high percentage of fatal accidents is 83.3%. The proportion of low consumption of marijuana and high percentage of fatal accidents is 16.7%.
In conclusion, we have seen that fatal accidents and legalization of marijuana in Washington state is not independent. There is an association between the two variables. We can firmly say that there a correlation between legalization of marijuana and traffic accidents.
References
Statista. (2018, June 5). Marijuana use among U.S. adults by state 2017-2018. Statista. https://www.statista.com/statistics/723822/cannabis-use-within-one-year-us-adults/
Tefft, B., & Arnold, L. (2010). Prevalence of Marijuana Involvement in Fatal Crashes: Washington Saving lives through research and education. https://aaafoundation.org/wp-content/uploads/2017/12/PrevalenceOfMarijuanaInvolvement.pdf
Tefft, B., & Arnold, L. (2020, January 30). Cannabis Use Among Drivers in Fatal Crashes in Washington State Before and After Legalization. AAA Foundation. https://aaafoundation.org/cannabis-use-among-drivers-in-fatal-crashes-in-washington-state-before-and-after-legalization/