MATH 1300 Week 7 Assignment: Final Project
- MATH 1300: Final Project
Final Project
Student Name
William Penn University
MATH1300
Professor Name
Submission Date
Final Project
Statistical analysis can help in the effective identification of the relationship among different factors. A data set for the traffic stops by the officers has been collected (UFL, 2016). Two main variables have been used to formulate and answer the research questions. These are the driver’s race and the officer’s race, which are both non-dichotomous variables (UFL, 2016). Five tests, including ANOVA, Independent Sample T-Test, Paired Sample T-test, Regression, and Chi-Square, have been used to analyze the interrelation among these variables. IBM SPSS has been used to generate the test results for each problem. The research questions appropriate for each test have been provided before the test and its interpretations in this project.
ANOVA
Is there any difference between the group means of races between traffic officers and drivers stopped by them?
H0: There is no significant difference in the group means of driver race and officer race (µ1=µ2).
H1: There is a significant difference in the group means of driver race and officer race (µ1≠µ2).
Test Table
| Sum of Squares | Df | Mean Square | F | Sig. | |
| Between Groups | 274.865 | 4 | 68.716 | 31.154 | .000 |
| Within Groups | 143167.995 | 64909 | 2.206 | ||
| Total | 143442.860 | 64913 |
The p=.000 < .05 (95% Confidence Interval) indicates the rejection of the null hypothesis. Hence, the alternate hypothesis is true, stating significant differences in the group means of driver race and officer race (µ1≠µ2).
Chi-Square
Is there any significant relationship between the race of traffic officers and the race of drivers stopped by them?
H0: There is no significant relationship in the group means of driver race and officer race.
H1: There is a significant relationship in the group means of driver race and officer race.
Test Table
| Value | Df | Asymp. Sig. (2-sided) | |
| Pearson Chi-Square | 198.501a | 16 | .000 |
| Likelihood Ratio | 202.309 | 16 | .000 |
| Linear-by-Linear Association | .071 | 1 | .790 |
| N of Valid Cases | 64914 |
The χ2 (16) =198.501, p=.000 < .05 indicates that the test is statistically significant. Therefore, the null hypothesis has been rejected according to the Pearson chi-square test. Hence, there is a significant relationship between the race of traffic officers and the race of drivers stopped by them.
Regression
Does the race of traffic officers affect their decision to stop drivers of different races?
H0: There is no significant impact of traffic officers’ race on their decision to stop drivers of different races.
H1: There is a significant impact of the traffic officer’s race on their decision to stop drivers of different races.
Test Table
| Model | R | R Square | Adjusted R-Square | Std. Error of the Estimate |
| 1 | .001a | .000 | .000 | 1.487 |
The value of the regression coefficient found in the analysis (R=.001) indicates a minimum possible impact. The R-squared value of .000 indicates no effect size. Significance of the regression model is given as:
| Model | Sum of Squares | Df | Mean Square | F | Sig. | |
| 1 | Regression | .157 | 1 | .157 | .071 | .790b |
| Residual | 143442.703 | 64912 | 2.210 | |||
| Total | 143442.860 | 64913 | ||||
The p=.790 > .05 (95% Confidence Interval) indicates that the regression model is not significant, which highlights the acceptance of null hypothesis. Hence, there is no significant impact of traffic officer’s race on their decision to stop the divers of different races.
Paired Sample T-Test
Is there any difference between the group means of races between traffic officers and drivers stopped by them?
H0: The true difference in the group means of driver race and officer race is zero (µ1=µ2).
H1: The true difference in the group means of driver race and officer race is not zero (µ1≠µ2).
Test Table
| Paired Differences | ||||||
| Mean | Std. Deviation | Std. Error Mean | 95% Confidence Interval of the Difference | |||
| Lower | Upper | |||||
| Pair 1 | OffRace – DrvRace | 1.170 | 1.779 | .007 | 1.156 | 1.184 |
| T | df | Sig. (2-tailed) | |||
| Pair 1 | OffRace – DrvRace | 167.590 | 64913 | .000 | |
The results of the paired sample t-test can be reported as t (64913) = 167.590, p = .000. The p-value is less than .05 (confidence interval 95%), indicating the rejection of the null hypothesis. Hence, the true difference in the means of officer race and driver race is not zero.
Independent Sample T-Test
Are there any differences in the drivers based on their races stopped during duty by African American and White officers?
H0: The means of the two populations are the same (µ1=µ2).
H1: The means of the two populations are not the same (µ1≠µ2).
References
UFL. (2016). Datasets. ufl.edu. https://users.stat.ufl.edu/~winner/datasets.html
Appendix
ONEWAY DrvRace BY OffRace
/MISSING ANALYSIS.
Oneway
| Notes | ||
| Output Created | 11-MAY-2024 01:36:36 | |
| Comments | ||
| Input | Active Dataset | DataSet3 |
| Filter | <none> | |
| Weight | <none> | |
| Split File | <none> | |
| N of Rows in Working Data File | 65535 | |
| Missing Value Handling | Definition of Missing | User-defined missing values are treated as missing. |
| Cases Used | Statistics for each analysis are based on cases with no missing data for any variable in the analysis. | |
| Syntax | ONEWAY DrvRace BY OffRace/MISSING ANALYSIS. | |
| Resources | Processor Time | 00:00:00.16 |
| Elapsed Time | 00:00:00.16 | |
[DataSet3]
| ANOVA | |||||
| DrvRace | |||||
| Sum of Squares | df | Mean Square | F | Sig. | |
| Between Groups | 274.865 | 4 | 68.716 | 31.154 | .000 |
| Within Groups | 143167.995 | 64909 | 2.206 | ||
| Total | 143442.860 | 64913 | |||
CROSSTABS
/TABLES=DrvRace BY OffRace
/FORMAT=AVALUE TABLES
/STATISTICS=CHISQ
/CELLS=COUNT
/COUNT ROUND CELL.
Crosstabs
| Notes | ||
| Output Created | 11-MAY-2024 01:37:33 | |
| Comments | ||
| Input | Active Dataset | DataSet3 |
| Filter | <none> | |
| Weight | <none> | |
| Split File | <none> | |
| N of Rows in Working Data File | 65535 | |
| Missing Value Handling | Definition of Missing | User-defined missing values are treated as missing. |
| Cases Used | Statistics for each table are based on all the cases with valid data in the specified range(s) for all variables in each table. | |
| Syntax | CROSSTABS/TABLES=DrvRace BY OffRace/FORMAT=AVALUE TABLES/STATISTICS=CHISQ/CELLS=COUNT/COUNT ROUND CELL. | |
| Resources | Processor Time | 00:00:00.05 |
| Elapsed Time | 00:00:00.05 | |
| Dimensions Requested | 2 | |
| Cells Available | 174762 | |
[DataSet3]
| Case Processing Summary | ||||||
| Cases | ||||||
| Valid | Missing | Total | ||||
| N | Percent | N | Percent | N | Percent | |
| DrvRace * OffRace | 64914 | 99.1% | 621 | 0.9% | 65535 | 100.0% |
| DrvRace * OffRace Crosstabulation | |||||||
| Count | |||||||
| OffRace | Total | ||||||
| 1 | 2 | 3 | 4 | 5 | |||
| DrvRace | 1 | 0 | 73 | 174 | 42 | 885 | 1174 |
| 2 | 151 | 1628 | 6443 | 1334 | 25632 | 35188 | |
| 3 | 0 | 1 | 15 | 2 | 31 | 49 | |
| 4 | 10 | 115 | 410 | 52 | 1312 | 1899 | |
| 5 | 55 | 1668 | 4271 | 933 | 19677 | 26604 | |
| Total | 216 | 3485 | 11313 | 2363 | 47537 | 64914 | |
| Chi-Square Tests | |||
| Value | df | Asymp. Sig. (2-sided) | |
| Pearson Chi-Square | 198.501a | 16 | .000 |
| Likelihood Ratio | 202.309 | 16 | .000 |
| Linear-by-Linear Association | .071 | 1 | .790 |
| N of Valid Cases | 64914 | ||
| a. 4 cells (16.0%) have expected count less than 5. The minimum expected count is .16. |
REGRESSION
/MISSING LISTWISE
/STATISTICS COEFF OUTS R ANOVA
/CRITERIA=PIN(.05) POUT(.10)
/NOORIGIN
/DEPENDENT DrvRace
/METHOD=ENTER OffRace.
Regression
| Notes | ||
| Output Created | 11-MAY-2024 01:39:45 | |
| Comments | ||
| Input | Active Dataset | DataSet3 |
| Filter | <none> | |
| Weight | <none> | |
| Split File | <none> | |
| N of Rows in Working Data File | 65535 | |
| Missing Value Handling | Definition of Missing | User-defined missing values are treated as missing. |
| Cases Used | Statistics are based on cases with no missing values for any variable used. | |
| Syntax | REGRESSION/MISSING LISTWISE/STATISTICS COEFF OUTS R ANOVA/CRITERIA=PIN(.05) POUT(.10)/NOORIGIN/DEPENDENT DrvRace/METHOD=ENTER OffRace. | |
| Resources | Processor Time | 00:00:00.06 |
| Elapsed Time | 00:00:00.10 | |
| Memory Required | 1540 bytes | |
| Additional Memory Required for Residual Plots | 0 bytes | |
[DataSet3]
| Variables Entered/Removeda | |||
| Model | Variables Entered | Variables Removed | Method |
| 1 | OffRaceb | . | Enter |
| a. Dependent Variable: DrvRace |
| b. All requested variables entered. |
| Model Summary | ||||
| Model | R | R Square | Adjusted R Square | Std. Error of the Estimate |
| 1 | .001a | .000 | .000 | 1.487 |
| a. Predictors: (Constant), OffRace |
| ANOVAa | ||||||
| Model | Sum of Squares | df | Mean Square | F | Sig. | |
| 1 | Regression | .157 | 1 | .157 | .071 | .790b |
| Residual | 143442.703 | 64912 | 2.210 | |||
| Total | 143442.860 | 64913 | ||||
| a. Dependent Variable: DrvRace |
| b. Predictors: (Constant), OffRace |
| Coefficientsa | ||||||
| Model | Unstandardized Coefficients | Standardized Coefficients | t | Sig. | ||
| B | Std. Error | Beta | ||||
| 1 | (Constant) | 3.264 | .027 | 120.344 | .000 | |
| OffRace | .002 | .006 | .001 | .267 | .790 | |
| a. Dependent Variable: DrvRace |
DATASET CLOSE DataSet2.
T-TEST PAIRS=OffRace WITH DrvRace (PAIRED)
/CRITERIA=CI (.9500)
/MISSING=ANALYSIS.
T-Test
| Notes | ||
| Output Created | 11-MAY-2024 01:44:03 | |
| Comments | ||
| Input | Active Dataset | DataSet3 |
| Filter | <none> | |
| Weight | <none> | |
| Split File | <none> | |
| N of Rows in Working Data File | 65535 | |
| Missing Value Handling | Definition of Missing | User defined missing values are treated as missing. |
| Cases Used | Statistics for each analysis are based on the cases with no missing or out-of-range data for any variable in the analysis. | |
| Syntax | T-TEST PAIRS=OffRace WITH DrvRace (PAIRED)/CRITERIA=CI(.9500)/MISSING=ANALYSIS. | |
| Resources | Processor Time | 00:00:00.05 |
| Elapsed Time | 00:00:00.05 | |
[DataSet3]
| Paired Samples Statistics | |||||
| Mean | N | Std. Deviation | Std. Error Mean | ||
| Pair 1 | OffRace | 4.44 | 64914 | .978 | .004 |
| DrvRace | 3.27 | 64914 | 1.487 | .006 | |
| Paired Samples Correlations | ||||
| N | Correlation | Sig. | ||
| Pair 1 | OffRace & DrvRace | 64914 | .001 | .790 |
| Paired Samples Test | ||||||
| Paired Differences | ||||||
| Mean | Std. Deviation | Std. Error Mean | 95% Confidence Interval of the Difference | |||
| Lower | Upper | |||||
| Pair 1 | OffRace – DrvRace | 1.170 | 1.779 | .007 | 1.156 | 1.184 |
| Paired Samples Test | |||||
| t | df | Sig. (2-tailed) | |||
| Pair 1 | OffRace – DrvRace | 167.590 | 64913 | .000 | |
T-TEST GROUPS=OffRace(3 5)
/MISSING=ANALYSIS
/VARIABLES=DrvRace
/CRITERIA=CI (.95).
T-Test
| Notes | ||
| Output Created | 11-MAY-2024 01:52:09 | |
| Comments | ||
| Input | Active Dataset | DataSet3 |
| Filter | <none> | |
| Weight | <none> | |
| Split File | <none> | |
| N of Rows in Working Data File | 65535 | |
| Missing Value Handling | Definition of Missing | User defined missing values are treated as missing. |
| Cases Used | Statistics for each analysis are based on the cases with no missing or out-of-range data for any variable in the analysis. | |
| Syntax | T-TEST GROUPS=OffRace(3 5)/MISSING=ANALYSIS/VARIABLES=DrvRace/CRITERIA=CI(.95). | |
| Resources | Processor Time | 00:00:00.11 |
| Elapsed Time | 00:00:00.11 | |
| Group Statistics | |||||
| OffRace | N | Mean | Std. Deviation | Std. Error Mean | |
| DrvRace | 3 | 11313 | 3.19 | 1.463 | .014 |
| 5 | 47537 | 3.28 | 1.490 | .007 | |
| Independent Samples Test | ||||||
| Levene’s Test for Equality of Variances | t-test for Equality of Means | |||||
| F | Sig. | t | df | |||
| DrvRace | Equal variances assumed | 179.412 | .000 | -5.667 | 58848 | |
| Equal variances not assumed | -5.729 | 17329.792 | ||||
| Independent Samples Test | |||||
| t-test for Equality of Means | |||||
| Sig. (2-tailed) | Mean Difference | Std. Error Difference | 95% Confidence Interval of the Difference | ||
| Lower | |||||
| DrvRace | Equal variances assumed | .000 | -.088 | .016 | -.118 |
| Equal variances not assumed | .000 | -.088 | .015 | -.118 | |
| Independent Samples Test | ||
| t-test for Equality of Means | ||
| 95% Confidence Interval of the Difference | ||
| Upper | ||
| DrvRace | Equal variances assumed | -.058 |
| Equal variances not assumed | -.058 | |